all_solutions listlengths 1 38 | answer stringlengths 7 23 | bucket stringclasses 1
value | canonical_solution stringlengths 7 23 | config dict | difficulty stringclasses 1
value | difficulty_proxy float64 -3.64 0 | generator_seed int64 21k 21k | info dict | n_operands int64 4 4 | num_solutions int64 1 38 | operand_range listlengths 2 2 | operands listlengths 4 4 | pass10 dict | problem_id stringlengths 29 29 | question stringlengths 388 392 | split stringclasses 1
value | subset stringclasses 1
value | target int64 10 98 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
"(24 + 23)",
"((24 * 1) + 23)",
"((24 / 1) + 23)",
"(1 * (24 + 23))",
"((24 + 23) / 1)",
"(24 + (1 * 23))",
"(24 + (23 / 1))"
] | (24 + 23) | bucket_a | (24 + 23) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.94591 | 21,001 | {
"canonical_solution": "(24 + 23)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required... | 4 | 7 | [
1,
25
] | [
10,
24,
1,
23
] | {
"completion_tokens": 3839,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 3,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01730 | Using the numbers [10, 24, 1, 23], write an arithmetic expression that equals 47.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 47 |
[
"(17 * 4)",
"((17 * 1) * 4)",
"((17 / 1) * 4)",
"(1 * (17 * 4))",
"((17 * 4) / 1)",
"(17 * (1 * 4))",
"(17 * (4 / 1))",
"((17 - 1) + (13 * 4))",
"((17 + (13 * 4)) - 1)",
"(17 + ((13 * 4) - 1))"
] | (17 * (4 / 1)) | bucket_a | (17 * (4 / 1)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.302585 | 21,001 | {
"canonical_solution": "(17 * (4 / 1))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 10 | [
1,
25
] | [
13,
17,
1,
4
] | {
"completion_tokens": 3467,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 1,
"no_box": 1,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_01737 | Using the numbers [13, 17, 1, 4], write an arithmetic expression that equals 68.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 68 |
[
"(22 - ((3 + 13) / 8))",
"(22 - ((13 - 3) - 8))",
"(22 - (13 - (3 + 8)))",
"(22 - ((13 - 8) - 3))",
"((3 + 22) - (13 - 8))",
"((3 + 8) + (22 - 13))",
"(8 + (22 - (13 - 3)))",
"(8 + ((3 + 22) - 13))",
"(8 + (3 + (22 - 13)))",
"((8 + 22) - (13 - 3))",
"(((3 + 8) + 22) - 13)",
"((8 + (3 + 22)) - ... | (3 + ((22 + 8) - 13)) | bucket_a | (3 + ((22 + 8) - 13)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(3 + ((22 + 8) - 13))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 16 | [
1,
25
] | [
3,
13,
8,
22
] | {
"completion_tokens": 2471,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"parse_error": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01743 | Using the numbers [3, 13, 8, 22], write an arithmetic expression that equals 20.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 20 |
[
"(((25 + 10) + 19) + 24)",
"((10 + (25 + 19)) + 24)",
"((25 + (10 + 19)) + 24)",
"((10 + 19) + (25 + 24))",
"((25 + 19) + (10 + 24))",
"(19 + ((25 + 10) + 24))",
"(19 + (10 + (25 + 24)))",
"(19 + (25 + (10 + 24)))",
"((25 + 10) + (19 + 24))",
"(10 + ((25 + 19) + 24))",
"(10 + (19 + (25 + 24)))",... | ((10 + 19) + (25 + 24)) | bucket_a | ((10 + 19) + (25 + 24)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((10 + 19) + (25 + 24))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 15 | [
1,
25
] | [
25,
10,
19,
24
] | {
"completion_tokens": 3614,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_01758 | Using the numbers [25, 10, 19, 24], write an arithmetic expression that equals 78.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 78 |
[
"(14 - 4)",
"(((14 + 9) - 9) - 4)",
"(((14 * 9) / 9) - 4)",
"(((14 - 9) + 9) - 4)",
"((9 + (14 - 9)) - 4)",
"((14 * (9 / 9)) - 4)",
"((14 / (9 / 9)) - 4)",
"((9 / 9) * (14 - 4))",
"((14 - 4) / (9 / 9))",
"((14 + 9) - (9 + 4))",
"((14 - 9) + (9 - 4))",
"(((14 + 9) - 4) - 9)",
"((9 + (14 - 4))... | ((14 - 4) * (9 / 9)) | bucket_a | ((14 - 4) * (9 / 9)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.135494 | 21,001 | {
"canonical_solution": "((14 - 4) * (9 / 9))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 23 | [
1,
25
] | [
14,
9,
9,
4
] | {
"completion_tokens": 1915,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_integer_intermediate": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01764 | Using the numbers [14, 9, 9, 4], write an arithmetic expression that equals 10.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 10 |
[
"(10 + (19 * 3))",
"((19 + 18) + (10 * 3))",
"(18 + (19 + (10 * 3)))",
"(19 + (18 + (10 * 3)))"
] | ((19 * 3) + 10) | bucket_a | ((19 * 3) + 10) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.386294 | 21,001 | {
"canonical_solution": "((19 * 3) + 10)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 4 | [
1,
25
] | [
19,
18,
10,
3
] | {
"completion_tokens": 4643,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_01771 | Using the numbers [19, 18, 10, 3], write an arithmetic expression that equals 67.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 67 |
[
"(((18 - 10) * 6) + 4)",
"((10 + (18 / 6)) * 4)",
"((18 - 6) + (10 * 4))",
"((18 + (10 * 4)) - 6)",
"((18 + 10) + (6 * 4))",
"(10 + (18 + (6 * 4)))",
"(18 + ((10 * 4) - 6))",
"(18 + (10 + (6 * 4)))"
] | (((4 * 10) - 6) + 18) | bucket_a | (((4 * 10) - 6) + 18) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.079442 | 21,001 | {
"canonical_solution": "(((4 * 10) - 6) + 18)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 8 | [
1,
25
] | [
18,
10,
6,
4
] | {
"completion_tokens": 4501,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_01782 | Using the numbers [18, 10, 6, 4], write an arithmetic expression that equals 52.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 52 |
[
"((7 + 23) + 15)",
"(23 + (7 + 15))",
"(7 + (23 + 15))",
"(((23 - 7) + 15) + 14)",
"((23 + (15 - 7)) + 14)",
"(((23 + 15) - 7) + 14)",
"((23 + 15) + (14 - 7))",
"((15 - 7) + (23 + 14))",
"(15 + ((23 - 7) + 14))",
"(15 + (23 + (14 - 7)))",
"(15 + ((23 + 14) - 7))",
"((23 - 7) + (15 + 14))",
"... | ((14 + (23 - 7)) + 15) | bucket_a | ((14 + (23 - 7)) + 15) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "((14 + (23 - 7)) + 15)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 18 | [
1,
25
] | [
7,
23,
15,
14
] | {
"completion_tokens": 4864,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_01794 | Using the numbers [7, 23, 15, 14], write an arithmetic expression that equals 45.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 45 |
[
"(((13 + 23) + 20) - 3)",
"((23 + (13 + 20)) - 3)",
"((13 + (23 + 20)) - 3)",
"((23 + 20) + (13 - 3))",
"((13 + 20) + (23 - 3))",
"(20 + ((13 + 23) - 3))",
"(20 + (23 + (13 - 3)))",
"(20 + (13 + (23 - 3)))",
"((13 + 23) + (20 - 3))",
"(23 + ((13 + 20) - 3))",
"(23 + (20 + (13 - 3)))",
"(23 + (... | (13 + ((23 + 20) - 3)) | bucket_a | (13 + ((23 + 20) - 3)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(13 + ((23 + 20) - 3))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
13,
23,
20,
3
] | {
"completion_tokens": 2620,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"non_positive_intermediate": 2,
"parse_error": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01796 | Using the numbers [13, 23, 20, 3], write an arithmetic expression that equals 53.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 53 |
[
"(6 * 8)",
"((1 * 6) * 8)",
"((6 / 1) * 8)",
"(6 * (1 * 8))",
"(6 * (8 / 1))",
"(1 * (6 * 8))",
"((6 * 8) / 1)"
] | (6 * 8) | bucket_a | (6 * 8) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.94591 | 21,001 | {
"canonical_solution": "(6 * 8)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_a... | 4 | 7 | [
1,
25
] | [
18,
1,
6,
8
] | {
"completion_tokens": 4160,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"no_box": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01805 | Using the numbers [18, 1, 6, 8], write an arithmetic expression that equals 48.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 48 |
[
"(25 - 8)",
"(((25 - 8) + 14) - 14)",
"(((25 + 14) - 8) - 14)",
"((25 + (14 - 8)) - 14)",
"(((25 - 8) * 14) / 14)",
"(((25 - 8) - 14) + 14)",
"(((25 - 14) - 8) + 14)",
"((25 - (8 + 14)) + 14)",
"((25 + 14) - (8 + 14))",
"((14 - 8) + (25 - 14))",
"((25 - 14) + (14 - 8))",
"(14 + ((25 - 8) - 14)... | ((14 + 25) - (14 + 8)) | bucket_a | ((14 + 25) - (14 + 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "((14 + 25) - (14 + 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 26 | [
1,
25
] | [
25,
8,
14,
14
] | {
"completion_tokens": 3889,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"non_integer_intermediate": 1,
"non_positive_intermediate": 3
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_01808 | Using the numbers [25, 8, 14, 14], write an arithmetic expression that equals 17.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 17 |
[
"22",
"(5 + 17)",
"(((22 + 12) + 5) - 17)",
"((12 + (22 + 5)) - 17)",
"((22 + (12 + 5)) - 17)",
"(((22 - 12) - 5) + 17)",
"(((22 - 5) - 12) + 17)",
"((22 - (12 + 5)) + 17)",
"((22 * (12 + 5)) / 17)",
"((22 + 17) - (12 + 5))",
"((22 * 17) / (12 + 5))",
"((12 + 5) + (22 - 17))",
"((22 + 5) - (... | (5 + 17) | bucket_a | (5 + 17) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.295837 | 21,001 | {
"canonical_solution": "(5 + 17)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 27 | [
1,
25
] | [
22,
12,
5,
17
] | {
"completion_tokens": 1957,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_01822 | Using the numbers [22, 12, 5, 17], write an arithmetic expression that equals 22.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 22 |
[
"((8 + 11) - 6)",
"(11 + (8 - 6))",
"(8 + (11 - 6))",
"((11 - 8) + 10)",
"(11 + (10 - 8))",
"((11 + 10) - 8)",
"((6 - (11 - 8)) + 10)",
"(((8 + 6) - 11) + 10)",
"((8 - (11 - 6)) + 10)",
"((8 + 10) - (11 - 6))",
"((8 + 6) - (11 - 10))",
"(((8 * 11) - 10) / 6)",
"(6 + (10 - (11 - 8)))",
"(6 ... | (((8 + 10) + 6) - 11) | bucket_a | (((8 + 10) + 6) - 11) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.218876 | 21,001 | {
"canonical_solution": "(((8 + 10) + 6) - 11)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 25 | [
1,
25
] | [
8,
11,
6,
10
] | {
"completion_tokens": 3794,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 2,
"parse_error": 2,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01825 | Using the numbers [8, 11, 6, 10], write an arithmetic expression that equals 13.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 13 |
[
"(18 - 8)",
"(8 + 2)",
"10",
"((18 + 2) - 10)",
"(2 + (18 - 10))",
"(18 - (10 - 2))",
"(((18 - 8) * 2) - 10)",
"(((18 / 2) - 8) * 10)",
"(10 / ((18 / 2) - 8))",
"((18 + 2) / (10 - 8))",
"(((18 - 8) + 10) / 2)",
"((18 + (10 - 8)) / 2)",
"(((18 + 10) - 8) / 2)",
"((2 * 10) - (18 - 8))",
"(... | (8 + 2) | bucket_a | (8 + 2) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.833213 | 21,001 | {
"canonical_solution": "(8 + 2)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_a... | 4 | 17 | [
1,
25
] | [
8,
18,
2,
10
] | {
"completion_tokens": 4487,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 1,
"parse_error": 4,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01843 | Using the numbers [8, 18, 2, 10], write an arithmetic expression that equals 10.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 10 |
[
"(3 * 25)",
"(((11 * 3) + 25) + 17)",
"(25 * (17 - (11 + 3)))",
"(25 * ((17 - 11) - 3))",
"(25 * ((17 - 3) - 11))",
"(25 + ((11 * 3) + 17))",
"((11 * 3) + (25 + 17))"
] | (3 * 25) | bucket_a | (3 * 25) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.94591 | 21,001 | {
"canonical_solution": "(3 * 25)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 7 | [
1,
25
] | [
11,
3,
25,
17
] | {
"completion_tokens": 3857,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01847 | Using the numbers [11, 3, 25, 17], write an arithmetic expression that equals 75.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 75 |
[
"(7 + 21)",
"((1 * 7) + 21)",
"((7 / 1) + 21)",
"(7 + (1 * 21))",
"(7 + (21 / 1))",
"(1 * (7 + 21))",
"((7 + 21) / 1)",
"((15 - (1 + 7)) + 21)",
"(((15 - 1) - 7) + 21)",
"(((15 - 7) - 1) + 21)",
"((15 - 7) + (21 - 1))",
"((15 - 1) + (21 - 7))",
"(15 + (21 - (1 + 7)))",
"(15 + ((21 - 1) - 7... | (1 * (21 + 7)) | bucket_a | (1 * (21 + 7)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.091042 | 21,001 | {
"canonical_solution": "(1 * (21 + 7))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 22 | [
1,
25
] | [
1,
7,
15,
21
] | {
"completion_tokens": 2127,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_01870 | Using the numbers [1, 7, 15, 21], write an arithmetic expression that equals 28.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 28 |
[
"(7 * 8)",
"((7 * 1) * 8)",
"((7 / 1) * 8)",
"(1 * (7 * 8))",
"((7 * 8) / 1)",
"(7 * (1 * 8))",
"(7 * (8 / 1))",
"((8 - 1) * 8)",
"(8 * (8 - 1))",
"(((7 + 1) * 8) - 8)",
"(((7 - 1) * 8) + 8)",
"(8 + ((7 - 1) * 8))",
"((8 * 8) - (7 + 1))",
"(((8 * 8) - 7) - 1)",
"(((8 * 8) - 1) - 7)"
] | (8 * 7) | bucket_a | (8 * 7) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(8 * 7)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_a... | 4 | 15 | [
1,
25
] | [
7,
1,
8,
8
] | {
"completion_tokens": 3544,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"no_box": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_01876 | Using the numbers [7, 1, 8, 8], write an arithmetic expression that equals 56.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ex... | train | easy | 56 |
[
"((16 + 18) - 1)",
"(18 + (16 - 1))",
"(16 + (18 - 1))",
"((16 + 1) + 16)",
"(1 + (16 + 16))",
"(16 + (1 + 16))",
"((18 - 1) + 16)",
"((18 + 16) - 1)",
"(1 + ((18 - 16) * 16))",
"(1 + (16 * (18 - 16)))"
] | ((16 + 1) + 16) | bucket_a | ((16 + 1) + 16) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.302585 | 21,001 | {
"canonical_solution": "((16 + 1) + 16)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 10 | [
1,
25
] | [
16,
18,
1,
16
] | {
"completion_tokens": 2151,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"parse_error": 2,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_01902 | Using the numbers [16, 18, 1, 16], write an arithmetic expression that equals 33.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 33 |
[
"(4 + (11 * 7))",
"((16 / 4) + (11 * 7))",
"((11 + 16) * (7 - 4))",
"((4 * (16 + 7)) - 11)"
] | ((11 * 7) + 4) | bucket_a | ((11 * 7) + 4) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.386294 | 21,001 | {
"canonical_solution": "((11 * 7) + 4)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 4 | [
1,
25
] | [
11,
4,
16,
7
] | {
"completion_tokens": 5921,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01904 | Using the numbers [11, 4, 16, 7], write an arithmetic expression that equals 81.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 81 |
[
"(6 * (21 - 16))",
"((19 - (16 - 6)) + 21)",
"(((6 + 19) - 16) + 21)",
"((6 + (19 - 16)) + 21)",
"((19 - 16) + (6 + 21))",
"((6 + 19) + (21 - 16))",
"(19 + (21 - (16 - 6)))",
"(19 + ((6 + 21) - 16))",
"(19 + (6 + (21 - 16)))",
"((19 + 21) - (16 - 6))",
"(((6 + 19) + 21) - 16)",
"((19 + (6 + 21... | (19 + ((21 - 16) + 6)) | bucket_a | (19 + ((21 - 16) + 6)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(19 + ((21 - 16) + 6))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 16 | [
1,
25
] | [
6,
16,
19,
21
] | {
"completion_tokens": 3031,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_01911 | Using the numbers [6, 16, 19, 21], write an arithmetic expression that equals 30.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 30 |
[
"(((22 + 3) + 18) + 4)",
"((3 + (22 + 18)) + 4)",
"((22 + (3 + 18)) + 4)",
"((3 + 18) + (22 + 4))",
"((22 + 18) + (3 + 4))",
"(18 + ((22 + 3) + 4))",
"(18 + (3 + (22 + 4)))",
"(18 + (22 + (3 + 4)))",
"((22 + 3) + (18 + 4))",
"((18 * 4) - (22 + 3))",
"(3 + ((22 + 18) + 4))",
"(3 + (18 + (22 + 4... | ((18 + 3) + (22 + 4)) | bucket_a | ((18 + 3) + (22 + 4)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "((18 + 3) + (22 + 4))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 18 | [
1,
25
] | [
22,
3,
18,
4
] | {
"completion_tokens": 3491,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 3,
"no_box": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01916 | Using the numbers [22, 3, 18, 4], write an arithmetic expression that equals 47.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 47 |
[
"(14 - 2)",
"(2 * (14 - 8))",
"(3 * (8 / 2))",
"((3 * 8) / 2)",
"(((14 - 2) / 3) + 8)",
"(((14 / 2) - 3) + 8)",
"((14 + (2 * 3)) - 8)",
"((2 * 3) + (14 - 8))",
"(((14 * 2) + 8) / 3)",
"(3 * ((14 - 2) - 8))",
"(3 * ((14 - 8) - 2))",
"(3 * (14 - (2 + 8)))",
"(((14 / 2) + 8) - 3)",
"((3 * 8) ... | ((14 - 8) * 2) | bucket_a | ((14 - 8) * 2) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.944439 | 21,001 | {
"canonical_solution": "((14 - 8) * 2)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 19 | [
1,
25
] | [
14,
2,
3,
8
] | {
"completion_tokens": 3372,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01929 | Using the numbers [14, 2, 3, 8], write an arithmetic expression that equals 12.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 12 |
[
"((15 + 25) - 3)",
"(25 + (15 - 3))",
"(15 + (25 - 3))",
"(((15 + 25) - 6) + 3)",
"((25 + (15 - 6)) + 3)",
"((15 + (25 - 6)) + 3)",
"((25 - 6) + (15 + 3))",
"((15 - 6) + (25 + 3))",
"(((15 + 25) + 3) - 6)",
"((25 + (15 + 3)) - 6)",
"((15 + (25 + 3)) - 6)",
"((15 + 25) - (6 - 3))",
"(25 + ((1... | ((3 + 25) + (15 - 6)) | bucket_a | ((3 + 25) + (15 - 6)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "((3 + 25) + (15 - 6))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 18 | [
1,
25
] | [
15,
25,
6,
3
] | {
"completion_tokens": 4421,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_01933 | Using the numbers [15, 25, 6, 3], write an arithmetic expression that equals 37.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 37 |
[
"(15 + 19)",
"(((19 - 15) * 9) - 2)"
] | (15 + 19) | bucket_a | (15 + 19) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -0.693147 | 21,001 | {
"canonical_solution": "(15 + 19)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required... | 4 | 2 | [
1,
25
] | [
2,
15,
19,
9
] | {
"completion_tokens": 3662,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"wrong_value": 6
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01938 | Using the numbers [2, 15, 19, 9], write an arithmetic expression that equals 34.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 34 |
[
"(3 + (3 * 18))",
"(((3 * 14) - 3) + 18)",
"((3 * 14) + (18 - 3))",
"(((3 * 14) + 18) - 3)"
] | ((18 * 3) + 3) | bucket_a | ((18 * 3) + 3) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.386294 | 21,001 | {
"canonical_solution": "((18 * 3) + 3)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 4 | [
1,
25
] | [
3,
3,
14,
18
] | {
"completion_tokens": 4867,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_01947 | Using the numbers [3, 3, 14, 18], write an arithmetic expression that equals 57.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 57 |
[
"((2 + 15) + 2)",
"(15 + (2 + 2))",
"(15 + (2 * 2))",
"(2 + (15 + 2))",
"(((1 * 2) + 15) + 2)",
"(((2 / 1) + 15) + 2)",
"((2 + (1 * 15)) + 2)",
"((2 + (15 / 1)) + 2)",
"((1 * (2 + 15)) + 2)",
"(((2 + 15) / 1) + 2)",
"((2 + 15) + (1 * 2))",
"((2 + 15) + (2 / 1))",
"((1 * 15) + (2 + 2))",
"(... | (15 + (2 * (2 / 1))) | bucket_a | (15 + (2 * (2 / 1))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.367296 | 21,001 | {
"canonical_solution": "(15 + (2 * (2 / 1)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 29 | [
1,
25
] | [
1,
2,
15,
2
] | {
"completion_tokens": 4750,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01955 | Using the numbers [1, 2, 15, 2], write an arithmetic expression that equals 19.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 19 |
[
"(((25 - 9) + 20) + 15)",
"(((25 + 20) - 9) + 15)",
"((25 + (20 - 9)) + 15)",
"((20 - 9) + (25 + 15))",
"((25 + 20) + (15 - 9))",
"(20 + ((25 - 9) + 15))",
"(20 + ((25 + 15) - 9))",
"(20 + (25 + (15 - 9)))",
"((25 - 9) + (20 + 15))",
"(((25 + 20) + 15) - 9)",
"((20 + (25 + 15)) - 9)",
"((25 + ... | ((20 + 25) + (15 - 9)) | bucket_a | ((20 + 25) + (15 - 9)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((20 + 25) + (15 - 9))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
25,
9,
20,
15
] | {
"completion_tokens": 3490,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_01965 | Using the numbers [25, 9, 20, 15], write an arithmetic expression that equals 51.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 51 |
[
"(((24 + 6) - 21) + 25)",
"((6 + (24 - 21)) + 25)",
"((24 - (21 - 6)) + 25)",
"((24 + 25) - (21 - 6))",
"((24 - 21) + (6 + 25))",
"(((24 + 6) + 25) - 21)",
"((6 + (24 + 25)) - 21)",
"((24 + (6 + 25)) - 21)",
"((24 + 6) + (25 - 21))",
"(6 + ((24 - 21) + 25))",
"(6 + ((24 + 25) - 21))",
"(6 + (2... | ((6 + (24 - 21)) + 25) | bucket_a | ((6 + (24 - 21)) + 25) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((6 + (24 - 21)) + 25)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
24,
6,
21,
25
] | {
"completion_tokens": 2779,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"wrong_value": 5
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01976 | Using the numbers [24, 6, 21, 25], write an arithmetic expression that equals 34.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 34 |
[
"(6 + 13)",
"(13 + 6)",
"(((6 + 13) + 6) - 6)",
"((13 + (6 + 6)) - 6)",
"((6 + (13 + 6)) - 6)",
"(((6 + 13) * 6) / 6)",
"((6 * (13 + 6)) / 6)",
"(((6 + 13) - 6) + 6)",
"(((6 * 13) / 6) + 6)",
"(((13 - 6) + 6) + 6)",
"((13 * (6 / 6)) + 6)",
"((13 / (6 / 6)) + 6)",
"(((13 + 6) - 6) + 6)",
"(... | (13 + 6) | bucket_a | (13 + 6) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.295837 | 21,001 | {
"canonical_solution": "(13 + 6)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 27 | [
1,
25
] | [
6,
13,
6,
6
] | {
"completion_tokens": 1410,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_01983 | Using the numbers [6, 13, 6, 6], write an arithmetic expression that equals 19.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 19 |
[
"(((13 * 19) - 5) / 11)",
"(((19 - 13) + 5) + 11)",
"((19 - (13 - 5)) + 11)",
"(((19 + 5) - 13) + 11)",
"((19 + 5) - (13 - 11))",
"((19 + 11) - (13 - 5))",
"(5 + ((19 - 13) + 11))",
"(5 + (19 - (13 - 11)))",
"(5 + ((19 + 11) - 13))",
"((19 - 13) + (5 + 11))",
"(19 + (11 - (13 - 5)))",
"(19 + (... | ((19 - (13 - 11)) + 5) | bucket_a | ((19 - (13 - 11)) + 5) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "((19 - (13 - 11)) + 5)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 16 | [
1,
25
] | [
13,
19,
5,
11
] | {
"completion_tokens": 3589,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_01985 | Using the numbers [13, 19, 5, 11], write an arithmetic expression that equals 22.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 22 |
[
"(16 + 1)",
"(((22 - 16) + 1) + 10)",
"(((22 + 1) - 16) + 10)",
"((22 - (16 - 1)) + 10)",
"((22 + 10) - (16 - 1))",
"((22 + 1) - (16 - 10))",
"(1 + ((22 - 16) + 10))",
"(1 + ((22 + 10) - 16))",
"(1 + (22 - (16 - 10)))",
"((22 - 16) + (1 + 10))",
"(((22 + 1) + 10) - 16)",
"((1 + (22 + 10)) - 16... | (16 + 1) | bucket_a | (16 + 1) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(16 + 1)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 16 | [
1,
25
] | [
22,
16,
1,
10
] | {
"completion_tokens": 2566,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"non_integer_intermediate": 1,
"non_positive_intermediate": 1,
"parse_error": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_01998 | Using the numbers [22, 16, 1, 10], write an arithmetic expression that equals 17.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 17 |
[
"(2 * (18 + 1))",
"(2 * 19)",
"((18 + 1) + 19)",
"(1 + (18 + 19))",
"(18 + (1 + 19))",
"((2 * 1) * 19)",
"((2 / 1) * 19)",
"(1 * (2 * 19))",
"((2 * 19) / 1)",
"(2 * (1 * 19))",
"(2 * (19 / 1))",
"(((18 + 2) - 1) + 19)",
"((2 + (18 - 1)) + 19)",
"((18 + (2 - 1)) + 19)",
"((2 - 1) + (18 + ... | (2 * 19) | bucket_a | (2 * 19) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "(2 * 19)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 26 | [
1,
25
] | [
18,
2,
1,
19
] | {
"completion_tokens": 2832,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02010 | Using the numbers [18, 2, 1, 19], write an arithmetic expression that equals 38.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 38 |
[
"(23 + 12)",
"(((23 + 15) + 12) - 15)",
"((15 + (23 + 12)) - 15)",
"((23 + (15 + 12)) - 15)",
"(((23 - 15) + 12) + 15)",
"(((23 + 12) - 15) + 15)",
"((23 - (15 - 12)) + 15)",
"((15 * (23 + 12)) / 15)",
"((15 + 12) + (23 - 15))",
"((23 + 15) - (15 - 12))",
"((23 + 12) * (15 / 15))",
"((23 + 12)... | (23 + 12) | bucket_a | (23 + 12) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "(23 + 12)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required... | 4 | 26 | [
1,
25
] | [
23,
15,
12,
15
] | {
"completion_tokens": 2451,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_integer_intermediate": 1,
"non_positive_intermediate": 4,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02015 | Using the numbers [23, 15, 12, 15], write an arithmetic expression that equals 35.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 35 |
[
"25",
"(11 + 14)",
"(((25 - 11) / 14) + 24)",
"((14 / (25 - 11)) + 24)",
"((11 / (25 - 14)) + 24)",
"(((25 - 14) / 11) + 24)",
"((25 / (11 + 14)) + 24)",
"(((11 + 14) / 25) + 24)",
"((11 + 14) * (25 - 24))",
"((11 + 14) / (25 - 24))",
"(14 + (11 * (25 - 24)))",
"(14 + (11 / (25 - 24)))",
"(1... | ((14 + 11) * (25 - 24)) | bucket_a | ((14 + 11) * (25 - 24)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.995732 | 21,001 | {
"canonical_solution": "((14 + 11) * (25 - 24))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 20 | [
1,
25
] | [
25,
11,
14,
24
] | {
"completion_tokens": 4174,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02017 | Using the numbers [25, 11, 14, 24], write an arithmetic expression that equals 25.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 25 |
[
"(19 + 23)",
"(((19 + 4) + 23) - 4)",
"((4 + (19 + 23)) - 4)",
"((19 + (4 + 23)) - 4)",
"(((19 - 4) + 23) + 4)",
"(((19 + 23) - 4) + 4)",
"((19 + (23 - 4)) + 4)",
"((4 * (19 + 23)) / 4)",
"((4 + 23) + (19 - 4))",
"((23 - 4) + (19 + 4))",
"((19 + 23) * (4 / 4))",
"((19 + 23) / (4 / 4))",
"(23... | ((4 + (23 - 4)) + 19) | bucket_a | ((4 + (23 - 4)) + 19) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "((4 + (23 - 4)) + 19)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 26 | [
1,
25
] | [
19,
4,
23,
4
] | {
"completion_tokens": 2823,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02040 | Using the numbers [19, 4, 23, 4], write an arithmetic expression that equals 42.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 42 |
[
"(12 + 17)",
"(((20 / 20) * 12) + 17)",
"((12 / (20 / 20)) + 17)",
"(((20 + 12) - 20) + 17)",
"(((20 * 12) / 20) + 17)",
"((20 - (20 - 12)) + 17)",
"((20 + 12) - (20 - 17))",
"((20 + 17) - (20 - 12))",
"(12 + ((20 / 20) * 17))",
"(12 + (17 / (20 / 20)))",
"(12 + ((20 + 17) - 20))",
"(12 + ((20... | ((17 + 20) - (20 - 12)) | bucket_a | ((17 + 20) - (20 - 12)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.091042 | 21,001 | {
"canonical_solution": "((17 + 20) - (20 - 12))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 22 | [
1,
25
] | [
20,
20,
12,
17
] | {
"completion_tokens": 2739,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02041 | Using the numbers [20, 20, 12, 17], write an arithmetic expression that equals 29.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 29 |
[
"24",
"(((24 + 10) + 3) - 13)",
"((10 + (24 + 3)) - 13)",
"((24 + (10 + 3)) - 13)",
"(((24 - 10) - 3) + 13)",
"(((24 - 3) - 10) + 13)",
"((24 - (10 + 3)) + 13)",
"((24 * (10 + 3)) / 13)",
"((24 + 13) - (10 + 3))",
"((24 * 13) / (10 + 3))",
"((10 + 3) + (24 - 13))",
"((24 + 3) - (13 - 10))",
... | ((24 * 13) / (3 + 10)) | bucket_a | ((24 * 13) / (3 + 10)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "((24 * 13) / (3 + 10))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 26 | [
1,
25
] | [
24,
10,
3,
13
] | {
"completion_tokens": 2969,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_02043 | Using the numbers [24, 10, 3, 13], write an arithmetic expression that equals 24.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 24 |
[
"(10 * (1 + 1))",
"((1 + 10) + 9)",
"(10 + (1 + 9))",
"(1 + (10 + 9))",
"((10 + 1) + 9)",
"(((1 + 10) * 1) + 9)",
"(((1 + 10) / 1) + 9)",
"(((1 * 10) + 1) + 9)",
"(((10 / 1) + 1) + 9)",
"((10 + (1 * 1)) + 9)",
"((10 + (1 / 1)) + 9)",
"((1 * (10 + 1)) + 9)",
"(((10 + 1) / 1) + 9)",
"((1 + (... | ((9 + (1 * 10)) + 1) | bucket_a | ((9 + (1 * 10)) + 1) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.401197 | 21,001 | {
"canonical_solution": "((9 + (1 * 10)) + 1)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 30 | [
1,
25
] | [
1,
10,
1,
9
] | {
"completion_tokens": 2607,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02044 | Using the numbers [1, 10, 1, 9], write an arithmetic expression that equals 20.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 20 |
[
"((12 - 1) * 2)",
"((12 - 1) + 11)",
"((12 + 11) - 1)",
"(12 + (11 - 1))",
"(2 * 11)",
"((1 * 2) * 11)",
"((2 / 1) * 11)",
"(2 * (1 * 11))",
"(2 * (11 / 1))",
"(1 * (2 * 11))",
"((2 * 11) / 1)",
"(((12 + 1) - 2) + 11)",
"((1 + (12 - 2)) + 11)",
"((12 - (2 - 1)) + 11)",
"((12 + 11) - (2 -... | ((1 * 11) * 2) | bucket_a | ((1 * 11) * 2) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "((1 * 11) * 2)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 26 | [
1,
25
] | [
12,
1,
2,
11
] | {
"completion_tokens": 4164,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02048 | Using the numbers [12, 1, 2, 11], write an arithmetic expression that equals 22.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 22 |
[
"((8 - 5) * 23)",
"(((8 * 5) + 23) + 6)",
"((5 * (23 - 8)) - 6)",
"(23 + ((8 * 5) + 6))",
"(23 * (6 - (8 - 5)))",
"(23 * (5 - (8 - 6)))",
"(23 * ((5 + 6) - 8))",
"((8 * 5) + (23 + 6))"
] | (6 + (23 + (8 * 5))) | bucket_a | (6 + (23 + (8 * 5))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.079442 | 21,001 | {
"canonical_solution": "(6 + (23 + (8 * 5)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 8 | [
1,
25
] | [
8,
5,
23,
6
] | {
"completion_tokens": 4343,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"no_box": 1,
"parse_error": 3,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02052 | Using the numbers [8, 5, 23, 6], write an arithmetic expression that equals 69.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 69 |
[
"(15 + 23)",
"(((2 + 15) + 23) - 2)",
"((15 + (2 + 23)) - 2)",
"((2 + (15 + 23)) - 2)",
"(((15 - 2) + 23) + 2)",
"((15 + (23 - 2)) + 2)",
"(((15 + 23) - 2) + 2)",
"((2 * (15 + 23)) / 2)",
"(((15 + 23) / 2) * 2)",
"((15 + 23) * (2 / 2))",
"((15 + 23) / (2 / 2))",
"((2 + 23) + (15 - 2))",
"((2... | ((2 + 23) + (15 - 2)) | bucket_a | ((2 + 23) + (15 - 2)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "((2 + 23) + (15 - 2))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 26 | [
1,
25
] | [
2,
15,
23,
2
] | {
"completion_tokens": 1586,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 3,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02068 | Using the numbers [2, 15, 23, 2], write an arithmetic expression that equals 38.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 38 |
[
"(10 + 5)",
"((12 - 10) + 13)",
"((12 + 13) - 10)",
"(12 + (13 - 10))",
"((10 / 5) + 13)",
"(5 * (13 - 10))",
"((10 + 5) * (13 - 12))",
"((10 + 5) / (13 - 12))",
"(5 + (10 * (13 - 12)))",
"(5 + (10 / (13 - 12)))",
"((12 * 10) / (13 - 5))",
"(10 + ((12 + 13) / 5))",
"(10 + (5 * (13 - 12)))",
... | ((12 + 13) - 10) | bucket_a | ((12 + 13) - 10) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((12 + 13) - 10)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"r... | 4 | 15 | [
1,
25
] | [
12,
10,
5,
13
] | {
"completion_tokens": 2567,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02076 | Using the numbers [12, 10, 5, 13], write an arithmetic expression that equals 15.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 15 |
[
"(((9 + 24) + 22) - 14)",
"((24 + (9 + 22)) - 14)",
"((9 + (24 + 22)) - 14)",
"((24 + 22) - (14 - 9))",
"((9 + 22) + (24 - 14))",
"(22 + ((9 + 24) - 14))",
"(22 + (24 - (14 - 9)))",
"(22 + (9 + (24 - 14)))",
"((9 + 24) + (22 - 14))",
"(24 + ((9 + 22) - 14))",
"(24 + (22 - (14 - 9)))",
"(24 + (... | ((22 + (24 + 9)) - 14) | bucket_a | ((22 + (24 + 9)) - 14) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((22 + (24 + 9)) - 14)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
9,
24,
22,
14
] | {
"completion_tokens": 2466,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"parse_error": 2,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02083 | Using the numbers [9, 24, 22, 14], write an arithmetic expression that equals 41.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 41 |
[
"(19 + 2)",
"(23 - 2)",
"((19 + 23) / 2)",
"(((19 + 23) + 2) - 23)",
"((23 + (19 + 2)) - 23)",
"((19 + (23 + 2)) - 23)",
"(23 - ((23 - 19) - 2))",
"(23 - ((23 - 19) / 2))",
"(23 - (23 - (19 + 2)))",
"(23 - ((23 - 2) - 19))",
"((23 * (19 + 2)) / 23)",
"((23 + 2) - (23 - 19))",
"((19 + 23) - (... | (23 - ((23 - 2) - 19)) | bucket_a | (23 - ((23 - 2) - 19)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.332205 | 21,001 | {
"canonical_solution": "(23 - ((23 - 2) - 19))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 28 | [
1,
25
] | [
19,
23,
2,
23
] | {
"completion_tokens": 2139,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 4,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02106 | Using the numbers [19, 23, 2, 23], write an arithmetic expression that equals 21.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 21 |
[
"10",
"(18 - (10 - 2))",
"((2 + 18) - 10)",
"(2 + (18 - 10))"
] | (18 - (10 - 2)) | bucket_a | (18 - (10 - 2)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.386294 | 21,001 | {
"canonical_solution": "(18 - (10 - 2))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 4 | [
1,
25
] | [
2,
25,
10,
18
] | {
"completion_tokens": 5026,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"no_box": 1,
"parse_error": 4,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02110 | Using the numbers [2, 25, 10, 18], write an arithmetic expression that equals 10.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 10 |
[
"(((9 + 7) + 19) + 23)",
"((7 + (9 + 19)) + 23)",
"((9 + (7 + 19)) + 23)",
"((7 + 19) + (9 + 23))",
"((9 + 19) + (7 + 23))",
"(19 + ((9 + 7) + 23))",
"(19 + (7 + (9 + 23)))",
"(19 + (9 + (7 + 23)))",
"((9 + 7) + (19 + 23))",
"(7 + ((9 + 19) + 23))",
"(7 + (19 + (9 + 23)))",
"(7 + (9 + (19 + 23... | ((7 + 23) + (19 + 9)) | bucket_a | ((7 + 23) + (19 + 9)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((7 + 23) + (19 + 9))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
9,
7,
19,
23
] | {
"completion_tokens": 3852,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02128 | Using the numbers [9, 7, 19, 23], write an arithmetic expression that equals 58.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 58 |
[
"(((10 + 13) + 1) + 13)",
"((13 + (10 + 1)) + 13)",
"((10 + (13 + 1)) + 13)",
"((13 + 1) + (10 + 13))",
"((10 + 1) + (13 + 13))",
"(1 + ((10 + 13) + 13))",
"(1 + (13 + (10 + 13)))",
"(1 + (10 + (13 + 13)))",
"((10 + 13) + (1 + 13))",
"(13 + ((10 + 1) + 13))",
"(13 + (1 + (10 + 13)))",
"(13 + (... | ((10 + 1) + (13 + 13)) | bucket_a | ((10 + 1) + (13 + 13)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((10 + 1) + (13 + 13))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
10,
13,
1,
13
] | {
"completion_tokens": 4891,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02129 | Using the numbers [10, 13, 1, 13], write an arithmetic expression that equals 37.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 37 |
[
"((8 + 7) + 3)",
"(7 + (8 + 3))",
"(8 + (7 + 3))",
"((16 - (8 - 7)) + 3)",
"((7 + (16 - 8)) + 3)",
"(((7 + 16) - 8) + 3)",
"((7 + 16) - (8 - 3))",
"((16 - 8) + (7 + 3))",
"(16 + (3 - (8 - 7)))",
"(16 + (7 - (8 - 3)))",
"(16 + ((7 + 3) - 8))",
"(16 + (8 / (7 - 3)))",
"((16 + 3) - (8 - 7))",
... | ((7 + 3) + 8) | bucket_a | ((7 + 3) + 8) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.944439 | 21,001 | {
"canonical_solution": "((7 + 3) + 8)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"requ... | 4 | 19 | [
1,
25
] | [
8,
7,
16,
3
] | {
"completion_tokens": 4004,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_integer_intermediate": 1,
"parse_error": 3,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02142 | Using the numbers [8, 7, 16, 3], write an arithmetic expression that equals 18.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 18 |
[
"(23 * 2)",
"((23 + 21) + 2)",
"(21 + (23 + 2))",
"(23 + (21 + 2))"
] | (2 * 23) | bucket_a | (2 * 23) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.386294 | 21,001 | {
"canonical_solution": "(2 * 23)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 4 | [
1,
25
] | [
6,
23,
21,
2
] | {
"completion_tokens": 3674,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_02152 | Using the numbers [6, 23, 21, 2], write an arithmetic expression that equals 46.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 46 |
[
"(25 - (17 - 8))",
"((8 + 25) - 17)",
"(8 + (25 - 17))",
"(17 - 1)",
"((25 - 8) - 1)",
"(25 - (8 + 1))",
"((25 - 1) - 8)",
"((25 - (17 - 8)) * 1)",
"((25 - (17 - 8)) / 1)",
"(((8 + 25) - 17) * 1)",
"(((8 + 25) - 17) / 1)",
"((8 + (25 - 17)) * 1)",
"((8 + (25 - 17)) / 1)",
"((25 - 17) + (8 ... | (25 - (1 + 8)) | bucket_a | (25 - (1 + 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.465736 | 21,001 | {
"canonical_solution": "(25 - (1 + 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 32 | [
1,
25
] | [
8,
17,
25,
1
] | {
"completion_tokens": 2443,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 2,
"parse_error": 3,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02154 | Using the numbers [8, 17, 25, 1], write an arithmetic expression that equals 16.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 16 |
[
"(9 + 4)",
"((8 + 9) - 4)",
"(9 + (8 - 4))",
"(8 + (9 - 4))",
"((9 + 8) - 4)",
"(((8 + 9) - 8) + 4)",
"(((8 * 9) / 8) + 4)",
"(((9 - 8) + 8) + 4)",
"((9 * (8 / 8)) + 4)",
"((9 / (8 / 8)) + 4)",
"(((9 + 8) - 8) + 4)",
"(((9 * 8) / 8) + 4)",
"((8 + (9 - 8)) + 4)",
"((9 + 8) - (8 - 4))",
"(... | ((9 + 4) * (8 / 8)) | bucket_a | ((9 + 4) * (8 / 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.401197 | 21,001 | {
"canonical_solution": "((9 + 4) * (8 / 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 30 | [
1,
25
] | [
8,
9,
8,
4
] | {
"completion_tokens": 2076,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02156 | Using the numbers [8, 9, 8, 4], write an arithmetic expression that equals 13.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ex... | train | easy | 13 |
[
"(8 + 8)",
"((8 / 4) * 8)",
"((8 * 8) / 4)",
"(8 * (8 / 4))",
"(4 * 4)",
"((8 + 4) + 4)",
"((8 - 4) * 4)",
"(4 + (8 + 4))",
"(4 * (8 - 4))",
"(8 + (4 + 4))",
"((4 + 8) + 4)",
"(((8 + 4) + 8) - 4)",
"((4 + (8 + 8)) - 4)",
"((8 + (4 + 8)) - 4)",
"(((8 + 4) - 8) * 4)",
"(((8 * 4) / 8) * 4... | (8 * (8 / 4)) | bucket_a | (8 * (8 / 4)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.583519 | 21,001 | {
"canonical_solution": "(8 * (8 / 4))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"requ... | 4 | 36 | [
1,
25
] | [
8,
4,
8,
4
] | {
"completion_tokens": 2696,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02159 | Using the numbers [8, 4, 8, 4], write an arithmetic expression that equals 16.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ex... | train | easy | 16 |
[
"((6 * 3) * 3)",
"(3 * (6 * 3))",
"(6 * (3 * 3))",
"(3 * (3 + 15))",
"((3 + 3) * (15 - 6))",
"((6 + 3) + (3 * 15))",
"((6 - 3) * (3 + 15))",
"(3 * ((6 - 3) + 15))",
"(3 * ((6 + 15) - 3))",
"(3 * (6 + (15 - 3)))",
"(3 + (6 + (3 * 15)))",
"(6 * (15 - (3 + 3)))",
"(6 * ((15 - 3) - 3))",
"(6 +... | ((3 * 6) * 3) | bucket_a | ((3 * 6) * 3) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.639057 | 21,001 | {
"canonical_solution": "((3 * 6) * 3)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"requ... | 4 | 14 | [
1,
25
] | [
6,
3,
3,
15
] | {
"completion_tokens": 2704,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02167 | Using the numbers [6, 3, 3, 15], write an arithmetic expression that equals 54.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 54 |
[
"(((11 + 4) - 6) + 17)",
"((4 + (11 - 6)) + 17)",
"((11 - (6 - 4)) + 17)",
"((11 + 17) - (6 - 4))",
"((11 - 6) + (4 + 17))",
"(((11 + 4) + 17) - 6)",
"((4 + (11 + 17)) - 6)",
"((11 + (4 + 17)) - 6)",
"((11 + 4) + (17 - 6))",
"(4 + ((11 - 6) + 17))",
"(4 + ((11 + 17) - 6))",
"(4 + (11 + (17 - 6... | (17 + ((11 - 6) + 4)) | bucket_a | (17 + ((11 - 6) + 4)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(17 + ((11 - 6) + 4))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
11,
4,
6,
17
] | {
"completion_tokens": 4882,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"parse_error": 3,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_02168 | Using the numbers [11, 4, 6, 17], write an arithmetic expression that equals 26.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 26 |
[
"(((11 - 4) + 12) + 24)",
"((11 + (12 - 4)) + 24)",
"(((11 + 12) - 4) + 24)",
"((11 + 12) + (24 - 4))",
"((12 - 4) + (11 + 24))",
"(12 + ((11 - 4) + 24))",
"(12 + (11 + (24 - 4)))",
"(12 + ((11 + 24) - 4))",
"((11 - 4) + (12 + 24))",
"(11 + ((12 - 4) + 24))",
"(11 + (12 + (24 - 4)))",
"(11 + (... | ((11 + (24 - 4)) + 12) | bucket_a | ((11 + (24 - 4)) + 12) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((11 + (24 - 4)) + 12)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
4,
11,
12,
24
] | {
"completion_tokens": 3239,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02178 | Using the numbers [4, 11, 12, 24], write an arithmetic expression that equals 43.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 43 |
[
"(((24 + 20) + 10) + 19)",
"((20 + (24 + 10)) + 19)",
"((24 + (20 + 10)) + 19)",
"((20 + 10) + (24 + 19))",
"((24 + 10) + (20 + 19))",
"(10 + ((24 + 20) + 19))",
"(10 + (20 + (24 + 19)))",
"(10 + (24 + (20 + 19)))",
"((24 + 20) + (10 + 19))",
"(20 + ((24 + 10) + 19))",
"(20 + (10 + (24 + 19)))",... | (((19 + 10) + 20) + 24) | bucket_a | (((19 + 10) + 20) + 24) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(((19 + 10) + 20) + 24)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 15 | [
1,
25
] | [
24,
20,
10,
19
] | {
"completion_tokens": 2942,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02185 | Using the numbers [24, 20, 10, 19], write an arithmetic expression that equals 73.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 73 |
[
"(((25 - 19) + 23) + 4)",
"(((25 + 23) - 19) + 4)",
"((25 + (23 - 19)) + 4)",
"((23 - 19) + (25 + 4))",
"((25 + 23) - (19 - 4))",
"(23 + ((25 - 19) + 4))",
"(23 + ((25 + 4) - 19))",
"(23 + (25 - (19 - 4)))",
"((25 - 19) + (23 + 4))",
"(((25 + 23) + 4) - 19)",
"((23 + (25 + 4)) - 19)",
"((25 + ... | (((25 + 4) - 19) + 23) | bucket_a | (((25 + 4) - 19) + 23) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(((25 + 4) - 19) + 23)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
25,
19,
23,
4
] | {
"completion_tokens": 3688,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02208 | Using the numbers [25, 19, 23, 4], write an arithmetic expression that equals 33.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 33 |
[
"((24 - 11) + 19)",
"((24 + 19) - 11)",
"(24 + (19 - 11))",
"(((24 - 22) + 11) + 19)",
"((24 - (22 - 11)) + 19)",
"(((24 + 11) - 22) + 19)",
"((24 + 11) - (22 - 19))",
"((24 + 19) - (22 - 11))",
"(11 + ((24 - 22) + 19))",
"(11 + (24 - (22 - 19)))",
"(11 + ((24 + 19) - 22))",
"((24 - 22) + (11 ... | (19 + (24 - (22 - 11))) | bucket_a | (19 + (24 - (22 - 11))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "(19 + (24 - (22 - 11)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,... | 4 | 18 | [
1,
25
] | [
22,
24,
11,
19
] | {
"completion_tokens": 3936,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_02214 | Using the numbers [22, 24, 11, 19], write an arithmetic expression that equals 32.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 32 |
[
"(3 + 20)",
"(((3 + 8) - 8) + 20)",
"(((3 * 8) / 8) + 20)",
"((8 - (8 - 3)) + 20)",
"((3 * (8 / 8)) + 20)",
"((3 / (8 / 8)) + 20)",
"((8 / 8) * (3 + 20))",
"((3 + 20) / (8 / 8))",
"((3 + 8) + (20 - 8))",
"((8 + 20) - (8 - 3))",
"(((3 + 8) + 20) - 8)",
"((8 + (3 + 20)) - 8)",
"((3 + (8 + 20))... | ((8 + 20) - (8 - 3)) | bucket_a | ((8 + 20) - (8 - 3)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.091042 | 21,001 | {
"canonical_solution": "((8 + 20) - (8 - 3))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 22 | [
1,
25
] | [
3,
8,
8,
20
] | {
"completion_tokens": 2262,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02220 | Using the numbers [3, 8, 8, 20], write an arithmetic expression that equals 23.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 23 |
[
"(17 + 8)",
"(((17 - 7) - 8) + 23)",
"(((17 - 8) - 7) + 23)",
"((17 - (7 + 8)) + 23)",
"((17 + 23) - (7 + 8))",
"((7 * 23) - (17 * 8))",
"((17 - 8) + (23 - 7))",
"(((17 - 7) + 23) - 8)",
"(((17 + 23) - 7) - 8)",
"((17 + (23 - 7)) - 8)",
"((17 - 7) + (23 - 8))",
"(((17 - 8) + 23) - 7)",
"(((1... | (17 + 8) | bucket_a | (17 + 8) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.833213 | 21,001 | {
"canonical_solution": "(17 + 8)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 17 | [
1,
25
] | [
17,
7,
8,
23
] | {
"completion_tokens": 2308,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02224 | Using the numbers [17, 7, 8, 23], write an arithmetic expression that equals 25.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 25 |
[
"(22 + 22)",
"((1 * 22) + 22)",
"((22 / 1) + 22)",
"(22 + (1 * 22))",
"(22 + (22 / 1))",
"(1 * (22 + 22))",
"((22 + 22) / 1)"
] | ((22 + 22) * 1) | bucket_a | ((22 + 22) * 1) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.94591 | 21,001 | {
"canonical_solution": "((22 + 22) * 1)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 7 | [
1,
25
] | [
1,
22,
6,
22
] | {
"completion_tokens": 3914,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02231 | Using the numbers [1, 22, 6, 22], write an arithmetic expression that equals 44.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 44 |
[
"(16 + 6)",
"22",
"(((16 - 6) / 10) * 22)",
"(22 / ((16 - 6) / 10))",
"((10 / (16 - 6)) * 22)",
"(22 / (10 / (16 - 6)))",
"((6 / (16 - 10)) * 22)",
"(22 / (6 / (16 - 10)))",
"(((16 - 10) / 6) * 22)",
"(22 / ((16 - 10) / 6))",
"((16 / (6 + 10)) * 22)",
"(22 / (16 / (6 + 10)))",
"(((6 + 10) / ... | (6 + 16) | bucket_a | (6 + 16) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.295837 | 21,001 | {
"canonical_solution": "(6 + 16)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 27 | [
1,
25
] | [
16,
6,
10,
22
] | {
"completion_tokens": 2372,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02236 | Using the numbers [16, 6, 10, 22], write an arithmetic expression that equals 22.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 22 |
[
"((7 - 3) + 25)",
"(7 + (25 - 3))",
"((7 + 25) - 3)",
"(((14 - 3) - 7) + 25)",
"((14 - (3 + 7)) + 25)",
"(((14 - 7) - 3) + 25)",
"((14 - 7) + (25 - 3))",
"((14 + 25) - (3 + 7))",
"(((14 - 3) + 25) - 7)",
"((14 + (25 - 3)) - 7)",
"(((14 + 25) - 3) - 7)",
"((14 - 3) + (25 - 7))",
"(14 + (25 - ... | (7 + (25 - 3)) | bucket_a | (7 + (25 - 3)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "(7 + (25 - 3))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 18 | [
1,
25
] | [
3,
14,
7,
25
] | {
"completion_tokens": 2649,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"parse_error": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02261 | Using the numbers [3, 14, 7, 25], write an arithmetic expression that equals 29.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 29 |
[
"(((2 * 14) - 2) + 19)",
"(((14 * 2) - 2) + 19)",
"((14 * 2) + (19 - 2))",
"((14 / 2) + (2 * 19))",
"(((2 * 14) + 19) - 2)",
"((2 * 14) + (19 - 2))",
"(((14 * 2) + 19) - 2)"
] | ((2 * 19) + (14 / 2)) | bucket_a | ((2 * 19) + (14 / 2)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.94591 | 21,001 | {
"canonical_solution": "((2 * 19) + (14 / 2))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 7 | [
1,
25
] | [
2,
14,
2,
19
] | {
"completion_tokens": 4576,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 1,
"wrong_value": 5
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02264 | Using the numbers [2, 14, 2, 19], write an arithmetic expression that equals 45.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 45 |
[
"(21 + 4)",
"((1 * 21) + 4)",
"((21 / 1) + 4)",
"(21 + (1 * 4))",
"(21 + (4 / 1))",
"(1 * (21 + 4))",
"((21 + 4) / 1)",
"(((9 - 1) + 21) - 4)",
"((9 + (21 - 1)) - 4)",
"(((9 + 21) - 1) - 4)",
"((9 + 21) - (1 + 4))",
"((21 - 1) + (9 - 4))",
"(21 + ((9 - 1) - 4))",
"(21 + (9 - (1 + 4)))",
... | (4 + 21) | bucket_a | (4 + 21) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.091042 | 21,001 | {
"canonical_solution": "(4 + 21)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 22 | [
1,
25
] | [
1,
9,
21,
4
] | {
"completion_tokens": 1889,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02276 | Using the numbers [1, 9, 21, 4], write an arithmetic expression that equals 25.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 25 |
[
"(((10 - 3) + 12) + 13)",
"((10 + (12 - 3)) + 13)",
"(((10 + 12) - 3) + 13)",
"((10 + 12) + (13 - 3))",
"((12 - 10) * (3 + 13))",
"((12 - 3) + (10 + 13))",
"(12 + ((10 - 3) + 13))",
"(12 + (10 + (13 - 3)))",
"(12 + ((10 + 13) - 3))",
"((10 - 3) + (12 + 13))",
"(10 + ((12 - 3) + 13))",
"(10 + (... | (((13 + 10) - 3) + 12) | bucket_a | (((13 + 10) - 3) + 12) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(((13 + 10) - 3) + 12)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 16 | [
1,
25
] | [
3,
10,
12,
13
] | {
"completion_tokens": 3434,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 1,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_02288 | Using the numbers [3, 10, 12, 13], write an arithmetic expression that equals 32.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 32 |
[
"((8 * 6) + 5)",
"((8 + 15) + (6 * 5))",
"(15 + (8 + (6 * 5)))",
"(8 + ((15 - 6) * 5))",
"(8 + (15 + (6 * 5)))"
] | ((8 + 15) + (5 * 6)) | bucket_a | ((8 + 15) + (5 * 6)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.609438 | 21,001 | {
"canonical_solution": "((8 + 15) + (5 * 6))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 5 | [
1,
25
] | [
8,
15,
6,
5
] | {
"completion_tokens": 4775,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 3,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02292 | Using the numbers [8, 15, 6, 5], write an arithmetic expression that equals 53.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 53 |
[
"((7 * 8) - 22)",
"(((13 + 22) + 7) - 8)",
"((22 + (13 + 7)) - 8)",
"((13 + (22 + 7)) - 8)",
"((22 + 7) + (13 - 8))",
"((13 + 7) + (22 - 8))",
"(7 + ((13 + 22) - 8))",
"(7 + (22 + (13 - 8)))",
"(7 + (13 + (22 - 8)))",
"((13 + 22) - (8 - 7))",
"(22 + ((13 + 7) - 8))",
"(22 + (7 + (13 - 8)))",
... | (((22 + 7) - 8) + 13) | bucket_a | (((22 + 7) - 8) + 13) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "(((22 + 7) - 8) + 13)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 16 | [
1,
25
] | [
13,
22,
7,
8
] | {
"completion_tokens": 2832,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02306 | Using the numbers [13, 22, 7, 8], write an arithmetic expression that equals 34.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 34 |
[
"((18 + 22) + 3)",
"(22 + (18 + 3))",
"(18 + (22 + 3))"
] | ((18 + 3) + 22) | bucket_a | ((18 + 3) + 22) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.098612 | 21,001 | {
"canonical_solution": "((18 + 3) + 22)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 3 | [
1,
25
] | [
20,
18,
22,
3
] | {
"completion_tokens": 3072,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02310 | Using the numbers [20, 18, 22, 3], write an arithmetic expression that equals 43.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 43 |
[
"((1 + 10) + 12)",
"(10 + (1 + 12))",
"(1 + (10 + 12))",
"((1 + 12) + 10)",
"(12 + (1 + 10))",
"(1 + (12 + 10))"
] | ((12 + 1) + 10) | bucket_a | ((12 + 1) + 10) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.791759 | 21,001 | {
"canonical_solution": "((12 + 1) + 10)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 6 | [
1,
25
] | [
1,
10,
12,
10
] | {
"completion_tokens": 4335,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02319 | Using the numbers [1, 10, 12, 10], write an arithmetic expression that equals 23.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 23 |
[
"(((14 + 10) + 7) + 3)",
"((10 + (14 + 7)) + 3)",
"((14 + (10 + 7)) + 3)",
"((10 + 7) + (14 + 3))",
"((14 + 7) + (10 + 3))",
"(7 + ((14 + 10) + 3))",
"(7 + (10 + (14 + 3)))",
"(7 + (14 + (10 + 3)))",
"((14 + 10) + (7 + 3))",
"(10 + ((14 + 7) + 3))",
"(10 + (7 + (14 + 3)))",
"(10 + (14 + (7 + 3... | (10 + ((3 + 7) + 14)) | bucket_a | (10 + ((3 + 7) + 14)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(10 + ((3 + 7) + 14))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
14,
10,
7,
3
] | {
"completion_tokens": 2959,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 3,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02321 | Using the numbers [14, 10, 7, 3], write an arithmetic expression that equals 34.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 34 |
[
"(21 - (15 / 3))",
"(23 - (21 / 3))",
"(((21 + 15) - 23) + 3)",
"((15 - (23 - 21)) + 3)",
"((21 - (23 - 15)) + 3)",
"((21 + 3) - (23 - 15))",
"((15 + 3) - (23 - 21))",
"(((21 + 15) + 3) - 23)",
"((15 + (21 + 3)) - 23)",
"((21 + (15 + 3)) - 23)",
"((21 + 15) - (23 - 3))",
"(15 + (3 - (23 - 21))... | (((21 + 3) + 15) - 23) | bucket_a | (((21 + 3) + 15) - 23) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.833213 | 21,001 | {
"canonical_solution": "(((21 + 3) + 15) - 23)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 17 | [
1,
25
] | [
21,
15,
23,
3
] | {
"completion_tokens": 2250,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"non_positive_intermediate": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02336 | Using the numbers [21, 15, 23, 3], write an arithmetic expression that equals 16.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 16 |
[
"(9 + 7)",
"((18 - 9) + 7)",
"((18 + 7) - 9)",
"(18 - (9 - 7))",
"((18 + 9) - 11)",
"(9 + (18 - 11))",
"(18 - (11 - 9))",
"((7 - (18 / 9)) + 11)",
"(7 + (11 - (18 / 9)))",
"(7 + (18 / (11 - 9)))",
"((7 + 11) - (18 / 9))",
"(18 - ((7 + 11) / 9))"
] | (7 + 9) | bucket_a | (7 + 9) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.484907 | 21,001 | {
"canonical_solution": "(7 + 9)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_a... | 4 | 12 | [
1,
25
] | [
18,
9,
7,
11
] | {
"completion_tokens": 4131,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02337 | Using the numbers [18, 9, 7, 11], write an arithmetic expression that equals 16.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 16 |
[
"((8 + 9) + 1)",
"(9 + (8 + 1))",
"(8 + (9 + 1))",
"(((20 + 8) - 9) - 1)",
"((8 + (20 - 9)) - 1)",
"((20 - (9 - 8)) - 1)",
"((20 - 1) - (9 - 8))",
"((20 - 9) + (8 - 1))",
"(((20 + 8) - 1) - 9)",
"((8 + (20 - 1)) - 9)",
"((20 + (8 - 1)) - 9)",
"((20 + 8) - (9 + 1))",
"(8 + ((20 - 9) - 1))",
... | (9 + (8 + 1)) | bucket_a | (9 + (8 + 1)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "(9 + (8 + 1))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"requ... | 4 | 18 | [
1,
25
] | [
20,
8,
9,
1
] | {
"completion_tokens": 3469,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 4,
"non_positive_intermediate": 1,
"parse_error": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02341 | Using the numbers [20, 8, 9, 1], write an arithmetic expression that equals 18.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 18 |
[
"((12 + 14) + 21)",
"(14 + (12 + 21))",
"(12 + (14 + 21))",
"(((24 - 12) + 14) + 21)",
"((24 + (14 - 12)) + 21)",
"(((24 + 14) - 12) + 21)",
"((24 + 14) + (21 - 12))",
"((14 - 12) + (24 + 21))",
"(14 + ((24 - 12) + 21))",
"(14 + (24 + (21 - 12)))",
"(14 + ((24 + 21) - 12))",
"((24 - 12) + (14 ... | ((21 + 14) + 12) | bucket_a | ((21 + 14) + 12) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "((21 + 14) + 12)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"r... | 4 | 18 | [
1,
25
] | [
12,
24,
14,
21
] | {
"completion_tokens": 2075,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02349 | Using the numbers [12, 24, 14, 21], write an arithmetic expression that equals 47.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as a... | train | easy | 47 |
[
"(((19 - 4) + 14) + 3)",
"((19 + (14 - 4)) + 3)",
"(((19 + 14) - 4) + 3)",
"((19 + 14) - (4 - 3))",
"((14 - 4) + (19 + 3))",
"(14 + ((19 - 4) + 3))",
"(14 + (19 - (4 - 3)))",
"(14 + ((19 + 3) - 4))",
"((19 - 4) + (14 + 3))",
"(19 + ((14 - 4) + 3))",
"(19 + (14 - (4 - 3)))",
"(19 + ((14 + 3) - ... | ((19 - 4) + (14 + 3)) | bucket_a | ((19 - 4) + (14 + 3)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "((19 - 4) + (14 + 3))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 18 | [
1,
25
] | [
4,
19,
14,
3
] | {
"completion_tokens": 4902,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_integer_intermediate": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02361 | Using the numbers [4, 19, 14, 3], write an arithmetic expression that equals 32.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 32 |
[
"((7 * 5) - 8)",
"(((17 + 7) + 8) - 5)",
"((7 + (17 + 8)) - 5)",
"((17 + (7 + 8)) - 5)",
"((7 + 8) + (17 - 5))",
"((17 + 8) + (7 - 5))",
"(8 + ((17 + 7) - 5))",
"(8 + (7 + (17 - 5)))",
"(8 + (17 + (7 - 5)))",
"((17 + 7) + (8 - 5))",
"(7 + ((17 + 8) - 5))",
"(7 + (8 + (17 - 5)))",
"(7 + (17 +... | ((7 * 5) - 8) | bucket_a | ((7 * 5) - 8) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "((7 * 5) - 8)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"requ... | 4 | 16 | [
1,
25
] | [
17,
7,
8,
5
] | {
"completion_tokens": 4394,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02365 | Using the numbers [17, 7, 8, 5], write an arithmetic expression that equals 27.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 27 |
[
"((5 * (15 - 8)) - 2)",
"((8 + 15) + (5 * 2))",
"(15 + (8 + (5 * 2)))",
"((8 - 5) + (15 * 2))",
"(8 + (15 + (5 * 2)))",
"(8 + ((15 * 2) - 5))",
"((8 + (15 * 2)) - 5)"
] | (8 + ((5 * 2) + 15)) | bucket_a | (8 + ((5 * 2) + 15)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.94591 | 21,001 | {
"canonical_solution": "(8 + ((5 * 2) + 15))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 7 | [
1,
25
] | [
5,
8,
15,
2
] | {
"completion_tokens": 5330,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"no_box": 1,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02370 | Using the numbers [5, 8, 15, 2], write an arithmetic expression that equals 33.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 33 |
[
"(((1 + 18) + 13) - 3)",
"((18 + (1 + 13)) - 3)",
"((1 + (18 + 13)) - 3)",
"((18 + 13) - (3 - 1))",
"((1 + 13) + (18 - 3))",
"(13 + ((1 + 18) - 3))",
"(13 + (18 - (3 - 1)))",
"(13 + (1 + (18 - 3)))",
"((1 + 18) + (13 - 3))",
"(18 + ((1 + 13) - 3))",
"(18 + (13 - (3 - 1)))",
"(18 + (1 + (13 - 3... | ((13 - 3) + (18 + 1)) | bucket_a | ((13 - 3) + (18 + 1)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((13 - 3) + (18 + 1))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
1,
18,
13,
3
] | {
"completion_tokens": 3677,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02374 | Using the numbers [1, 18, 13, 3], write an arithmetic expression that equals 29.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 29 |
[
"(16 * 6)",
"((16 * 6) * 1)",
"((16 * 6) / 1)",
"(6 * (16 * 1))",
"(6 * (16 / 1))",
"(16 * (6 * 1))",
"(16 * (6 / 1))",
"((16 * 1) * 6)",
"((16 / 1) * 6)",
"(1 * (16 * 6))",
"(16 * (1 * 6))",
"((6 * (16 + 1)) - 6)",
"((6 * (16 - 1)) + 6)",
"(((16 + 1) * 6) - 6)",
"(6 + ((16 - 1) * 6))"
] | (16 * 6) | bucket_a | (16 * 6) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(16 * 6)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 15 | [
1,
25
] | [
16,
6,
1,
6
] | {
"completion_tokens": 3285,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02386 | Using the numbers [16, 6, 1, 6], write an arithmetic expression that equals 96.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 96 |
[
"(((19 + 13) - 7) + 23)",
"((13 + (19 - 7)) + 23)",
"((19 + (13 - 7)) + 23)",
"((13 - 7) + (19 + 23))",
"((19 - 7) + (13 + 23))",
"(((19 + 13) + 23) - 7)",
"((13 + (19 + 23)) - 7)",
"((19 + (13 + 23)) - 7)",
"((19 + 13) + (23 - 7))",
"(13 + ((19 - 7) + 23))",
"(13 + ((19 + 23) - 7))",
"(13 + (... | (19 + ((13 + 23) - 7)) | bucket_a | (19 + ((13 + 23) - 7)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "(19 + ((13 + 23) - 7))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
19,
13,
7,
23
] | {
"completion_tokens": 4860,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 3,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02387 | Using the numbers [19, 13, 7, 23], write an arithmetic expression that equals 48.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 48 |
[
"((5 + 9) + 25)",
"(9 + (5 + 25))",
"(5 + (9 + 25))",
"((18 - (9 - 5)) + 25)",
"(((5 + 18) - 9) + 25)",
"((5 + (18 - 9)) + 25)",
"((18 - 9) + (5 + 25))",
"((5 + 18) + (25 - 9))",
"(18 + (25 - (9 - 5)))",
"(18 + ((5 + 25) - 9))",
"(18 + (5 + (25 - 9)))",
"((18 + 25) - (9 - 5))",
"(((5 + 18) +... | (9 + (25 + 5)) | bucket_a | (9 + (25 + 5)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "(9 + (25 + 5))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 18 | [
1,
25
] | [
5,
9,
18,
25
] | {
"completion_tokens": 3789,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 2,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02405 | Using the numbers [5, 9, 18, 25], write an arithmetic expression that equals 39.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 39 |
[
"(((11 + 25) + 3) + 21)",
"((25 + (11 + 3)) + 21)",
"((11 + (25 + 3)) + 21)",
"((25 + 3) + (11 + 21))",
"((11 + 3) + (25 + 21))",
"(3 + ((11 + 25) + 21))",
"(3 + (25 + (11 + 21)))",
"(3 + (11 + (25 + 21)))",
"((11 + 25) + (3 + 21))",
"(25 + ((11 + 3) + 21))",
"(25 + (3 + (11 + 21)))",
"(25 + (... | ((21 + 3) + (25 + 11)) | bucket_a | ((21 + 3) + (25 + 11)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((21 + 3) + (25 + 11))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
11,
25,
3,
21
] | {
"completion_tokens": 3750,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"invalid_operands": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_02418 | Using the numbers [11, 25, 3, 21], write an arithmetic expression that equals 60.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 60 |
[
"(10 + (2 * 12))",
"((2 + (2 * 10)) + 12)",
"((2 * 10) + (2 + 12))",
"(2 + ((2 * 10) + 12))",
"(2 * ((10 / 2) + 12))"
] | (2 + (12 + (2 * 10))) | bucket_a | (2 + (12 + (2 * 10))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.609438 | 21,001 | {
"canonical_solution": "(2 + (12 + (2 * 10)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 5 | [
1,
25
] | [
2,
2,
10,
12
] | {
"completion_tokens": 5129,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02440 | Using the numbers [2, 2, 10, 12], write an arithmetic expression that equals 34.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 34 |
[
"((22 + 17) - 9)",
"(17 + (22 - 9))",
"(22 + (17 - 9))",
"(((16 + 22) - 17) + 9)",
"((22 - (17 - 16)) + 9)",
"((16 + (22 - 17)) + 9)",
"((22 - 17) + (16 + 9))",
"((22 + 9) - (17 - 16))",
"(((16 + 22) + 9) - 17)",
"((22 + (16 + 9)) - 17)",
"((16 + (22 + 9)) - 17)",
"((16 + 22) - (17 - 9))",
"... | ((17 + 22) - 9) | bucket_a | ((17 + 22) - 9) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.890372 | 21,001 | {
"canonical_solution": "((17 + 22) - 9)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 18 | [
1,
25
] | [
16,
22,
17,
9
] | {
"completion_tokens": 3176,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 2,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02443 | Using the numbers [16, 22, 17, 9], write an arithmetic expression that equals 30.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 30 |
[
"(19 - 5)",
"(5 + 9)",
"((19 - 5) * 1)",
"((19 - 5) / 1)",
"(19 - (5 * 1))",
"(19 - (5 / 1))",
"((19 * 1) - 5)",
"((19 / 1) - 5)",
"((5 + 9) * 1)",
"((5 + 9) / 1)",
"(9 + (5 * 1))",
"(9 + (5 / 1))",
"(5 + (9 * 1))",
"(5 + (9 / 1))",
"(((5 + 19) - 9) - 1)",
"((19 - (9 - 5)) - 1)",
"((... | (5 + 9) | bucket_a | (5 + 9) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.367296 | 21,001 | {
"canonical_solution": "(5 + 9)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_a... | 4 | 29 | [
1,
25
] | [
5,
19,
9,
1
] | {
"completion_tokens": 1759,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.6,
"reason_counts": {
"correct": 6,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 6
} | cd_bucket_a_train_21001_02482 | Using the numbers [5, 19, 9, 1], write an arithmetic expression that equals 14.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 14 |
[
"((20 - 15) + (3 * 12))",
"((20 + (3 * 12)) - 15)",
"(20 + ((3 * 12) - 15))"
] | (20 + ((12 * 3) - 15)) | bucket_a | (20 + ((12 * 3) - 15)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.098612 | 21,001 | {
"canonical_solution": "(20 + ((12 * 3) - 15))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 3 | [
1,
25
] | [
20,
15,
3,
12
] | {
"completion_tokens": 6571,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"no_box": 1,
"non_positive_intermediate": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02483 | Using the numbers [20, 15, 3, 12], write an arithmetic expression that equals 41.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 41 |
[
"((24 + 16) - 5)",
"(16 + (24 - 5))",
"(24 + (16 - 5))",
"((14 + 16) + 5)",
"(16 + (14 + 5))",
"(14 + (16 + 5))"
] | (16 + (14 + 5)) | bucket_a | (16 + (14 + 5)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -1.791759 | 21,001 | {
"canonical_solution": "(16 + (14 + 5))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"re... | 4 | 6 | [
1,
25
] | [
24,
14,
16,
5
] | {
"completion_tokens": 3651,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"parse_error": 3,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02488 | Using the numbers [24, 14, 16, 5], write an arithmetic expression that equals 35.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 35 |
[
"(4 + 8)",
"(4 * (11 - 8))",
"((25 * 4) - (11 * 8))",
"(4 * ((25 + 8) / 11))",
"((25 - 11) - (8 / 4))",
"(25 - (11 + (8 / 4)))",
"((4 * (25 + 8)) / 11)",
"((25 - (8 / 4)) - 11)"
] | ((11 - 8) * 4) | bucket_a | ((11 - 8) * 4) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.079442 | 21,001 | {
"canonical_solution": "((11 - 8) * 4)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 8 | [
1,
25
] | [
11,
25,
4,
8
] | {
"completion_tokens": 3090,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02495 | Using the numbers [11, 25, 4, 8], write an arithmetic expression that equals 12.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 12 |
[
"(((25 - 15) - 1) + 24)",
"((25 - (15 + 1)) + 24)",
"(((25 - 1) - 15) + 24)",
"((25 - 1) + (24 - 15))",
"((25 + 24) - (15 + 1))",
"(((25 - 15) + 24) - 1)",
"((25 + (24 - 15)) - 1)",
"(((25 + 24) - 15) - 1)",
"((25 - 15) + (24 - 1))",
"(25 + (24 - (15 + 1)))",
"(25 + ((24 - 15) - 1))",
"(25 + (... | ((24 - (1 + 15)) + 25) | bucket_a | ((24 - (1 + 15)) + 25) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((24 - (1 + 15)) + 25)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
15,
25,
1,
24
] | {
"completion_tokens": 1586,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"parse_error": 1,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02499 | Using the numbers [15, 25, 1, 24], write an arithmetic expression that equals 33.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 33 |
[
"((17 * 2) - 10)",
"(19 + (10 / 2))",
"(((17 + 19) - 2) - 10)",
"((19 + (17 - 2)) - 10)",
"((17 + (19 - 2)) - 10)",
"((19 - 2) + (17 - 10))",
"((17 - 2) + (19 - 10))",
"(((17 + 19) - 10) - 2)",
"((19 + (17 - 10)) - 2)",
"((17 + (19 - 10)) - 2)",
"(2 * ((19 - 17) + 10))",
"(2 * (19 - (17 - 10))... | (2 * (19 - (17 - 10))) | bucket_a | (2 * (19 - (17 - 10))) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.044522 | 21,001 | {
"canonical_solution": "(2 * (19 - (17 - 10)))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 21 | [
1,
25
] | [
17,
19,
2,
10
] | {
"completion_tokens": 2838,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"invalid_operands": 2,
"parse_error": 2,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02504 | Using the numbers [17, 19, 2, 10], write an arithmetic expression that equals 24.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 24 |
[
"(((25 + 2) + 19) - 6)",
"((2 + (25 + 19)) - 6)",
"((25 + (2 + 19)) - 6)",
"((2 + 19) + (25 - 6))",
"((25 + 19) - (6 - 2))",
"(19 + ((25 + 2) - 6))",
"(19 + (2 + (25 - 6)))",
"(19 + (25 - (6 - 2)))",
"((25 + 2) + (19 - 6))",
"(2 + ((25 + 19) - 6))",
"(2 + (19 + (25 - 6)))",
"(2 + (25 + (19 - 6... | ((25 - (6 - 2)) + 19) | bucket_a | ((25 - (6 - 2)) + 19) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.70805 | 21,001 | {
"canonical_solution": "((25 - (6 - 2)) + 19)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 15 | [
1,
25
] | [
25,
2,
19,
6
] | {
"completion_tokens": 4780,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 3,
"parse_error": 2,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02529 | Using the numbers [25, 2, 19, 6], write an arithmetic expression that equals 40.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 40 |
[
"21",
"((21 + 8) - 8)",
"((21 * 8) / 8)",
"((21 - 8) + 8)",
"(8 + (21 - 8))",
"(21 * (8 / 8))",
"(21 / (8 / 8))",
"(20 + (8 / 8))"
] | (21 / (8 / 8)) | bucket_a | (21 / (8 / 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.079442 | 21,001 | {
"canonical_solution": "(21 / (8 / 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 8 | [
1,
25
] | [
21,
20,
8,
8
] | {
"completion_tokens": 2017,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"non_positive_intermediate": 2,
"parse_error": 3
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02542 | Using the numbers [21, 20, 8, 8], write an arithmetic expression that equals 21.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 21 |
[
"((3 * (13 + 12)) + 13)",
"(13 + (3 * (12 + 13)))"
] | (13 + ((12 + 13) * 3)) | bucket_a | (13 + ((12 + 13) * 3)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -0.693147 | 21,001 | {
"canonical_solution": "(13 + ((12 + 13) * 3))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 2 | [
1,
25
] | [
13,
3,
12,
13
] | {
"completion_tokens": 7144,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"no_box": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02543 | Using the numbers [13, 3, 12, 13], write an arithmetic expression that equals 88.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 88 |
[
"(24 - (22 - 19))",
"((19 + 24) - 22)",
"(19 + (24 - 22))",
"(((19 + 4) + 22) - 24)",
"((4 + (19 + 22)) - 24)",
"((19 + (4 + 22)) - 24)",
"((4 + 22) - (24 - 19))",
"((19 + 22) - (24 - 4))",
"(22 - (24 - (19 + 4)))",
"(22 - ((24 - 19) - 4))",
"(22 - ((24 - 4) - 19))",
"((19 + 4) - (24 - 22))",
... | ((19 + 22) - (24 - 4)) | bucket_a | ((19 + 22) - (24 - 4)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.944439 | 21,001 | {
"canonical_solution": "((19 + 22) - (24 - 4))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 19 | [
1,
25
] | [
19,
4,
22,
24
] | {
"completion_tokens": 2564,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"non_positive_intermediate": 3,
"parse_error": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02545 | Using the numbers [19, 4, 22, 24], write an arithmetic expression that equals 21.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an... | train | easy | 21 |
[
"(7 + 23)",
"((7 + 23) * 1)",
"((7 + 23) / 1)",
"(23 + (7 * 1))",
"(23 + (7 / 1))",
"(7 + (23 * 1))",
"(7 + (23 / 1))",
"(((15 - 7) + 23) - 1)",
"(((15 + 23) - 7) - 1)",
"((15 + (23 - 7)) - 1)",
"((23 - 7) + (15 - 1))",
"((15 + 23) - (7 + 1))",
"(23 + ((15 - 7) - 1))",
"(23 + ((15 - 1) - 7... | (7 + 23) | bucket_a | (7 + 23) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.091042 | 21,001 | {
"canonical_solution": "(7 + 23)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_... | 4 | 22 | [
1,
25
] | [
15,
7,
23,
1
] | {
"completion_tokens": 3161,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"parse_error": 1,
"wrong_value": 3
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02548 | Using the numbers [15, 7, 23, 1], write an arithmetic expression that equals 30.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 30 |
[
"(15 * (8 - 6))",
"(((17 + 6) + 15) - 8)",
"((6 + (17 + 15)) - 8)",
"((17 + (6 + 15)) - 8)",
"((6 + 15) + (17 - 8))",
"((17 + 15) - (8 - 6))",
"(15 + ((17 + 6) - 8))",
"(15 + (6 + (17 - 8)))",
"(15 + (17 - (8 - 6)))",
"((17 + 6) + (15 - 8))",
"(6 + ((17 + 15) - 8))",
"(6 + (15 + (17 - 8)))",
... | ((15 + 6) + (17 - 8)) | bucket_a | ((15 + 6) + (17 - 8)) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.772589 | 21,001 | {
"canonical_solution": "((15 + 6) + (17 - 8))",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 16 | [
1,
25
] | [
17,
6,
15,
8
] | {
"completion_tokens": 6554,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 2,
"non_positive_intermediate": 2,
"parse_error": 1,
"wrong_value": 1
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02549 | Using the numbers [17, 6, 15, 8], write an arithmetic expression that equals 30.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 30 |
[
"(8 * (2 + 1))",
"((8 * 2) + 8)",
"(8 + (2 * 8))",
"((2 + 1) * 8)",
"(((8 * 2) * 1) + 8)",
"(((8 * 2) / 1) + 8)",
"((2 * (8 * 1)) + 8)",
"((2 * (8 / 1)) + 8)",
"((8 * (2 * 1)) + 8)",
"((8 * (2 / 1)) + 8)",
"(((8 / 2) - 1) * 8)",
"((8 * 1) + (2 * 8))",
"((8 / 1) + (2 * 8))",
"(1 * ((8 * 2) ... | ((8 * 2) + 8) | bucket_a | ((8 * 2) + 8) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.258097 | 21,001 | {
"canonical_solution": "((8 * 2) + 8)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"requ... | 4 | 26 | [
1,
25
] | [
8,
2,
1,
8
] | {
"completion_tokens": 3310,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"invalid_operands": 1,
"non_positive_intermediate": 1,
"wrong_value": 4
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02553 | Using the numbers [8, 2, 1, 8], write an arithmetic expression that equals 24.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ex... | train | easy | 24 |
[
"(24 - (1 + 6))",
"((24 - 1) - 6)",
"((24 - 6) - 1)",
"(24 - ((2 - 1) + 6))",
"(24 - ((2 + 6) - 1))",
"(24 - (2 + (6 - 1)))",
"((24 - 2) - (6 - 1))",
"((6 - 1) + (24 / 2))",
"((1 + 24) - (2 + 6))",
"((24 - (2 - 1)) - 6)",
"((1 + (24 - 2)) - 6)",
"(((1 + 24) - 2) - 6)",
"(6 + ((24 / 2) - 1))"... | ((24 - 1) - 6) | bucket_a | ((24 - 1) - 6) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -3.044522 | 21,001 | {
"canonical_solution": "((24 - 1) - 6)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"req... | 4 | 21 | [
1,
25
] | [
2,
1,
6,
24
] | {
"completion_tokens": 2460,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.4,
"reason_counts": {
"correct": 4,
"parse_error": 4,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 4
} | cd_bucket_a_train_21001_02562 | Using the numbers [2, 1, 6, 24], write an arithmetic expression that equals 17.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an e... | train | easy | 17 |
[
"(((9 + 16) + 12) - 5)",
"((16 + (9 + 12)) - 5)",
"((9 + (16 + 12)) - 5)",
"((16 + 12) + (9 - 5))",
"((9 + 12) + (16 - 5))",
"(12 + ((9 + 16) - 5))",
"(12 + (16 + (9 - 5)))",
"(12 + (9 + (16 - 5)))",
"((9 + 16) + (12 - 5))",
"(16 + ((9 + 12) - 5))",
"(16 + (12 + (9 - 5)))",
"(16 + (9 + (12 - 5... | (((12 + 16) + 9) - 5) | bucket_a | (((12 + 16) + 9) - 5) | {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
"required_any_ops": [],
"required_ops": [],
"solution_operands_max": 4,
"solution_... | bucket_a | -2.944439 | 21,001 | {
"canonical_solution": "(((12 + 16) + 9) - 5)",
"config": {
"allowed_ops": [
"+",
"-",
"*",
"/"
],
"enumeration_cap": 1000,
"max_generation_attempts": 20000,
"max_solutions": 500,
"min_solutions": 1,
"n_operands": 4,
"operand_max": 25,
"operand_min": 1,
... | 4 | 19 | [
1,
25
] | [
9,
16,
12,
5
] | {
"completion_tokens": 5203,
"model": "Qwen/Qwen3-0.6B",
"observed_success_fraction": 0.5,
"reason_counts": {
"correct": 5,
"no_box": 1,
"parse_error": 2,
"wrong_value": 2
},
"rollouts": 10,
"success_count": 5
} | cd_bucket_a_train_21001_02565 | Using the numbers [9, 16, 12, 5], write an arithmetic expression that equals 32.
You may use +, -, *, / and parentheses. Each number may be used at most once; you do not need to use every number. Intermediate values must be positive integers.
Keep any reasoning brief. Write your final answer inside \boxed{...} as an ... | train | easy | 32 |
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