domain listlengths 1 3 | difficulty float64 1 9.5 | problem stringlengths 38 9.01k | solution stringlengths 2 4.63k | answer stringlengths 1 167 | source stringclasses 37
values | model_id stringclasses 1
value | dataset_name stringclasses 1
value | reward dict | generations dict |
|---|---|---|---|---|---|---|---|---|---|
["Mathematics -> Algebra -> Algebra -> Algebraic Expressions","Mathematics -> Algebra -> Equations a(...TRUNCATED) | 9 | "Find all functions $f: \\mathbb{R}^{+} \\rightarrow \\mathbb{R}^{+}$ such that\n$$f(xf(x + y)) = yf(...TRUNCATED) | "\nTo solve the functional equation \\( f: \\mathbb{R}^{+} \\rightarrow \\mathbb{R}^{+} \\) given by(...TRUNCATED) | f(x) = \frac{1}{x} | balkan_mo_shortlist | google/gemma-3-12b-it | omni_math | {"reward_mean":1.0,"rewards":[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.(...TRUNCATED) | {"completions":["Let $P(x, y)$ be the assertion $f(xf(x + y)) = yf(x) + 1$.\n\n$P(1, x) \\implies f((...TRUNCATED) |
[
"Mathematics -> Geometry -> Plane Geometry -> Triangulations"
] | 5.25 | "Let $A B C$ be a triangle with incircle tangent to the perpendicular bisector of $B C$. If $B C=A E(...TRUNCATED) | "Let the incircle and $B C$ touch at $D$, the incircle and perpendicular bisector touch at $X, Y$ be(...TRUNCATED) | 100 \sqrt{2} | HMMT_2 | google/gemma-3-12b-it | omni_math | {"reward_mean":0.0,"rewards":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) | {"completions":["Let $a, b, c$ be the lengths of sides $B C, C A, A B$ respectively. Let $s$ be the (...TRUNCATED) |
[
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 9 | "Let $a, b, c, p, q, r$ be positive integers with $p, q, r \\ge 2$. Denote\n\\[Q=\\{(x, y, z)\\in \\(...TRUNCATED) | "\nLet \\(a, b, c, p, q, r\\) be positive integers with \\(p, q, r \\ge 2\\). Denote\n\\[ Q = \\{(x,(...TRUNCATED) | p^a q^b r^c | china_team_selection_test | google/gemma-3-12b-it | omni_math | {"reward_mean":0.0062402496099844,"rewards":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | {"completions":["Let $a, b, c, p, q, r$ be positive integers with $p, q, r \\ge 2$. Let $Q = \\{(x, (...TRUNCATED) |
["Mathematics -> Number Theory -> Prime Numbers","Mathematics -> Number Theory -> Factorization","Ma(...TRUNCATED) | 9 | "For a positive integer $n$, let $d(n)$ be the number of positive divisors of $n$, and let $\\varphi(...TRUNCATED) | "\nTo determine whether there exists a constant \\( C \\) such that \n\\[\n\\frac{\\varphi(d(n))}{d((...TRUNCATED) | $\text{ No }$ | imo_shortlist | google/gemma-3-12b-it | omni_math | {"reward_mean":0.0,"rewards":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) | {"completions":["Let $n$ be a positive integer. Let $d(n)$ be the number of positive divisors of $n$(...TRUNCATED) |
["Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Combination(...TRUNCATED) | 4.5 | "Let $a_{0}, a_{1}, a_{2}, \\ldots$ be an infinite sequence where each term is independently and uni(...TRUNCATED) | "Do casework on what $a_{0}$ is. If $a_{0}=1$ then $k=1$. If $a_{0}=4$ then $k=2$. If $a_{0}=3$ then(...TRUNCATED) | \frac{35}{16} | HMMT_2 | google/gemma-3-12b-it | omni_math | {"reward_mean":0.0,"rewards":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) | {"completions":["Let $a_0, a_1, a_2, \\ldots$ be an infinite sequence where each term is independent(...TRUNCATED) |
["Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Combination(...TRUNCATED) | 4 | "You are given a $10 \\times 2$ grid of unit squares. Two different squares are adjacent if they sha(...TRUNCATED) | "Since each row has only two squares, it is impossible for two marked squares to be in the same row.(...TRUNCATED) | 36 | HMMT_2 | google/gemma-3-12b-it | omni_math | {"reward_mean":0.0,"rewards":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) | {"completions":["Let the $10 \\times 2$ grid be represented by a $10 \\times 2$ matrix. We want to c(...TRUNCATED) |
[
"Mathematics -> Algebra -> Algebra -> Equations and Inequalities"
] | 5.5 | "Determine all real numbers $a$ such that the inequality $|x^{2}+2 a x+3 a| \\leq 2$ has exactly one(...TRUNCATED) | "Let $f(x)=x^{2}+2 a x+3 a$. Note that $f(-3 / 2)=9 / 4$, so the graph of $f$ is a parabola that goe(...TRUNCATED) | 1,2 | HMMT_2 | google/gemma-3-12b-it | omni_math | {"reward_mean":0.9251170046801872,"rewards":[0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0(...TRUNCATED) | {"completions":["Let $f(x) = x^2 + 2ax + 3a$. We want to find all real numbers $a$ such that the ine(...TRUNCATED) |
["Mathematics -> Number Theory -> Factorization","Mathematics -> Algebra -> Equations and Inequaliti(...TRUNCATED) | 4 | "How many pairs of integers $(a, b)$, with $1 \\leq a \\leq b \\leq 60$, have the property that $b$ (...TRUNCATED) | "The divisibility condition is equivalent to $b-a$ being divisible by both $a$ and $a+1$, or, equiva(...TRUNCATED) | 106 | HMMT_2 | google/gemma-3-12b-it | omni_math | {"reward_mean":0.0483619344773791,"rewards":[0.0,0.0,0.0,0.0,0.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | {"completions":["Let $a$ and $b$ be integers such that $1 \\leq a \\leq b \\leq 60$. We are given th(...TRUNCATED) |
[
"Mathematics -> Discrete Mathematics -> Algorithms"
] | 9 | "Each of the six boxes $B_1$, $B_2$, $B_3$, $B_4$, $B_5$, $B_6$ initially contains one coin. The fol(...TRUNCATED) | "\nTo solve this problem, we need to analyze the types of operations and their effects on the coin d(...TRUNCATED) | $\text{No}$ | imo | google/gemma-3-12b-it | omni_math | {"reward_mean":0.9344773790951638,"rewards":[1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | {"completions":["Let $c_i$ be the number of coins in box $B_i$ for $i=1, \\dots, 6$. Initially, $c_i(...TRUNCATED) |
[
"Mathematics -> Algebra -> Intermediate Algebra -> Other"
] | 3.5 | "When a single number is added to each member of the sequence 20, 50, 100, the sequence becomes expr(...TRUNCATED) | $\frac{5}{3}$. | \frac{5}{3} | HMMT_2 | google/gemma-3-12b-it | omni_math | {"reward_mean":0.9984399375975039,"rewards":[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | {"completions":["Let the single number added to each member of the sequence 20, 50, 100 be $k$. Then(...TRUNCATED) |
End of preview. Expand in Data Studio
wtd/completions-omni_math-gemma-3-12b-it
Per-question data collected with google/gemma-3-12b-it on the omni_math dataset.
Generation schedule
| Temperature | # completions |
|---|---|
| 0.0 | 1 |
| 0.2 | 128 |
| 0.4 | 128 |
| 0.6 | 128 |
| 0.8 | 128 |
| 1.0 | 128 |
Reward mean histogram
| Bin | Count |
|---|---|
| 0.0–0.1 | ████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████ (120) |
| 0.1–0.2 | ███████████ (11) |
| 0.2–0.3 | ███ (3) |
| 0.3–0.4 | ████████████ (12) |
| 0.4–0.5 | █████ (5) |
| 0.5–0.6 | █████████ (9) |
| 0.6–0.7 | █████ (5) |
| 0.7–0.8 | ███████ (7) |
| 0.8–0.9 | ███████████ (11) |
| 0.9–1.0 | ████████████████████████████████████ (36) |
| 1.0–1.1 | █████████████████████████████████████ (37) |
Schema
reward(dict): {"scorer": str, "rewards": list[float], "reward_mean": float}.generations(dict): {"model_id": str, "completions": list[str], "temperatures": list[float]}.model_id(str): model used for generation.dataset_name(str): source dataset (omni_math,chemistry, orreward_bench).- All original question fields from the source dataset are preserved.
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