Datasets:

hudsongouge
/

AoPS-Scrape

problem_id int64	class_id int64	lesson_id int64	aops_problem_id int64	problem_type string	problem_text string	answer string	answer_type string	alt_answers string	solution_text string	formatting_tips string	available_hints int64	can_hint int64	problem_has_solution int64	scraped_at string	scrape_date string	content_hash string	placement_count int64	alternate_placements string
16,887	395	4	null	short	If $x \diamond y = \frac{\sqrt{xy}}{\|x-y\|}$, find $4 \diamond (9 \diamond 1)$ to the nearest tenth. [i](You may use a calculator for this problem.)[/i]	null	standard	null	First note that \[9\diamond 1 = \frac{\sqrt{9}}{\lvert 9-1\rvert} = \frac{3}{8}. \] Then \[4\diamond \frac{3}{8} = \frac{\sqrt{\frac{12}{8}}}{\lvert 4-\frac{3}{8}\rvert}=\frac{\sqrt{\frac 32}}{\frac{29}8}= 0.337\ldots \approx \boxed{0.3}\]	null	0	0	1	2024-11-19 18:23:17	2024-11-19	null	null	null
35,313	527	14	null	free	For this problem, define a [b]nonstandard die[/b] as a $6$-sided die that is equally likely to come up on each side, but has a different set of numbers than the usual $1,2,3,4,5,6$ on its sides. A standard die will be the usual fair die bearing the numbers $1,2,3,4,5,6$. Is it possible to design a pair of nonstandard ...	null	standard	null	The generating function representing all possible rolls of two standard dice (in such a way that the coefficient of $x^n$ is the number of rolls that add up to $n$) is \begin{align} (x+x^2+x^3+x^4+x^5+x^6)^2 &= x^2(1+x+x^2+x^3+x^4+x^5)^2 \\ &= x^2(1+x+x^2)^2(1+x^3)^2 \\ &= x^2(1+x+x^2)^2(1+x)^2(1-x+x^2)^2. \end{align...	null	2	1	1	2024-11-19 19:51:15	2024-11-19	null	null	null
38,958	561	2	null	free	The integers $1,2,3,4,5,6,7,8,9$ are placed in a list so that each value is either bigger than all the numbers that precede it or is smaller than all the numbers that precede it. For example, $4,5,6,3,2,7,1,8,9$ is one such list (compare each member of the list to the numbers before it---the number is either bigger th...	null	standard	null	(a) The last number must be either 1 or 9 because these are the only two numbers which are either smaller than or bigger than all of the other numbers in the list. (b) Suppose the 1 is last. The number immediately preceding it could be 9, since that 9 would be larger than all the numbers before it. The preceding ...	null	1	1	1	2024-11-19 20:08:13	2024-11-19	null	null	null
38,959	561	2	null	free	How many different [i]non-congruent[/i] isosceles triangles can be formed by connecting three of the dots in a 3x3 square array of dots as (roughly like the one shown below): [asy] size(50); dot((0,0));dot((0,1));dot((0,2)); dot((1,0));dot((1,1));dot((1,2)); dot((2,0));dot((2,1));dot((2,2)); [/asy] How about for a 4x...	null	standard	null	3x3 array: We can construct only segments of length $1$, $2$, $\sqrt 2$, $2\sqrt 2$ and $\sqrt 5$ (by taking the upper middle dot to the lower corner). We cannot construct any isosceles triangles with base length $1$ or $\sqrt 5$. By inspection, we can construct two isosceles triangles with base length $2$, two with...	null	0	0	1	2024-11-19 20:08:13	2024-11-19	null	null	null
38,937	562	1	null	free	Professor Munchausen has announced a great mathematical discovery, claiming that each term in the infinite arithmetic sequence \[199, \ 409, \ 619, \ 829, \ \dots\] is a prime number. (The first term is 199 and the common difference is 210.) Is he telling the truth?	null	standard	null	The $n^{\text{th}}$ term of the sequence is given by $199 + 210(n - 1)$. But if $n = 200$, then $199 + 210 \cdot 199 = 199 \cdot 211$, which is composite. Therefore, Professor Munchausen is lying, as usual.	null	0	0	1	2024-11-19 20:08:11	2024-11-19	null	null	null
38,938	562	1	null	free	A professor has 90 students in a class. He arranges them in $n$ rows with an equal number of students in each row. If there are at least 3 rows of students and each row contains at least 3 students, what are the possible values of $n$?	null	standard	null	Since each row has an equal number of students, 90 is a multiple of $n$, or $n\|90$. Since there are at least 3 rows and at least 3 students per row, $n$ can be any multiple between 3 and $\frac{90}{3} = 30$. These factors are 3, 5, 6, 9, 10, 15, 18, and 30.	null	0	0	1	2024-11-19 20:08:11	2024-11-19	null	null	null
38,939	562	1	null	free	The positive integers are listed in six columns, and all the primes are shown in red: \[ \begin{array}{cccccc} 1 & \textcolor{red}{2} & \textcolor{red}{3} & 4 & \textcolor{red}{5} & 6 \\ \textcolor{red}{7} & 8 & 9 & 10 & \textcolor{red}{11} & 12 \\ \textcolor{red}{13} & 14 & 15 & 16 & \textcolor{red}{17} & 18 \\ \textc...	null	standard	null	All the numbers in the second, fourth, and sixth column are even, so the only prime that can appear in any of these columns must be 2. All the numbers in the third and sixth columns are divisible by 3, so the only prime that can appear in any of these columns must be 3. Therefore, all remaining primes must appear in ...	null	0	0	1	2024-11-19 20:08:11	2024-11-19	null	null	null
38,940	565	1	null	free	In 2-Pile Nim, there are 2 piles of chips. On each turn, you can take any number of chips from one pile (and yes, you can remove all the chips in a pile at once). The goal, as before, is to take the last chip. Change the Nim program from Week 1 so it plays this game instead. You should prompt for the number of chips in...	null	standard	null	The posted version plays the generalized game where the players can select the number of piles. The players can also choose different numbers of chips for each pile. I felt that displaying all the piles at once would make the screen too cluttered. So the current player first chooses a pile from the listbox, and then h...	null	1	1	1	2024-11-19 20:08:13	2024-11-19	null	null	null
38,976	565	2	null	free	Add multiple players to the Boggle game from Week 2. Each person should get three minutes on the same grid of letters. Once all the players are done, compare their lists and eliminate any word that appears on multiple lists. Then add the scores. The highest total wins.	null	standard	null	My code hardcodes 2-player Boggle. You could change it by getting an input value for ${\tt self.\_\_numPlayers}$ in the ${\tt BoggleFrame}$ constructor. The game itself uses a dialog box to read the names of the players first. Then it gives the first player 3 minutes to click as many words as possible. Instead of a Ne...	null	0	0	1	2024-11-19 20:08:15	2024-11-19	null	null	null
39,012	565	3	null	free	In the game Memory, there are $2N$ face-down cards arranged in a rectangular grid. Each card has one of $N$ different symbols on it; each symbol appears exactly twice. The symbols are distributed at random in the grid. On each turn, the current player reveals two cards. If the cards match, the cards go to that player,...	null	standard	null	My game uses shell input to read the size of the board and the number and names of the players. I assume the board will be a square, so it asks for the number of columns, verifying that it is an even number. You could do this for an arbitrary number of pairs to match up, but you would then have to figure out the approp...	null	0	0	1	2024-11-19 20:08:18	2024-11-19	null	null	null
39,049	565	4	null	free	Add the sprite (whose image, $\texttt{smallDiamond.png}$, is posted as a "handout" on the Overview tab) to the complete Catch The Ball game at a random location. When the star touches the sprite, you should increase the star's speed from 1 to 50 for two seconds. After the diamond is touched, you should no longer displa...	null	standard	null	To solve this problem, I made a new class called ${\tt SpeedyDiamond}$ off of ${\tt BouncingBall}.$ The diamond can be visible or not depending on whether the star has recently touched it or not. Updating the diamond involves deciding whether we need to put it back on the screen. The ${\tt StarSprite}$ also needs to b...	null	0	0	1	2024-11-19 20:08:21	2024-11-19	null	null	null
39,083	565	5	null	free	Extend the Hangman game from Week 5 with the following: When the user hits Enter in the middle of a game, he or she enters solve mode. The player must fill in all remaining asterisks in order. So if the word was RTBG, he or she would enter U, then A, then A, then A to complete RUTABAGA. If the player makes any mist...	null	standard	null	Most of the changes here are to the ${\tt Word}$ class. I added methods to determine the next letter to guess while the user is ``solving'' the puzzle (so we can make sure they guess right), to reveal that letter when the user does guess right, and to reveal a random letter when the user employs a hint. In the main lo...	null	0	0	1	2024-11-19 20:08:24	2024-11-19	null	null	null
39,117	565	6	null	free	This problem is to make a simple version of the classic game Frogger. The player's avatar (which you can make a simple circle or an image) starts at the bottom of the screen and must make it to the top. Cars (again drawn as simply or as complicated as you like) cross the screen going from left to right or right to left...	null	standard	null	There are three classes in this solution. ${\tt Car}$ is an adaptation of the ${\tt Car}$ class from Week 6. It's not controlled by the user; it simply moves from left to right (or vice versa). The constructor creates the car, puts in the appropriate lane, and points it in the correct direction. ${\tt Update}$ simply m...	null	0	0	1	2024-11-19 20:08:27	2024-11-19	null	null	null
39,155	565	7	null	free	One of my favorite arcade games of all time is Arkanoid. It's a variation of Breakout where at random times when a brick is destroyed, a capsule appears in its place which starts falling to the bottom of the screen (passing over any bricks in its way). If the player can touch the capsule with the paddle, he or she gets...	null	standard	null	This program shows an implementation for two types of capsules. The "Elongate" or "Enlarge" capsule doubles the size of the paddle. The "Laser" capsule allows the user to shoot laser beams (called bullets) at the bricks by clicking the mouse. Hitting a brick with a bullet is the same as hitting it with a ball, except t...	null	0	0	1	2024-11-19 20:08:30	2024-11-19	null	null	null
39,194	565	8	null	free	The commercial version of Hedgehogs in a Hurry is more complex than the one from Week 8. First, the board is wider; it has nine columns, including the start and end. More importantly, one square in each row is a pit. Here is a screenshot with the pits represented by black squares: [img]http://aops-classroom.s3.amazona...	null	standard	null	Much of the code from the original version of Hedgehogs works fine here. We need to add a way to make the board larger and add the black pits. We also need to determine when a square is actually a pit---are there any hedgehogs in columns prior to the pit? If not, then we turn the square back to "normal". If it is a pit...	null	0	0	1	2024-11-19 20:08:33	2024-11-19	null	null	null
39,222	565	9	null	free	Use the ${\tt Card}$ class in Week 9 to create a solitaire card game of your choice. It can use a standard deck of playing cards, or you can make a customized deck with your own images. You can pick a game from ${\tt www.solitaire-rules.com}$, another solitaire website, a book of card games, or some other source. Feel ...	null	standard	null	I chose to implement the game Accordion. The player deals a row of cards; my implementation deals 4 cards to start, but you could choose any number. In one variation, you deal the entire deck. The goal is to condense the cards into one pile. You can move an entire pile (of any number of cards) on top of the pile either...	null	0	0	1	2024-11-19 20:08:36	2024-11-19	null	null	null
39,260	565	10	null	free	For the last group of Challenge Problems, your task is to create your own original computer game in Python using the techniques we've discussed during the course. This game can be of any genre you like and have any rules or difficulty level(s) you like subject to the following constraints: \begin{enumerate} \item Yo...	null	standard	null	Due to the nature of this assignment, we will not be posting a solution this week.	null	0	0	1	2024-11-19 20:08:39	2024-11-19	null	null	null
39,294	565	11	null	free	Turn in a prototype of the project you proposed in Week 10. Your program should have the basic functionality of the final version. In particular, all game play should be present. You don't need to have fancy graphics yet, or all the levels of the final version. We'd just like to see what progress you've made. Feel free...	null	standard	null	Due to the nature of this assignment, we will not be posting a solution this week.	null	0	0	1	2024-11-19 20:08:42	2024-11-19	null	null	null
39,322	565	12	null	free	Complete your prototype from Week 11. Your submitted game should be fully functional. Include as a comment at the beginning of your code complete instructions for playing the game - how to start a game, what the controls are, what the different parts of the display are, how to win the game, how to lose the game, etc. I...	null	standard	null	null	null	0	0	0	2024-11-19 20:08:45	2024-11-19	null	null	null
39,646	569	8	null	short	Altitudes $\overline{AP}$ and $\overline{BQ}$ of an acute triangle $\triangle ABC$ intersect at point $H$. [asy] size(150); defaultpen(linewidth(0.8)); pair B = (0,0), C = (3,0), A = (2,2), P = foot(A,B,C), Q = foot(B,A,C),H = intersectionpoint(B--Q,A--P); draw(A--B--C--cycle); draw(A--P^^B--Q); label("$A$",A,N); labe...	null	standard	null	Since $\angle HQA = \angle CPA$ and $\angle PAC = \angle CAP$, we have $\triangle HAQ \sim \triangle CAP$. Therefore, we have \[\frac{PA}{AQ} = \frac{AC}{AH}.\] So, we have \[PA = \frac{AC}{AH} \cdot AQ = \frac{15}{6} (15-11) = 10.\] Then $PH = PA - HA = 10 - 6 = 4$. Now, altitude $CR$ also passes through $H$. [asy...	null	1	0	1	2024-11-19 20:11:00	2024-11-19	null	null	null
39,959	569	22	null	short	The angles of a triangle form an arithmetic sequence, and the sides are equal to $x - 2$, $x$, and $x + 1$. Find $x$.	null	standard	null	Since the angles form an arithmetic sequence, the middle angle must be $180^\circ/3 = 60^\circ$. Then the side of length $x$ must be opposite the $60^\circ$ angle. The law of cosines gives us \[x^2 = (x-2)^2 + (x+1)^2 - 2(x-2)(x+1) \cos 60^\circ.\] Since $\cos 60^\circ = \frac12$, we have \[x^2 = (x-2)^2 + (x+1)^2 -...	null	0	0	1	2024-11-19 20:11:34	2024-11-19	null	null	null
39,961	569	22	null	short	In triangle $ABC$, $\cos B = \frac{3}{5}$ and $\cos C = \frac{12}{13}$. Find $\cos A$.	null	standard	null	First, we construct a right triangle where the cosine of one of the angles is equal to 3/5. We can do this with a 3-4-5 right triangle. [asy] unitsize(0.1 cm); pair A, B, C; A = (15,20); B = (0,0); C = (63,0); draw(A--B--(15,0)--cycle); label("$3$", (B + (15,0))/2, S); label("$4$", (A + (15,0))/2, E); label("$5$"...	null	2	0	1	2024-11-19 20:11:34	2024-11-19	null	null	null
39,963	569	22	null	free	If $A$ is an angle such that $\tan A + \sec A = 2$, then find all possible values of $\cos A$.	null	standard	null	[b]Solution 1[/b]: Since $\tan A = \sin A/\cos A$ and $\sec A = 1/\cos A$, we can re-write the given equation as \[\frac{\sin A}{\cos A} + \frac{1}{\cos A} = 2.\] Multiplying both sides by $\cos A$, we get $\sin A + 1 = 2 \cos A$, so $\sin A = 2 \cos A - 1$. Squaring both sides, we get \[\sin^2 A = 4 \cos^2 A - 4 \cos...	null	0	0	1	2024-11-19 20:11:34	2024-11-19	null	null	null

End of preview. Expand in Data Studio

AoPS-Scrape

Problems and solutions scraped from Art of Problem Solving (AoPS) Online class homework endpoints.

Obtained legally in accordance with AoPS's Terms of Service. This is not unauthorized redistribution of pirated material — access was through a legitimate authenticated AoPS Online class session.

Splits

Splits are named by scrape date (YYYY_MM_DD), plus a cross-date content-deduplicated split:

Split	Rows	Notes
`deduplicated`	29,964	One row per unique problem+solution across every date split (no class/lesson duplicates)
`2024_11_19`	1,117	Nov 2024 scrape (raw placements)
`2024_11_20`	9,336	Nov 2024 scrape (raw placements)
`2026_07_09`	6,336	Jul 2026 full scrape, content-deduplicated within scrape
`2026_07_10`	18,829	Jul 2026 full scrape, content-deduplicated within scrape
`2026_07_11`	3,920	Jul 2026 full scrape, content-deduplicated within scrape

Totals:

Date splits (as uploaded): 39,538 rows
deduplicated: 29,964 unique problems after collapsing cross-class and cross-date duplicates
2026 underlying scrape: 1,454,319 placements across class ids 1–10000 (6,811 classes with homework) before within-scrape dedup

Prefer deduplicated for a single training/eval set with no duplicate problem statements. Date splits remain available for scrape-dated analysis.

Canonical rows still include class_id / lesson_id for the chosen placement; duplicates across classes/lessons/dates are collapsed via content_hash.

Columns

Column	Type	Description
`problem_id`	int	Local / canonical id
`class_id`	int	AoPS class id (canonical placement)
`lesson_id`	int	Lesson number within class
`aops_problem_id`	int	AoPS problem id when available (2026+; null in 2024-only rows)
`problem_type`	string	e.g. `short`, `amc`, `aime`, `discussion`, `free`, …
`problem_text`	string	Problem statement (LaTeX / markup)
`answer`	string	Official answer when present
`answer_type`	string	Answer grading type
`alt_answers`	string	Alternate accepted answers
`solution_text`	string	Solution text (LaTeX / markup)
`formatting_tips`	string	JSON string of formatting tips
`available_hints`	int	Number of hints that exist for the problem
`can_hint`	int	Whether the account can request a hint
`problem_has_solution`	int	Whether a solution was present
`scraped_at`	string	Timestamp of scrape
`scrape_date`	string	`YYYY-MM-DD` derived from `scraped_at`
`content_hash`	string	SHA256 of problem+solution text
`placement_count`	int	How many class/lesson placements shared this content
`alternate_placements`	string	JSON list of other placements

Known limitations

These are intentional / structural gaps from the get_class_homework endpoint, not accidental omissions:

No hint text. The homework payload only exposes hint metadata (available_hints, can_hint). Actual hint content is behind a separate reveal/request flow and is not included.
Official answers are usually empty. Prefer solution_text over answer.
HTML / formatted variants not stored. Only plain problem_text / solution_text are saved (not problem_fmt / solution_fmt).
Extra metadata dropped. Fields such as header, collection_id, identifier, version, order, markup, and files are not persisted.
No attached media download. Image/file attachments are not downloaded.
Scope is class homework only. Transcripts, ebooks, wiki contest problems, and forum content are out of scope.
Access-dependent coverage. Only classes/lessons visible to the authenticated session are scraped.
Deduplication. 2026 date splits and deduplicated collapse identical problem+solution text. 2024 date splits remain raw placements; overlapping 2024/2026 content is collapsed only in deduplicated.

Source

Scraped via the AoPS Online class AJAX endpoint (/m/class/ajax.php, a=get_class_homework) using an authenticated platsessionid cookie. Scraper source: hg0428/aops-reverse-engineer.

Notes

Future scrapes should be added as new date-named splits rather than overwriting existing ones, then regenerate deduplicated.
2026 scrape covered class ids 1–10000 with dual authenticated workers; network-blip classes were re-probed before export.
The split name all is reserved by Hugging Face datasets, so the cross-date union is published as deduplicated.

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