Datasets:

Seungjun
/

clean-math-sft-pool-30k

id stringlengths 64 64	problem stringlengths 16 2.74k	gold_answer stringlengths 1 208	dataset_source stringclasses 3 values	sub_source stringclasses 21 values	domain stringclasses 9 values	math_level int64	synthetic bool 0 classes	answer_type stringclasses 8 values	gold_answer_original stringlengths 1 208	quality_action stringclasses 2 values	responses list	extracted_answers list	correct list	response_tokens list	finish_reasons list	num_correct int64 0 8	7B_responses listlengths 8 8 ⌀	7B_extracted_answers listlengths 8 8 ⌀	7B_correct listlengths 8 8 ⌀	7B_response_tokens listlengths 8 8 ⌀	7B_finish_reasons listlengths 8 8 ⌀	7B_num_correct int64 0 8 ⌀
9c2c2583b4e1157af57945c31370eb6a7f32d44a27be107f9e996a372ba14e80	How many positive common divisors do $10^{100}$ and $10^{121}+10^{813}+10$ have?	4	numina	olympiads	Number Theory	null	null	integer	4	unchanged	[ "First, let's find the prime factorizations and expressions for the two numbers.\n\n* $10^{100} = (2^1 \\cdot 5^1)^{10} = 2^{10} \\cdot 5^{10}$\n* $10^{121} = 10 \\cdot 10^{120} = 10 \\cdot (2^1 \\cdot 5^1)^{11} = 2^{11} \\cdot 5^{11}$\n* $10 = 2^1 \\cdot 5^1$\n\nNow, let's find the greatest common divisor (GCD) of...	[ "1440", "4", "1", "4", "10201", "2", "", "101 \\times 101" ]	[ false, true, false, true, false, false, false, false ]	[ 589, 401, 483, 563, 855, 716, 55, 960 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	2	[ "To determine how many positive common divisors \$10^{100}\$ and \$10^{121} + 10^{813} + 10\$ have, we start by analyzing their prime factorizations.\n\nFirst, consider the expression \$10^{100}\$:\n\\[\n10^{100} = (2 \\cdot 5)^{100} = 2^{100} \\cdot 5^{100}\n\\]\n\nNext, we analyze \\(10^{121} + 10^{813} + 1...	[ "", "", "10^{121} + 10^{813} + 10 = 2 \\cdot 5 \\cdot (10^{120} + 10^{812} + 1)", "", "", "", "2^{100} \\cdot 5^{100}", "" ]	[ false, false, false, false, false, false, false, false ]	[ 3072, 3072, 3072, 3072, 3072, 3072, 3072, 3072 ]	[ "length", "length", "length", "length", "length", "length", "length", "length" ]	0
35cb06088304e3a6d6bdfaf3f9a0f9718ad25666fa57d8eeffa8b45bdf272658	"Two identical circles of radius \$r\$ are externally tangent to each other and internally tangent(...TRUNCATED)	2	numina	synthetic_math	Geometry	null	null	integer	2	unchanged	["Solution: The given ellipse equation \$9x^2 + 4y^2 = 36\$ can be rewriten as \\(\\frac{x^2}{4} +(...TRUNCATED)	[ "1", "\\frac{2}{5}", "\\frac{3\\sqrt{2}}{2}", "\\frac{3}{5}", "5", "\\frac{\\sqrt{5}}{2}", "3", "1" ]	[ false, false, false, false, false, false, false, false ]	[ 555, 538, 2829, 691, 31, 581, 1098, 500 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	0	["Given two identical circles of radius \$ r \$ that are externally tangent to each other and inte(...TRUNCATED)	[ "", "", "", "1", "", "2x_1 = 2r \\implies x_1 = r", "", "1" ]	[ false, false, false, false, false, false, false, false ]	[ 3072, 3072, 3072, 279, 3072, 3072, 3072, 354 ]	[ "length", "length", "length", "stop", "length", "length", "length", "stop" ]	0
ea6682d5027c56c9bd1c19a6672625bb287d340ade0d11d2138c7a257511787c	"A set contains 96 distinct blocks. Each block is one of 2 materials (plastic, wood), 3 sizes (small(...TRUNCATED)	26	numina	synthetic_math	Combinatorics	null	null	integer	26	unchanged	["Let's count the total number of blocks first:\n\nFor material:\n- Plastic (1 option)\n\nFor size:\(...TRUNCATED)	[ "1046", "", "14", "0", "120", "36", "24", "4" ]	[ false, false, false, false, false, false, false, false ]	[ 630, 451, 471, 192, 459, 422, 374, 463 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	0	["To determine how many blocks in the set differ from the 'plastic medium red circle' in exactly 3 w(...TRUNCATED)	[ "10", "33", "", "", "50", "50", "50", "10" ]	[ false, false, false, false, false, false, false, false ]	[ 385, 501, 3072, 3072, 723, 536, 674, 459 ]	[ "stop", "stop", "length", "length", "stop", "stop", "stop", "stop" ]	0
1b9bb4f1d0ad5d5e830fba8619d1d04c32809a4a08fc695ef1eb2fc7f08b4033	"Consider the set of all points $(x,y)$ in the coordinate plane where one coordinate is exactly thre(...TRUNCATED)	4	numina	synthetic_math	Geometry	null	null	integer	4	unchanged	["('~' indicates a newline)\n\nFirst, let's find the specific equations we are dealing with:\n\n1. $(...TRUNCATED)	[ "", "4", "4", "2", "4", "4", "4", "" ]	[ false, true, true, false, true, true, true, false ]	[ 191, 367, 468, 257, 281, 353, 258, 98 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	5	null	null	null	null	null	null
896d806706a3763b4e12e11a64648d5da67f3c50c07636ebe327074932cfa9e7	"Each pair $(x, y)$ of nonnegative integers is assigned number $f(x, y)$ according the conditions:\n(...TRUNCATED)	2^n	numina	aops_forum	Logic and Puzzles	null	null	expression/text	2^n	unchanged	["We shall approach this problem step-by-step to determine the amount of nonnegative integers $x$ th(...TRUNCATED)	[ "0", "", "\\infty", "2", "", "m+n=f(a,a)=f(2a,a)=f(m,2m)=2n", "3", "n + 1" ]	[ false, false, false, false, false, false, false, false ]	[ 883, 906, 977, 733, 945, 215, 323, 618 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	0	["We start by analyzing the properties of the function \$ f(x, y) \$. The function is defined recu(...TRUNCATED)	[ "", "", "", "", "", "", "", "" ]	[ false, false, false, false, false, false, false, false ]	[ 3072, 3072, 3072, 3072, 3072, 3072, 3072, 3072 ]	[ "length", "length", "length", "length", "length", "length", "length", "length" ]	0
c4950d372d1d11716b1f0aecd4543766e12ecf2b1dcdba51448e7d119b5720f7	Rewrite $\sqrt[3]{2^9 \cdot 3^3 \cdot 7^3}$ as an integer.	168	numina	synthetic_math	Number Theory	null	null	integer	168	unchanged	["To rewrite $\\sqrt[3]{2^9 \\cdot 3^3 \\cdot 7^3}$ as an integer, we can simplify the expression st(...TRUNCATED)	[ "168", "168", "168", "", "168", "168", "", "" ]	[ true, true, true, false, true, true, false, false ]	[ 415, 177, 191, 301, 335, 222, 271, 153 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	5	null	null	null	null	null	null
585a355b68cb78c179bca7de267c8710bc06052ae647bb2d09ea97955c295b99	"In a trapezoid, the midline is equal to 7, the height is equal to $\\frac{15 \\sqrt{3}}{7}$, and th(...TRUNCATED)	610	numina	olympiads	Geometry	null	null	integer	610	unchanged	["Let's call the shorter base of the trapezoid $a$, the longer base $b$, and the height $h = \\frac{(...TRUNCATED)	[ "", "63", "0", "12", "13.53", "", "", "" ]	[ false, false, false, false, false, false, false, false ]	[ 756, 496, 651, 499, 941, 743, 441, 751 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	0	["Given a trapezoid with a midline equal to 7, a height equal to \$\\frac{15 \\sqrt{3}}{7}\$, and (...TRUNCATED)	["","","m = \\frac{a + b}{2} = 7 \\implies a + b = 14","","","b = a + 2x \\implies 14 = a + 2x \\imp(...TRUNCATED)	[ false, false, false, false, false, false, false, false ]	[ 3072, 3072, 3072, 3072, 3072, 3072, 3072, 3072 ]	[ "length", "length", "length", "length", "length", "length", "length", "length" ]	0
b0a4205b611b027c9ed384377b4e10be077d3e8455d65347b917c87cebefbacb	"## Task 2 - 250522\n\nFrom the Mathcity train station, a bus departs at every full quarter hour and(...TRUNCATED)	16	numina	olympiads	Logic and Puzzles	null	null	integer	16	unchanged	["Great question! Here’s how you can tackle this problem step by step:\n\n### Step 1: Determine Pi(...TRUNCATED)	[ "2", "", "", "", "", "4", "", "12" ]	[ false, false, false, false, false, false, false, false ]	[ 416, 54, 908, 1706, 451, 786, 61, 586 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	0	["To determine how many oncoming bus drivers bus driver Franz >>\n\n inhal-the operativeskoń等方(...TRUNCATED)	[ "", "", "", "", "", "", "", "" ]	[ false, false, false, false, false, false, false, false ]	[ 3072, 3072, 3072, 3072, 3072, 3072, 3072, 3072 ]	[ "length", "length", "length", "length", "length", "length", "length", "length" ]	0
1e6821c7c8737c52c7d0f8548f6052e061bccaad090ab99c33265f0596251367	A3. What is the largest integer for which each pair of consecutive digits is a square?	81649	numina	olympiads	Number Theory	null	null	integer	81649	unchanged	["To solve this problem, we need to consider the possible digits squares that can be consecutive in (...TRUNCATED)	[ "88893560241", "91", "", "649114", "", "81490", "", "9" ]	[ false, false, false, false, false, false, false, false ]	[ 455, 280, 26, 449, 718, 403, 425, 145 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	0	["To determine the largest integer for which each pair of consecutive digits is a square, we need to(...TRUNCATED)	[ "", "64", "", "", "", "", "", "81649" ]	[ false, false, false, false, false, false, false, true ]	[ 3072, 3072, 3072, 3072, 3072, 3072, 3072, 288 ]	[ "length", "length", "length", "length", "length", "length", "length", "stop" ]	1
148d95702d330a8d0246ac6148f9fb265a0b0aecf122ed17392ddf68d9d6ee26	How many integers $m$ satisfy the inequality $-5\pi \le m \le 12\pi$?	53	numina	synthetic_math	Inequalities	null	null	integer	53	unchanged	["Find the range of values of $m$ that meet the inequality by subtracting the lower bound from the u(...TRUNCATED)	[ "14", "89", "51-23+1=29", "53", "", "54", "52", "" ]	[ false, false, false, true, false, false, false, false ]	[ 205, 288, 180, 501, 295, 265, 263, 423 ]	[ "stop", "stop", "stop", "stop", "stop", "stop", "stop", "stop" ]	1	["To determine how many integers \$ m \$ satisfy the inequality \$-5\\pi \\le m \\le 12\\pi\$, w(...TRUNCATED)	[ "53", "", "53", "53", "53", "53", "53", "53" ]	[ true, false, true, true, true, true, true, true ]	[ 382, 3072, 336, 385, 294, 386, 330, 378 ]	[ "stop", "length", "stop", "stop", "stop", "stop", "stop", "stop" ]	7

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Text-only cleanup: b7702a05c3bb-89c664a431b5

The default train split now contains 27,211 rows after removing 1,694 rows matching translation instructions, Han characters, or explicit visual-reference/image-markup rules. Category counts overlap.

Source commit: b7702a05c3bbb2d2c59fcc77e87cc630f40b605e. Retained columns and gold answers are unchanged. This is text screening, not mathematical validation of references. Rules, exclusions, and summary: cleaning/text-only/b7702a05c3bb-89c664a431b5. Previous dataset-card content is retained below for provenance; its older counts may describe the source rather than the current default split.

Eight Qwen2.5-3B base responses

Eligible original rows are preserved after audited quality screening. Confirmed gold corrections retain the prior answer in gold_answer_original; quality_action identifies changed answers. Quarantined rows and all corrections are in quality_decisions.jsonl. Added generation columns: responses, extracted_answers, correct, response_tokens, finish_reasons (eight values each), and num_correct (0–8). Final boxed answers take priority; explicit unboxed conclusions and unambiguous final math lines are also supported. Extraction never searches for the reference value in the reasoning. Math-Verify grades the extracted answer; truncated responses are still graded but marked length. Token counts are generation token IDs, excluding the prompt. No SFT or RL checkpoint is used. See annotated/provenance.json and summary.json. The dataset retains its upstream terms; source metadata is recorded in provenance.

Eight Qwen2.5-Math-7B-Instruct responses on the 3B 0/1/2 subset

All original rows and 3B columns are retained unchanged. Only rows whose original num_correct is 0, 1, or 2 receive eight new samples. Added columns: 7B_responses, 7B_extracted_answers, 7B_correct, 7B_response_tokens, 7B_finish_reasons, 7B_num_correct. The six new columns are null on unselected rows; null means not evaluated, not incorrect. Math-Verify grades the extracted final answer using the previous grading policy, including the other-answer notation handling. Native instruct chat template and EOS are used. Native context is 4096 tokens; per-answer limits and truncation are recorded. See annotated-7b/3014d5c12fd58055/provenance.json, summary.json, and grading_audit.jsonl.

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