uuid large_stringclasses 1
value | expected_answer large_stringlengths 1 492 | problem large_stringlengths 34 1.25k | original_expected_answer large_stringlengths 1 492 | changed_answer_to_majority bool 1
class | data_source large_stringclasses 2
values | messages listlengths 2 2 | used_in listlengths 1 1 | metadata dict | license large_stringclasses 2
values | tools listlengths 0 0 | url large_stringlengths 3 129 ⌀ | user_name large_stringlengths 3 25 ⌀ | user_url large_stringlengths 3 68 ⌀ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\( a_1 = a > 0 \) and \( a_{2n} = \sqrt{|c_{2n}| + |c_{2n+1}| + \frac{1}{n}} \) for \( n \geq 1 \). | Let $\{c_n\}$ be a sequence of real numbers with $\lim_{n\to\infty} c_n = 0$. Define $c_n = a_nb_n$ such that $a_n \geqslant 0$, $\lim_{n\to\infty} a_n = \lim_{n\to\infty} b_n = 0$, and $a^2_{2n+1} = a_{2n}^2 + \frac{1}{n}$ for all $n \in \mathbb{N}$. Determine how to define $a_1$ and $a_{2n}$ for every $n \geq 1$ to e... | \( a_1 = a > 0 \) and \( a_{2n} = \sqrt{|c_{2n}| + |c_{2n+1}| + \frac{1}{n}} \) for \( n \geq 1 \). | false | aops | [
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet $\\{c_n\\}$ be a sequence of real numbers with $\\lim_{n\\to\\infty} c_n = 0$. Define $c_n = a_nb_n$ such that $a_n \\geqslant 0$, $\\lim_{n\\to\\infty} a_n = \\lim_{n\\to\\infty} b_n = 0$, and... | [
"nano_v3"
] | {
"reason_high_no_tool": {
"accuracy": 0.125,
"count": 8,
"pass": 1
},
"reason_high_with_tool": {
"accuracy": 0,
"count": 8,
"pass": 0
},
"reason_low_no_tool": {
"accuracy": 0,
"count": 8,
"pass": 0
},
"reason_low_with_tool": {
"accuracy": 0.125,
"count": 8,
... | cc-by-4.0 | [] | null | null | null | |
$(a+b+c)(ab+bc+ac)$ | Factor the given expressions: $a^2b+ab^2+a^2c+b^2c+bc^2+3abc$. | $(a+b+c)(ab+bc+ac)$ | false | aops | [
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFactor the given expressions: $a^2b+ab^2+a^2c+b^2c+bc^2+3abc$.",
"name": "",
"reasoning_content": "",
"role": "user",
"tool_call_id": "",
"tool_calls": []
},
{
"content"... | [
"nano_v3"
] | {
"reason_high_no_tool": {
"accuracy": 0.125,
"count": 8,
"pass": 1
},
"reason_high_with_tool": {
"accuracy": 0,
"count": 8,
"pass": 0
},
"reason_low_no_tool": {
"accuracy": 0.125,
"count": 8,
"pass": 1
},
"reason_low_with_tool": {
"accuracy": 0,
"count": 8,
... | cc-by-4.0 | [] | null | null | null | |
\( q^{kn} \cdot \prod_{i=1}^{n} \left(1 - q^{-(k+1-i)}\right) \) | How many ordered sequences of $k$ vectors in $\mathbb{F}_q^n$ span the space? ($\mathbb{F}_q$ denotes a finite field with $q$ elements.) | \( q^{kn} \cdot \prod_{i=1}^{n} \left(1 - q^{-(k+1-i)}\right) \) | false | aops | [
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nHow many ordered sequences of $k$ vectors in $\\mathbb{F}_q^n$ span the space? ($\\mathbb{F}_q$ denotes a finite field with $q$ elements.)",
"name": "",
"reasoning_content": "",
"role":... | [
"nano_v3"
] | {
"reason_high_no_tool": {
"accuracy": 0.125,
"count": 8,
"pass": 1
},
"reason_high_with_tool": {
"accuracy": 0,
"count": 8,
"pass": 0
},
"reason_low_no_tool": {
"accuracy": 0,
"count": 8,
"pass": 0
},
"reason_low_with_tool": {
"accuracy": 0,
"count": 8,
"pa... | cc-by-4.0 | [] | null | null | null | |
\((a, b) = (a, a^2 + k)\) where \( k \) is a positive divisor of \( a^3 \). | Find all positive integers $(a, b)$ such that $a^2 - b \mid ab$. | \((a, b) = (a, a^2 + k)\) where \( k \) is a positive divisor of \( a^3 \). | false | aops | [
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all positive integers $(a, b)$ such that $a^2 - b \\mid ab$.",
"name": "",
"reasoning_content": "",
"role": "user",
"tool_call_id": "",
"tool_calls": []
},
{
"conte... | [
"nano_v3"
] | {
"reason_high_no_tool": {
"accuracy": 0.125,
"count": 8,
"pass": 1
},
"reason_high_with_tool": {
"accuracy": 0,
"count": 8,
"pass": 0
},
"reason_low_no_tool": {
"accuracy": 0,
"count": 8,
"pass": 0
},
"reason_low_with_tool": {
"accuracy": 0,
"count": 8,
"pa... | cc-by-4.0 | [] | null | null | null | |
6016 | "You have a stack of coins numbered from 1 to 2006, with coin 1 at the bottom and coin 2006 at the t(...TRUNCATED) | 6016 | false | aops | [{"content":"Solve the following math problem. Make sure to put the answer (and only answer) inside (...TRUNCATED) | [
"nano_v3"
] | {"reason_high_no_tool":{"accuracy":0.25,"count":8,"pass":2},"reason_high_with_tool":{"accuracy":0.0,(...TRUNCATED) | cc-by-4.0 | [] | null | null | null | |
\((x - t)^2 + \left(y - \frac{3t}{2}\right)^2 = t^2 + \left(\frac{3t}{2} - 13\right)^2\) | "Given points \\( A = (0, 13) \\) and \\( B = (12, 5) \\) that lie on a circle centered at the origi(...TRUNCATED) | \((x - t)^2 + \left(y - \frac{3t}{2}\right)^2 = t^2 + \left(\frac{3t}{2} - 13\right)^2\) | false | aops | [{"content":"Solve the following math problem. Make sure to put the answer (and only answer) inside (...TRUNCATED) | [
"nano_v3"
] | {"reason_high_no_tool":{"accuracy":0.125,"count":8,"pass":1},"reason_high_with_tool":{"accuracy":0.0(...TRUNCATED) | cc-by-4.0 | [] | null | null | null | |
6 | What is the minimum number of coordinates needed to uniquely locate a regular hexagon? | 6 | false | aops | [{"content":"Solve the following math problem. Make sure to put the answer (and only answer) inside (...TRUNCATED) | [
"nano_v3"
] | {"reason_high_no_tool":{"accuracy":0.125,"count":8,"pass":1},"reason_high_with_tool":{"accuracy":0.0(...TRUNCATED) | cc-by-4.0 | [] | null | null | null | |
10 | "An ordinary deck of 52 cards with 4 aces is shuffled, and cards are drawn one by one until the firs(...TRUNCATED) | 10 | false | aops | [{"content":"Solve the following math problem. Make sure to put the answer (and only answer) inside (...TRUNCATED) | [
"nano_v3"
] | {"reason_high_no_tool":{"accuracy":0.125,"count":8,"pass":1},"reason_high_with_tool":{"accuracy":0.0(...TRUNCATED) | cc-by-4.0 | [] | null | null | null | |
"\\(\\frac{\\pi^2}{2} - \\pi \\arctan \\left[ \\frac{\\dfrac{1}{\\sqrt[4]{5}} + \\sqrt{2} \\sin \\le(...TRUNCATED) | Evaluate the integral $$\int_0^{\pi} \arctan \left( 1 + 2 \cos^2 x \right) \text{d}x.$$ | "\\(\\frac{\\pi^2}{2} - \\pi \\arctan \\left[ \\frac{\\dfrac{1}{\\sqrt[4]{5}} + \\sqrt{2} \\sin \\le(...TRUNCATED) | false | aops | [{"content":"Solve the following math problem. Make sure to put the answer (and only answer) inside (...TRUNCATED) | [
"nano_v3"
] | {"reason_high_no_tool":{"accuracy":0.125,"count":8,"pass":1},"reason_high_with_tool":{"accuracy":0.0(...TRUNCATED) | cc-by-4.0 | [] | null | null | null | |
"\\(\\lambda_k = \\frac{5}{3} + \\frac{68}{3} \\cos\\left(\\frac{1}{3} \\arccos \\frac{17\\sqrt{34}}(...TRUNCATED) | "Find the eigenvalues of the matrix $\\begin{bmatrix} 1 & 3 & 1 \\\\ 3 & 2 & 1 \\\\ 1 & 1 & 2 \\end{(...TRUNCATED) | "\\(\\lambda_k = \\frac{5}{3} + \\frac{68}{3} \\cos\\left(\\frac{1}{3} \\arccos \\frac{17\\sqrt{34}}(...TRUNCATED) | false | aops | [{"content":"Solve the following math problem. Make sure to put the answer (and only answer) inside (...TRUNCATED) | [
"nano_v3"
] | {"reason_high_no_tool":{"accuracy":0.25,"count":8,"pass":2},"reason_high_with_tool":{"accuracy":0.0,(...TRUNCATED) | cc-by-4.0 | [] | null | null | null |
End of preview. Expand in Data Studio
Nemotron-Math-v2 Truly Hard No-Tool Subset
Problems where ALL 6 reasoning regimes score <= 3/8 (37.5%). These are the hardest problems in Nemotron-Math-v2.
Splits
| Split | Accuracy | Before (dedup) | After (truly hard) |
|---|---|---|---|
| pass0of8 | 0/8 | 6,944 | 3,217 |
| pass1of8 | 1/8 | 3,637 | 1,321 |
| pass2of8 | 2/8 | 4,719 | 733 |
| pass3of8 | 3/8 | 8,363 | 1,444 |
| Total | 23,663 | 6,715 |
Filter
All 6 regimes must have accuracy <= 0.375:
- reason_high_with_tool / reason_high_no_tool
- reason_medium_with_tool / reason_medium_no_tool
- reason_low_with_tool / reason_low_no_tool
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