id stringlengths 6 8 | alias stringlengths 24 50 | problem stringlengths 24 5.03k | answer int64 -16,384 80.2B | graph stringlengths 0 6.44k | domain stringclasses 4
values | secondary_domain stringclasses 4
values | goal stringclasses 4
values | evaluator_id stringclasses 1
value | root_lemma stringclasses 89
values | lemma_paths listlengths 0 5 | recipe_id stringlengths 0 6 | seed_template_id stringclasses 96
values | ending_id stringclasses 13
values | olympiad_level int64 2 9 | num_spawns int64 0 3 ⌀ | lemma_set listlengths 1 7 ⌀ | num_lemmas int64 1 7 ⌀ | generation_time float64 0 43.9 | created_at stringlengths 27 27 | verification dict | problem_hash stringlengths 6 6 | parent_id stringlengths 0 6 | variant stringclasses 3
values | license stringclasses 1
value | llm_solvers listlengths 1 13 ⌀ | solution_status int64 0 2 ⌀ | lemma_applicability listlengths 0 12 | irt_difficulty dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
4bd7be | comb_count_derangements_v1_865884756_3517 | Let $m = 13013$. Define $n$ to be the largest prime number $n_1$ such that $2 \leq n_1 \leq d$, where $d$ is the smallest divisor of $m$ that is at least 2. Compute the subfactorial of $n$, denoted $!n$. | 1,854 | graphs = [
Graph(
let={
"_m": Const(13013),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), d... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | comb_count_derangements_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T17:29:26.330683Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T17:29:26.333738Z"
} | 58877d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 897
},
"timestamp": "2026-02-18T02:43:22.201Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_lat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c41db | nt_min_phi_inverse_v1_784195855_2667 | Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1225$. Let $k = 16$. Define $\text{result}$ as the smallest positive integer $n$ such that $1 \le n \le s$ and $\phi(n) = k$, where $\phi$ is Euler's totient function. Let $Q$ be the remainder when $44121 \cdot \text{re... | 1,917 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1225)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(16)... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.013 | 2026-02-08T05:55:12.560295Z | {
"verified": true,
"answer": 1917,
"timestamp": "2026-02-08T05:55:12.573179Z"
} | d99264 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2194
},
"timestamp": "2026-02-12T16:57:33.715Z",
"answer": 1917
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
3537ec | nt_count_gcd_equals_v1_1520064083_5296 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq \sum_{d \mid 1230} \varphi(d)$ and $n$ is divisible by 123. Define $U$ to be the sum of all elements in $S$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq U$ and $\gcd(n, 103) = 1$. Compute the number of elements in $T$. | 6,700 | graphs = [
Graph(
let={
"_n": Const(123),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), SumOverDivisors(n=Const(value=1230), var='d', expr=EulerPhi(n=Var(name='d')))), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0))))),
... | NT | null | COUNT | sympy | K3 | [
"K3/SUM_DIVISIBLE"
] | df60a7 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"K3",
"SUM_DIVISIBLE"
] | 2 | 1.027 | 2026-02-08T06:43:36.299801Z | {
"verified": true,
"answer": 6700,
"timestamp": "2026-02-08T06:43:37.326908Z"
} | c603e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 841
},
"timestamp": "2026-02-13T04:06:50.774Z",
"answer": 6700
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
}... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
48dd33 | comb_count_permutations_fixed_v1_677425708_1708 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $k = 4$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Compute the remainder when $44121 \cdot r$ is divided by $63650$. | 63,524 | graphs = [
Graph(
let={
"_n": Const(63650),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T04:23:09.734280Z | {
"verified": true,
"answer": 63524,
"timestamp": "2026-02-08T04:23:09.736593Z"
} | 62acb5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 6282
},
"timestamp": "2026-02-09T23:48:08.970Z",
"answer": 63524
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
950bb1 | comb_count_permutations_fixed_v1_168721529_101 | Let $m = 19$. Define $n$ to be the number of positive integers $k$ such that $1 \leq k \leq m$ and $\gcd\left(k, \sum_{d \mid 14} \phi(d)\right) = 1$. Let $r = \binom{n}{6} \cdot !(n-6)$, where $!(n-6)$ denotes the number of derangements of $n-6$ elements. Let $Q = 44121 \cdot r$. Compute the remainder when $Q$ is divi... | 32,046 | graphs = [
Graph(
let={
"_m": Const(19),
"_n": Const(50206),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Eq(GCD(a=Var("n"), b=SumOverDivisors(n=Const(value=14), var='d', expr=EulerPhi(n=Var(name='d'))))... | NT | COMB | COUNT | sympy | K3 | [
"K3/C4"
] | c1614d | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"C4",
"K3"
] | 2 | 0.005 | 2026-02-08T12:48:33.728885Z | {
"verified": true,
"answer": 32046,
"timestamp": "2026-02-08T12:48:33.733553Z"
} | 1bf054 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 981
},
"timestamp": "2026-02-08T21:03:25.220Z",
"answer": 32046
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{... | {
"lo": -2.02,
"mid": 1.85,
"hi": 5.2
} | ||
838b90 | alg_poly3_sum_v1_601307018_610 | Let $M$ be the number of positive integers $n$ with $1 \le n \le 50400$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $S$ be the set of integers $v$ with $18 \le v \le M$ for which there exist integers $a, b$ such that $1 \le a, b \le 20$ and $13a^2 + 4ab + b^2 = v$. Let $T = |S|$. Compute t... | 60,456 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(50400)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C/QF_PSD_DISTINCT"
] | f49f5c | alg_poly3_sum_v1 | null | 7 | 0 | [
"L3C",
"QF_PSD_DISTINCT"
] | 2 | 0.276 | 2026-03-10T01:08:14.009326Z | {
"verified": true,
"answer": 60456,
"timestamp": "2026-03-10T01:08:14.285221Z"
} | 95aeae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 312,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T23:40:23.371Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
62e626 | nt_sum_gcd_range_mod_v1_1742523217_4610 | Let $N$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 142$. Let $k$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 57600$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $M = 10687$. Find the remainder when $\text{sum}$ is divi... | 10,053 | graphs = [
Graph(
let={
"_n": Const(142),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1",
"B3"
] | 655d51 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.236 | 2026-02-08T08:58:50.476789Z | {
"verified": true,
"answer": 10053,
"timestamp": "2026-02-08T08:58:50.712863Z"
} | 715120 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 3506
},
"timestamp": "2026-02-13T23:09:11.758Z",
"answer": 10053
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
925653 | nt_sum_gcd_range_mod_v1_1248542787_360 | Let $N$ be the sum of $\phi(d)$ over all positive divisors $d$ of $7744$, where $\phi$ denotes Euler's totient function. Let $k = 108$ and let
\[
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
\]
Define $M = 10177$ and let $\text{result} = \text{sum} \bmod M$. Finally, let $Q = 11111 - \text{result}$.
Compute the value of $Q... | 5,411 | graphs = [
Graph(
let={
"N": SumOverDivisors(n=Const(value=7744), var='d', expr=EulerPhi(n=Var(name='d'))),
"k": Const(108),
"M": Const(10177),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.344 | 2026-02-08T03:05:00.899883Z | {
"verified": true,
"answer": 5411,
"timestamp": "2026-02-08T03:05:01.243607Z"
} | cbc7a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 3333
},
"timestamp": "2026-02-09T03:17:26.063Z",
"answer": 5407
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
c4c775 | nt_max_prime_below_v1_349078426_156 | Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $\ell$ be the number of elements in $T$. Define $S$ to be the set of all prime numbers $n$ such that $n \ge \ell$ and $n \le 80000$. Determine the value of the lar... | 79,999 | graphs = [
Graph(
let={
"upper": Const(80000),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.526 | 2026-02-08T12:51:37.926263Z | {
"verified": true,
"answer": 79999,
"timestamp": "2026-02-08T12:51:40.452439Z"
} | 259e81 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 3196
},
"timestamp": "2026-02-15T06:18:41.786Z",
"answer": 79999
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"sta... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
e55aae | nt_count_divisible_v1_48377204_2858 | Let $d = 1 + 2 + 3 + 4$. Compute the number of positive integers $n$ such that $1 \leq n \leq 63001$ and $n$ is divisible by $d$. | 6,300 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(63001),
"divisor": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper"))... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 6.366 | 2026-02-08T17:02:01.390756Z | {
"verified": true,
"answer": 6300,
"timestamp": "2026-02-08T17:02:07.756622Z"
} | 4d349f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 374
},
"timestamp": "2026-02-16T08:57:02.092Z",
"answer": 6301
},
{
"id": 11,
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
150629 | comb_count_partitions_v1_1978505735_565 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 76$. Compute the number of integer partitions of $n$. | 26,015 | graphs = [
Graph(
let={
"_n": Const(76),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_partitions_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T15:27:34.458984Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T15:27:34.461190Z"
} | 8d1408 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1161
},
"timestamp": "2026-02-24T20:57:31.479Z",
"answer": 26015
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
a44af6 | nt_count_gcd_equals_v1_784195855_3003 | Let $n$ be a positive integer such that $1 \leq n \leq 26896$ and $\gcd(n, 29) = 1$. Let $r$ be the number of such integers $n$. Let $S$ be the set of all positive integers $p$ for which there exists an integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $t$ be the number of elements in $S$. Compute the ... | 5,000 | graphs = [
Graph(
let={
"upper": Const(26896),
"k": Const(29),
"d": Const(1),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
"Q... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 14fbb8 | nt_count_gcd_equals_v1 | quadratic_mod | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.435 | 2026-02-08T06:11:03.566370Z | {
"verified": true,
"answer": 5000,
"timestamp": "2026-02-08T06:11:06.001185Z"
} | 7ce4f1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 2221
},
"timestamp": "2026-02-12T20:58:10.124Z",
"answer": 5000
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
faaeef | comb_count_surjections_v1_579913215_97 | Let $n = 4$. Define $k$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$. Let $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute the remainder when $28221 \cdot r$ is divided by $92777$. Determine the value of this expression. | 27,865 | graphs = [
Graph(
let={
"n": Const(4),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Cons... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T12:52:05.718661Z | {
"verified": true,
"answer": 27865,
"timestamp": "2026-02-08T12:52:05.722443Z"
} | 0e256c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T16:30:32.199Z",
"answer": 28265
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
c7b558 | comb_factorial_compute_v1_601307018_840 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 10$ such that $$
102a^2b^2 + \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 40,\ -1028a_1^3b_1 -1028a_1b_1^3 + \left|\{ t : \exists a_1,b_1\in\mathbb{Z}^+,\ 1\le a_1\le282,\ 1\le b_1\le142,\ t=12a_1+9b_1,\ 21\le t\le4662 \}\right| \cdot... | 47,240 | graphs = [
Graph(
let={
"_c": Const(3),
"_m": Const(4),
"_n": Const(17),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(10)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/POLY4_COUNT",
"LIN_FORM/POLY4_COUNT"
] | 9af31b | comb_factorial_compute_v1 | null | 8 | 0 | [
"LIN_FORM",
"POLY4_COUNT"
] | 2 | 0.061 | 2026-03-10T01:27:54.860385Z | {
"verified": true,
"answer": 47240,
"timestamp": "2026-03-10T01:27:54.921219Z"
} | 22d53c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 369,
"completion_tokens": 4323
},
"timestamp": "2026-04-18T15:00:57.048Z",
"answer": 44121
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY4_COUNT"... | {
"lo": 3.52,
"mid": 5.88,
"hi": 8.98
} | ||
122eff | nt_min_with_divisor_count_v1_1918700295_1845 | Compute the smallest positive integer $n$ such that $n \leq 97969$ and the number of positive divisors of $n$ is exactly 10. | 48 | graphs = [
Graph(
let={
"upper": Const(97969),
"div_count": Const(10),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("re... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 19.929 | 2026-02-08T06:04:55.022418Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T06:05:14.951209Z"
} | bc91fc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 940
},
"timestamp": "2026-02-12T20:42:07.668Z",
"answer": 48
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
2f9c47 | comb_sum_binomial_row_v1_1218484723_4981 | Compute the 16th power of the number of integers $a$ with $0 \le a \le 42$ such that
$$
3 \left( (3a^3 - 3a + 2) \bmod 43 \right)^3 - 3 \left( (3a^3 - 3a + 2) \bmod 43 \right) + 2 \equiv a \pmod{43}
$$
and $ (3a^3 - 3a + 2) \bmod 43 \ne a $. | 65,536 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(16),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(42)), Eq(Mod(value=Sum(Mul(Const(3), Pow(Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(3))), Mul(... | COMB | null | SUM | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"POLY_ORBIT_COUNT"
] | 1 | 0.002 | 2026-02-25T06:36:49.425227Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-25T06:36:49.426741Z"
} | a220da | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 12217
},
"timestamp": "2026-03-29T18:50:35.837Z",
"answer": 0
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
529534 | comb_catalan_compute_v1_1520064083_3473 | Let $T$ be the set of all integers $t$ with $5 \leq t \leq 16$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Let $n$ be the number of elements in $T$. Define $C_n$ to be the $n$-th Catalan number. Compute the remainder when $44121 \cdot C_n$ is divided by ... | 19,716 | graphs = [
Graph(
let={
"_n": Const(91486),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:41:51.867120Z | {
"verified": true,
"answer": 19716,
"timestamp": "2026-02-08T05:41:51.869028Z"
} | 715baa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1493
},
"timestamp": "2026-02-24T04:18:19.599Z",
"answer": 19716
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
cf893c | lin_form_endings_v1_397696148_2756 | Let $S$ be the set of all integers $t$ such that $32 \leq t \leq 408$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 24$, $1 \leq b \leq 6$, and $t = 12a + 20b$. Let $N$ be the number of elements in $S$. Compute the remainder when $6493 \cdot N$ is divided by $50714$. | 7,037 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=24)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:32:35.818944Z | {
"verified": true,
"answer": 7037,
"timestamp": "2026-02-08T13:32:35.820316Z"
} | 2b9185 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 3386
},
"timestamp": "2026-02-24T18:30:43.840Z",
"answer": 7037
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
e91c17 | diophantine_fbi2_count_v1_124444284_2615 | Let $k = 60$. Determine the number of integers $d$ such that $2 \leq d \leq 56$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 58$. | 8 | graphs = [
Graph(
let={
"k": Const(60),
"a": Const(1),
"b": Const(3),
"upper": Const(55),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(56)), Divides(divisor=Var("d"), dividend=Ref(... | NT | null | COUNT | sympy | LIN_FORM | [
"COUNT_PRIMES",
"B3"
] | 38fcc0 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3",
"COUNT_PRIMES",
"LIN_FORM"
] | 3 | 0.139 | 2026-02-08T04:50:53.582552Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T04:50:53.721369Z"
} | eeda8d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 644
},
"timestamp": "2026-02-11T22:17:31.283Z",
"answer": 8
},
{
"id":... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
e34851 | modular_mod_compute_v1_717093673_2940 | Let $ d $ be the smallest integer greater than or equal to $ 2 $ that divides $ 8385964537 $. Let $ a = 19 $, and let $ r $ be the remainder when $ a $ is divided by $ d $. Compute the remainder when $ 44121 \cdot r $ is divided by $ 93496 $. | 90,331 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(19),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(8385964537))))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_mod_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T17:17:58.841424Z | {
"verified": true,
"answer": 90331,
"timestamp": "2026-02-08T17:17:58.843220Z"
} | 1294a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 7722
},
"timestamp": "2026-02-17T23:13:20.491Z",
"answer": 90331
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dc7449 | sequence_count_fib_divisible_v1_1918700295_1344 | Let $m = 34969$ and $n = 44121$. Let $T$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x \cdot y = m$. Let $s$ be the minimum value of $x + y$ over all pairs $(x, y) \in T$. Let $d$ be the largest prime number not exceeding 16. Let $R$ be the set of all positive integers $n$ such that $1 \leq... | 15,693 | graphs = [
Graph(
let={
"_m": Const(34969),
"_n": Const(44121),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m"))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.037 | 2026-02-08T05:47:27.333790Z | {
"verified": true,
"answer": 15693,
"timestamp": "2026-02-08T05:47:27.370416Z"
} | 0a7eb6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 1886
},
"timestamp": "2026-02-12T14:14:47.729Z",
"answer": 15693
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
61fe15 | modular_count_residue_v1_458359167_17 | Let $n = 429$. Let $m = 27$ and let $u = 46656$. Define $r$ to be the number of positive integers $k$ such that $1 \leq k \leq e$, where $e$ is the largest integer for which $13^e$ divides $n!$, and $\gcd(k, 6) = 1$.
Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq u$ and $n \equiv r \pmod{m}$.... | 1,728 | graphs = [
Graph(
let={
"_n": Const(429),
"upper": Const(46656),
"m": Const(27),
"r": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxKDivides(target=Factorial(Ref("_n")), base=Const(13))), Eq(GCD(a=Var("n"),... | NT | null | COUNT | sympy | V1 | [
"V1/C4"
] | d84fad | modular_count_residue_v1 | null | 7 | 0 | [
"C4",
"V1"
] | 2 | 1.683 | 2026-02-08T02:57:04.894442Z | {
"verified": true,
"answer": 1728,
"timestamp": "2026-02-08T02:57:06.577529Z"
} | ca3f8d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 1876
},
"timestamp": "2026-02-08T20:12:50.424Z",
"answer": 1728
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "o... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
86dc21 | nt_count_gcd_equals_v1_1742523217_2513 | Let $k$ be the number of integers $t$ such that $24 \leq t \leq 140$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 7$, and $t = 14a + 10b$. Let $d = 1$ and let the upper bound be $44444$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 44444$ an... | 30,476 | graphs = [
Graph(
let={
"upper": Const(44444),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 4.747 | 2026-02-08T04:48:43.218565Z | {
"verified": true,
"answer": 30476,
"timestamp": "2026-02-08T04:48:47.965409Z"
} | 23d243 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1674
},
"timestamp": "2026-02-11T22:05:20.742Z",
"answer": 30476
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4b2cba | antilemma_k3_v1_1439011603_2993 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $57729$, where $\phi$ denotes Euler's totient function. Find the remainder when $62973 \cdot x$ is divided by $52618$. | 43,315 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=57729), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(62973),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(52618)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:08:47.804015Z | {
"verified": true,
"answer": 43315,
"timestamp": "2026-02-08T17:08:47.804773Z"
} | 868fd3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 1651
},
"timestamp": "2026-02-17T19:18:32.244Z",
"answer": 43315
},
{... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
028188 | sequence_count_fib_divisible_v1_48377204_1980 | Let $d = 17$. Compute the number of positive integers $n$ such that $1 \leq n \leq 909$ and $d$ divides the $n$-th Fibonacci number. | 101 | graphs = [
Graph(
let={
"upper": Const(909),
"d": Const(17),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | B3 | [
"B3",
"V1"
] | 07b21c | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3",
"V1"
] | 2 | 0.077 | 2026-02-08T16:32:07.564512Z | {
"verified": true,
"answer": 101,
"timestamp": "2026-02-08T16:32:07.641725Z"
} | 525da9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 2517
},
"timestamp": "2026-02-17T06:24:11.263Z",
"answer": 101
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5d11e3 | comb_binomial_compute_v1_2051736721_6047 | Let $$n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,$$ where $\phi(k)$ is Euler's totient function. Let $k$ be the largest prime number satisfying $2 \le k \le 8$. Compute $\binom{n}{k}$. | 6,435 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k1", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(5), Var("k1"))))),
"k": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"MAX_PRIME_BELOW",
"K2"
] | e3ad1e | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2",
"LTE_DIFF",
"MAX_PRIME_BELOW"
] | 3 | 0.007 | 2026-02-08T18:55:00.674315Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T18:55:00.681052Z"
} | 2e5512 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 528
},
"timestamp": "2026-02-16T18:31:10.504Z",
"answer": 6435
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma":... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
944b02 | nt_min_crt_v1_1978505735_5484 | Let $m = 5$ and $k = 9$. Find the smallest positive integer $n$ such that $1 \leq n \leq 45$, $n \equiv 2 \pmod{5}$, and $n \equiv 7 \pmod{9}$. Let $F_k$ denote the $k$-th Fibonacci number, with $F_1 = 1$, $F_2 = 1$, and $F_{k} = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the smallest positive integer $k$ such that $F_... | 12 | graphs = [
Graph(
let={
"m": Const(5),
"k": Const(9),
"a": Const(2),
"b": Const(7),
"upper": Const(45),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | NT | null | EXTREMUM | sympy | B1 | [
"K13/B3"
] | 382a12 | nt_min_crt_v1 | null | 4 | 0 | [
"B1",
"B3",
"K13"
] | 3 | 0.231 | 2026-02-08T19:01:46.213817Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T19:01:46.444453Z"
} | 73276b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1276
},
"timestamp": "2026-02-18T21:08:22.846Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2ecdd7 | antilemma_k2_v1_1470522791_11 | Compute
$$
\sum_{k=1}^{49} \phi(k) \left\lfloor \frac{49}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 1,225 | graphs = [
Graph(
let={
"_n": Const(49),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(49), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 3 | 0 | [
"K13",
"K2"
] | 2 | 0.002 | 2026-02-08T12:47:31.476753Z | {
"verified": true,
"answer": 1225,
"timestamp": "2026-02-08T12:47:31.478392Z"
} | d44e12 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 697
},
"timestamp": "2026-02-15T05:04:09.097Z",
"answer": 1225
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ef8263 | algebra_poly_eval_v1_717093673_2115 | Let $p$ be the number of positive integers $p'$ less than some $q'$ such that $p' q' = 18$, $\gcd(p', q') = 1$, and $p' < q'$. Let $d = 13$. Define
$$
E = \frac{144d^5 + 78d^4 + 105d^3 + 68d^p - 12d - 9}{m},
$$
where $m$ is the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy ... | 22,927 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(3),
"m": Const(13),
"result": Div(Sum(Mul(Const(144), Pow(Ref("m"), Const(5))), Mul(Const(78), Pow(Ref("m"), Ref("_m"))), Mul(Const(105), Pow(Ref("m"), Ref("_n"))), Mul(Const(68), Pow(Ref("m"), CountOverSet(s... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | algebra_poly_eval_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.013 | 2026-02-08T16:33:45.889752Z | {
"verified": true,
"answer": 22927,
"timestamp": "2026-02-08T16:33:45.902697Z"
} | d939f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 2865
},
"timestamp": "2026-02-17T08:12:56.563Z",
"answer": 22927
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b18e43 | diophantine_sum_product_min_v1_151522320_460 | Let $n = 11$. Let $S = 12$. Let $T$ be the set of all integers $t$ such that $18 \leq t \leq 240$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 16$, $1 \leq b \leq 10$, and $t = 10a + 8b$. Let $P$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = |T|$.... | 57,598 | graphs = [
Graph(
let={
"_n": Const(11),
"S": Const(12),
"P": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=Solu... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T03:20:50.224285Z | {
"verified": true,
"answer": 57598,
"timestamp": "2026-02-08T03:20:50.230228Z"
} | d7d146 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 5199
},
"timestamp": "2026-02-10T13:17:31.648Z",
"answer": 57598
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
29b071 | nt_count_divisors_in_range_v1_655260480_4349 | Let $n = 1680$. Let $a = 10$. Let $b$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 115$, $1 \leq i \leq 114$, and $1 \leq j \leq 115$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 21 | graphs = [
Graph(
let={
"n": Const(1680),
"a": Const(10),
"b": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(115)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(114)), right=Integ... | NT | null | COUNT | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.098 | 2026-02-08T17:53:33.446025Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T17:53:33.544051Z"
} | ec3336 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 2622
},
"timestamp": "2026-02-18T09:35:53.523Z",
"answer": 21
},
{
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fca3f1 | diophantine_fbi2_min_v1_677425708_2070 | Let
$$
n = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor,
$$
and define
$$
k = \sum_{i=1}^{n} \phi(i) \left\lfloor \frac{n}{i} \right\rfloor.
$$
Let $d$ be the smallest integer such that $5 \leq d \leq 31$, $d$ divides $k$, and $k/d \geq 2$.
Compute $d$. | 7 | graphs = [
Graph(
let={
"_n": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=Const... | NT | null | EXTREMUM | sympy | K2 | [
"K2/K2"
] | ddede2 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.006 | 2026-02-08T04:45:25.055308Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T04:45:25.061350Z"
} | 0892bf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 1149
},
"timestamp": "2026-02-10T05:27:15.273Z",
"answer": 7
},
{
"id":... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
784efd | modular_mod_compute_v1_458359167_3946 | Let $N$ be the number of ordered pairs $(x,y)$ of integers with $1 \le x \le 13$ and $1 \le y \le 143$.
Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x+y=172$, and let $P$ be the set of all values of $xy$ as $(x,y)$ ranges over $S$. Let $M$ be the maximum element of $P$.
Let $m$ be t... | 877 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(143)))),
"a": Const(30625),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), conditio... | NT | COMB | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/MIN_PRIME_FACTOR",
"B1/C3"
] | e3b155 | modular_mod_compute_v1 | bell_mod | 6 | 0 | [
"B1",
"C3",
"COUNT_CARTESIAN",
"MIN_PRIME_FACTOR"
] | 4 | 0.004 | 2026-02-08T11:26:51.435326Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T11:26:51.439608Z"
} | 2f3186 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 333,
"completion_tokens": 1292
},
"timestamp": "2026-02-14T14:23:01.352Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1384a8 | comb_count_surjections_v1_1918700295_2538 | Let $ N $ be the number of ordered pairs $ (x_1, x_2) $ of positive odd integers such that $ x_1 + x_2 = 14 $. Let $ k = 6 $. Define $ R = k! \cdot S(N, k) $, where $ S(N, k) $ denotes the Stirling number of the second kind. Compute $ 28900 - R $. | 13,780 | graphs = [
Graph(
let={
"_n": Const(14),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.027 | 2026-02-08T07:56:56.965022Z | {
"verified": true,
"answer": 13780,
"timestamp": "2026-02-08T07:56:56.992509Z"
} | 065ff1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 910
},
"timestamp": "2026-02-24T08:39:28.314Z",
"answer": 13780
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
d78d42_n | alg_qf_psd_min_v1_1218484723_1187 | A logistics company operates four warehouses, each capable of storing between 1 and 23 units of a special material. The total operational cost is modeled by the expression $4664d^2 + 3392cd + 13144c^2 + 19928a^2 - 8480ab - 1696bd + 10176ad + 5088bc + E b^2 + 5936ac$, where $a, b, c, d$ are the storage levels and $E = 9... | 61,904 | ALG | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | alg_qf_psd_min_v1 | null | 6 | null | [
"C2"
] | 1 | 1.202 | 2026-02-25T02:58:41.394040Z | null | dd908e | d78d42 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 3370
},
"timestamp": "2026-03-30T16:27:31.767Z",
"answer": 61904
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
f961cb | diophantine_sum_product_min_v1_1978505735_1118 | Let $S = 14$ and $P = 24$. Define $r$ to be the smallest positive integer $x$ such that $1 \leq x \leq 13$ and $x(S - x) = P$. Let $M$ be the largest prime number $n$ such that $2 \leq n \leq 98$. Compute the remainder when
$$
353702 \cdot (|r| \bmod M) + 329703 \cdot \left( r^2 + 1 \right) \bmod 101 + 215534 \cdot \le... | 18,264 | graphs = [
Graph(
let={
"_n": Const(101),
"S": Const(14),
"P": Const(24),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(13)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 045f57 | diophantine_sum_product_min_v1 | crt_mix_3 | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.015 | 2026-02-08T15:50:58.316203Z | {
"verified": true,
"answer": 18264,
"timestamp": "2026-02-08T15:50:58.331006Z"
} | 7f8c54 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 763
},
"timestamp": "2026-02-16T14:45:23.934Z",
"answer": 18264
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
59d0c1 | modular_modexp_compute_v1_1439011603_1691 | Let $d$ be the smallest integer greater than or equal to $2$ that divides $1752967$. Compute $3^d \mod 26244$. Let $R$ denote this remainder. Define $Q = (37109 \times R) \mod 82347$. Find the value of $Q$. | 80,904 | graphs = [
Graph(
let={
"_n": Const(37109),
"a": Const(3),
"e": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1752967))))),
"m": Const(26244),
"result": ModExp(base=Ref("a"... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_modexp_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T16:13:29.906380Z | {
"verified": true,
"answer": 80904,
"timestamp": "2026-02-08T16:13:29.908300Z"
} | 8d1901 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 4317
},
"timestamp": "2026-02-16T23:01:37.057Z",
"answer": 80904
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f58ff9 | nt_count_phi_equals_v1_677425708_485 | Let $p_1 = 47$. Define $t$ to be the number of prime factors of $p_1$ counted with multiplicity. Let $p = 31t$ and $q = 17$, and define $n = pq$. Let $e$ be the remainder when the number of positive divisors of $n$ is divided by 2. Let $\mathcal{S}$ be the set of all positive integers $n$ such that $1 \leq n \leq 1444$... | 4 | graphs = [
Graph(
let={
"p1": Const(47),
"t": BigOmega(n=Ref(name='p1')),
"p": Mul(Const(31), Ref("t")),
"q": Const(17),
"n": Mul(Ref("p"), Ref("q")),
"e": Mod(value=NumDivisors(n=Ref("n")), modulus=Const(2)),
"upper": Const... | NT | null | COUNT | sympy | B1 | [
"DIVISOR_PARITY",
"BIG_OMEGA_ONE"
] | 47ec5c | nt_count_phi_equals_v1 | null | 6 | 2 | [
"B1",
"BIG_OMEGA_ONE",
"DIVISOR_PARITY"
] | 3 | 2.303 | 2026-02-08T03:33:43.810293Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T03:33:46.113250Z"
} | c4c542 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 306,
"completion_tokens": 5735
},
"timestamp": "2026-02-10T04:42:50.992Z",
"answer": 4
},
{
"id"... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
83d36b | nt_count_divisible_v1_655260480_3502 | Let $d = \sum_{k=1}^{3} k$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 31337$ and $n$ is divisible by $d$. Let $r$ be the number of elements in $T$. Compute the remainder when $58809 \cdot r$ is divided by $81854$. | 66,244 | graphs = [
Graph(
let={
"_n": Const(58809),
"upper": Const(31337),
"divisor": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.99 | 2026-02-08T17:24:45.216616Z | {
"verified": true,
"answer": 66244,
"timestamp": "2026-02-08T17:24:46.206125Z"
} | 1dc44c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1397
},
"timestamp": "2026-02-18T01:37:31.969Z",
"answer": 66244
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
825336 | comb_count_permutations_fixed_v1_1440796553_1459 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $S$ be the set of all ordered pairs $(k, j)$ with $k \in \{1,2,3\}$ and $j \in \{1,2,\dots,7\}$. Define $k = \frac{4}{28}$ times the sum of $k$ over all elements of $S$. Let $\binom{n}{k}$ denote the binomial co... | 18,672 | graphs = [
Graph(
let={
"_n": Const(88028),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC",
"B1"
] | bf2255 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"B1",
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 3 | 0.006 | 2026-02-08T14:00:59.755771Z | {
"verified": true,
"answer": 18672,
"timestamp": "2026-02-08T14:00:59.762179Z"
} | 87d554 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 2126
},
"timestamp": "2026-02-24T19:33:33.903Z",
"answer": 18672
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
2ccbee | algebra_poly_eval_v1_677425708_2434 | Let $b = \sum_{k=1}^{3} k$. Compute $$3b^4 + 10b^3 + 7b^2 + 9b - 5.$$ | 6,349 | graphs = [
Graph(
let={
"_n": Const(9),
"b": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": Sum(Mul(Const(3), Pow(Ref("b"), Const(4))), Mul(Const(10), Pow(Ref("b"), Const(3))), Mul(Const(7), Pow(Ref("b"), Const(2))), Mul(Ref("_n"), Ref("b")), C... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_poly_eval_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T05:03:27.790075Z | {
"verified": true,
"answer": 6349,
"timestamp": "2026-02-08T05:03:27.791901Z"
} | 91be84 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 319
},
"timestamp": "2026-02-11T22:12:15.531Z",
"answer": 6359
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
8076d2 | nt_max_prime_below_v1_1116507919_57 | Let $n = 11$ and $M = 43264$. Let $D$ be the set of all integers $d \geq 2$ that divide $20449$. Let $d_{\min}$ be the smallest element of $D$. Define $L$ to be the largest integer $k$ such that $11^k$ divides $n \cdot d_{\min}$. Consider the set of all prime numbers $n$ such that $L \leq n \leq M$. Let $P$ be the larg... | 55,509 | graphs = [
Graph(
let={
"_n": Const(11),
"upper": Const(43264),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), MaxKDivides(target=Mul(Ref("_n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divis... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K13"
] | 1ae094 | nt_max_prime_below_v1 | null | 6 | 0 | [
"K13",
"MIN_PRIME_FACTOR"
] | 2 | 0.922 | 2026-02-08T02:24:07.373636Z | {
"verified": true,
"answer": 55509,
"timestamp": "2026-02-08T02:24:08.295239Z"
} | fe4e7a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 4924
},
"timestamp": "2026-02-08T18:58:08.951Z",
"answer": 59577
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_... | {
"lo": 3.18,
"mid": 5.53,
"hi": 8.02
} | ||
1c0d02 | geo_count_lattice_rect_v1_1520064083_9703 | Let $a = 70$ and $b = 27$. Define a lattice point as a point in the coordinate plane with integer coordinates. Consider the rectangle consisting of all points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the number of lattice points contained in this rectangle. | 1,988 | graphs = [
Graph(
let={
"a": Const(70),
"b": Const(27),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T10:58:49.115376Z | {
"verified": true,
"answer": 1988,
"timestamp": "2026-02-08T10:58:49.116427Z"
} | 2404f1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 256
},
"timestamp": "2026-02-24T12:34:04.715Z",
"answer": 1988
},
{
"id... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
f1a62d | comb_factorial_compute_v1_1419126231_74 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le N$, where $N = \left|\left\{ (a_2, b_2) : 1 \le a_2, b_2 \le 40,\ 8a_2 b_2^3 + 2b_2^4 + 8a_2^3 b_2 + 12a_2^2 b_2^2 + 2a_2^4 = 8954912 \right\}\right|$, and such that $2a^2 - 4ab + 2b^2 = 1458$. Let $S = n!$. Find the remainder ... | 49,451 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(61471),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var(... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/POLY4_COUNT/QF_PSD_ORBIT",
"POLY3_COUNT/QF_PSD_ORBIT"
] | de19b4 | comb_factorial_compute_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"POLY4_COUNT",
"QF_PSD_ORBIT"
] | 3 | 0.022 | 2026-02-25T09:37:46.915958Z | {
"verified": true,
"answer": 49451,
"timestamp": "2026-02-25T09:37:46.938010Z"
} | 037dab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 4036
},
"timestamp": "2026-03-30T06:50:06.579Z",
"answer": 49451
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "QF_P... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
ccdff3 | sequence_fibonacci_compute_v1_784195855_5402 | Let $n$ be the number of positive integers $j$ such that $1 \leq j \leq 22$ and $j^5 \leq 5153632$. Determine the value of the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_m = F_{m-1} + F_{m-2}$ for $m \geq 3$. | 17,711 | graphs = [
Graph(
let={
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(22)), Leq(Pow(Var("j"), Ref("_n")), Const(5153632))), domain='positive_integers')),
"result": Fibonacci(arg=Ref(name='n')),
... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T07:53:05.325559Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T07:53:05.326207Z"
} | f126ea | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1099
},
"timestamp": "2026-02-13T13:13:05.406Z",
"answer": 17711
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b7c3d8 | algebra_quadratic_discriminant_v1_397696148_224 | Let $a = 2$, $n = 2$, and $b = \sum_{k=1}^{3} k$. Let $c = -8$. Define $\text{result} = b^n - 4ac$. Compute the remainder when $36232 \cdot \text{result}$ is divided by $81843$. | 22,108 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2),
"b": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"c": Const(-8),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Mod(value=Mul(... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T11:23:12.070242Z | {
"verified": true,
"answer": 22108,
"timestamp": "2026-02-08T11:23:12.072122Z"
} | e8eac8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 900
},
"timestamp": "2026-02-14T13:28:47.613Z",
"answer": 22108
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3a6c2c | algebra_poly_eval_v1_168721529_933 | Let $z = 21$. Define $\text{result}$ to be the value of the expression
$$
\frac{72z^5 - 350z^4 + 400z^3 - 34z^2 + 44z + 228}{c},
$$
where $c$ is the number of integers $t$ such that there exist positive integers $a$ and $b$ satisfying $1 \le a \le 424$, $1 \le b \le 240$, $17 \le t \le 3088$, and $t = 5a + 4b + 8$. Com... | 75,058 | graphs = [
Graph(
let={
"_n": Const(2),
"z": Const(21),
"result": Div(Sum(Mul(Const(72), Pow(Ref("z"), Const(5))), Mul(Const(-350), Pow(Ref("z"), Const(4))), Mul(Const(400), Pow(Ref("z"), Const(3))), Mul(Const(-34), Pow(Ref("z"), Ref("_n"))), Mul(Const(44), Ref("z")), Con... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.009 | 2026-02-08T13:21:05.390335Z | {
"verified": true,
"answer": 75058,
"timestamp": "2026-02-08T13:21:05.399064Z"
} | f7ea99 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 7163
},
"timestamp": "2026-02-11T07:44:42.206Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1... | {
"lo": 2.06,
"mid": 5.24,
"hi": 8.53
} | ||
0d08f7 | comb_factorial_compute_v1_1419126231_1083 | Let $n$ be the minimum value of $3ab^2 + 3a^2b + b^3$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 14$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(14),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(14)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")))), expr=Sum(Mul(Const(3), Var("a"), Po... | COMB | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | comb_factorial_compute_v1 | null | 4 | 0 | [
"POLY3_MIN"
] | 1 | 0.002 | 2026-02-25T10:37:37.229380Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T10:37:37.231410Z"
} | 81afde | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1066
},
"timestamp": "2026-03-30T11:19:49.460Z",
"answer": 5040
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
b9ea43 | comb_factorial_compute_v1_458359167_3574 | Let $n$ be the smallest divisor of $41503$ that is greater than or equal to $2$. Compute $49284 - n!$. | 44,244 | graphs = [
Graph(
let={
"_n": Const(49284),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(41503))))),
"result": Factorial(Ref("n")),
"Q": Sub(Ref("_n"), Ref("result")),
},... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T08:26:22.278234Z | {
"verified": true,
"answer": 44244,
"timestamp": "2026-02-08T08:26:22.279245Z"
} | 6522a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 637
},
"timestamp": "2026-02-13T18:44:37.286Z",
"answer": 44244
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
3615c3 | antilemma_cartesian_v1_397696148_716 | Let $N = 76679$. Compute the value of $$ x + 2^{x \bmod y} \bmod N, $$ where $x$ is the number of ordered pairs $(a, b)$ with $1 \leq a \leq 10$ and $1 \leq b \leq 16$, and $y$ is the number of ordered pairs $(u, v)$ of positive odd integers such that $u + v = 32$. | 161 | graphs = [
Graph(
let={
"_n": Const(76679),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(16)))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=CountOverSet(se... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_CARTESIAN"
] | 392991 | antilemma_cartesian_v1 | mod_exp | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T11:42:53.473096Z | {
"verified": true,
"answer": 161,
"timestamp": "2026-02-08T11:42:53.474285Z"
} | 40586c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 809
},
"timestamp": "2026-02-24T14:30:33.501Z",
"answer": 161
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
a50e22 | nt_count_coprime_v1_458359167_1416 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 18$. Let $P$ be the set of all products $xy$ where $(x, y) \in S$. Let $M$ be the maximum value in $P$. Now, let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = M$. Let $k$ be the minimum value of ... | 1,831 | graphs = [
Graph(
let={
"_n": Const(64424),
"upper": Const(11449),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_coprime_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.874 | 2026-02-08T04:36:16.202224Z | {
"verified": true,
"answer": 1831,
"timestamp": "2026-02-08T04:36:17.075730Z"
} | f3592a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 1730
},
"timestamp": "2026-02-10T17:20:21.619Z",
"answer": 1831
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"l... | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
843d7c | sequence_lucas_compute_v1_784195855_10327 | Let $P$ be the set of all prime numbers between 2 and 71, inclusive. Let $n$ be the largest prime number not exceeding the size of $P$. Compute the $n$-th Lucas number. Determine the value of this number. | 9,349 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(71)), IsPri... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/MAX_PRIME_BELOW"
] | d51604 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T17:34:25.458170Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T17:34:25.460508Z"
} | d16b91 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 725
},
"timestamp": "2026-02-18T07:37:55.640Z",
"answer": 9349
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
db47a4 | comb_catalan_compute_v1_1915831931_4166 | Let $n$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 2$ and $1 \leq j \leq 5$. Let $\text{result} = C_n$, the $n$-th Catalan number. Compute the remainder when $69202 \cdot \text{result}$ is divided by $92097$. | 52,652 | graphs = [
Graph(
let={
"_n": Const(92097),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"_c": Const(69202),
"Q": Mod(value=... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T18:10:23.608239Z | {
"verified": true,
"answer": 52652,
"timestamp": "2026-02-08T18:10:23.611650Z"
} | 6803d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1834
},
"timestamp": "2026-02-18T14:31:29.984Z",
"answer": 52652
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
78bd64 | alg_poly4_min_v1_601307018_7759 | Let $M$ be the largest positive integer $d$ such that $d^2 \leq 1224336$ and $d \mid 1224336$. Find the minimum value $Q$ of $$17733b^4 + \min\{x + y : x > 0, y > 0, xy = 10969344, x \leq y\} \cdot a^2b^2 + 69a^4 + M a^3 b + 17664a b^3$$ over all positive integers $a, b$ with $1 \leq a, b \leq 142$. | 43,194 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(1224336)), Leq(Mul(Var("d"), Var("d")), Const(1224336))))),
"result": MinOverSet(set=MapOverSet(set=Solu... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/B3"
] | c21b41 | alg_poly4_min_v1 | null | 6 | 0 | [
"B3",
"B3_CLOSEST"
] | 2 | 0.101 | 2026-03-10T08:20:45.231709Z | {
"verified": true,
"answer": 43194,
"timestamp": "2026-03-10T08:20:45.333069Z"
} | 524def | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 7404
},
"timestamp": "2026-04-19T07:28:05.415Z",
"answer": 43194
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
418b5c | nt_count_intersection_v1_1520064083_642 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25000000$. For each such pair, compute $x + y$. Let $N$ be the minimum value of $x + y$ over all such pairs. Let $a = 7$ and $b = 12$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $7 \mid n$, and $\gcd(n,... | 476 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25000000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(7),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 4 | 0 | [
"B3"
] | 1 | 3.675 | 2026-02-08T03:30:46.308189Z | {
"verified": true,
"answer": 476,
"timestamp": "2026-02-08T03:30:49.983657Z"
} | 577f8a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 5564
},
"timestamp": "2026-02-10T14:55:43.543Z",
"answer": 476
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
4cd72f | diophantine_product_count_v1_1915831931_1562 | Let $k = 360$ and $N = 14884$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = N$. Let $\text{upper}$ be the minimum value of $x + y$ over all such pairs. Define $\text{result}$ to be the number of positive integers $x_1$ such that $1 \leq x_1 \leq \text{upper}$, $x_1$ divides $k$, a... | 22 | graphs = [
Graph(
let={
"_n": Const(14884),
"k": Const(360),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.034 | 2026-02-08T16:15:41.827066Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T16:15:41.861124Z"
} | 1d6be3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1940
},
"timestamp": "2026-02-17T00:30:56.581Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a3d96a | modular_mod_compute_v1_898971024_2517 | Let $n = 95215$. Define $m$ to be the number of integers $j$ with $0 \le j \le 95215$ such that $\binom{n}{j}$ is odd. Let $a = -58564$ and define $\text{result} = a \bmod m$. Compute the remainder when $44121 \cdot \text{result}$ is divided by $96001$. | 24,408 | graphs = [
Graph(
let={
"_n": Const(95215),
"a": Const(-58564),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(95215)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnega... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_mod_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T16:47:50.595362Z | {
"verified": true,
"answer": 24408,
"timestamp": "2026-02-08T16:47:50.597920Z"
} | 398df2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 2292
},
"timestamp": "2026-02-17T13:00:17.911Z",
"answer": 24408
},
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b4e029 | algebra_quadratic_discriminant_v1_1915831931_1101 | Let $a = 3$, $b = 5$, and $c = 11$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Compute $\left| 5^{|S|} - 4 \cdot 3 \cdot 11 \right|$. | 107 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(5),
"c": Const(11),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(na... | NT | null | COMPUTE | sympy | V8 | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.042 | 2026-02-08T15:53:33.601306Z | {
"verified": true,
"answer": 107,
"timestamp": "2026-02-08T15:53:33.643423Z"
} | 7a258d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 614
},
"timestamp": "2026-02-16T16:24:28.146Z",
"answer": 107
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
811eb4 | lin_form_endings_v1_153355830_1083 | Let $a = 56$ and $b = 98$. Define
$$
r = \left\lfloor \frac{56}{\gcd(a, b)} \right\rfloor.
$$
Let $k = 14923$ and $M = 67771$. Compute the remainder when $k \cdot r$ is divided by $M$. | 59,692 | graphs = [
Graph(
let={
"a_coeff": Const(56),
"b_coeff": Const(98),
"_inner_result": Floor(Div(Const(56), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(14923),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T04:23:33.670345Z | {
"verified": true,
"answer": 59692,
"timestamp": "2026-02-08T04:23:33.670785Z"
} | 25c817 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 284
},
"timestamp": "2026-02-15T17:05:19.192Z",
"answer": 29846
},
{
"id": 11... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
6176cd | nt_count_divisible_and_v1_784195855_115 | Let $ d_1 = 10 $ and $ d_2 = 12 $. Let $ r $ be the number of positive integers $ n \leq 70260 $ such that
\[
n \equiv \sum_{d \mid \gcd(2,6)} \mu(d) \pmod{10}
\]
and $ n \equiv 0 \pmod{12} $, where $ \mu $ denotes the M\"obius function.
Let $ Q = \sum_{n=1}^{|r|} \tau(n) $, where $ \tau(n) $ is the number of positive... | 8,460 | graphs = [
Graph(
let={
"upper": Const(70260),
"d1": Const(10),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), SumOverDivisor... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | 8084fa | nt_count_divisible_and_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | 2 | 3.092 | 2026-02-08T02:58:20.450859Z | {
"verified": true,
"answer": 8460,
"timestamp": "2026-02-08T02:58:23.543150Z"
} | fa0c52 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 2092
},
"timestamp": "2026-02-08T22:49:10.997Z",
"answer": 8460
},
{
"... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"l... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
a8c8a2 | antilemma_k3_v1_1742523217_4421 | Let $n = 59646$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 59,646 | graphs = [
Graph(
let={
"_n": Const(59646),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T07:17:13.119713Z | {
"verified": true,
"answer": 59646,
"timestamp": "2026-02-08T07:17:13.120057Z"
} | 14fb13 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 4371
},
"timestamp": "2026-02-13T09:19:33.929Z",
"answer": 59646
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
e10fa7 | algebra_quadratic_discriminant_v1_1520064083_3599 | Let $a = -5$ and $b = -6$. Let $c$ be the minimum value of $x + y$ over all pairs of positive integers $(x,y)$ such that $xy$ equals the maximum value of $xy$ over all pairs of positive integers $(x,y)$ satisfying $x + y = 8$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ ... | 196 | graphs = [
Graph(
let={
"_c": Const(8),
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=150)), Eq(left=GCD(a... | NT | null | COMPUTE | sympy | B3 | [
"COPRIME_PAIRS/B3",
"B1/B3"
] | 7e9ed9 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B1",
"B3",
"COPRIME_PAIRS"
] | 3 | 0.076 | 2026-02-08T05:46:47.394328Z | {
"verified": true,
"answer": 196,
"timestamp": "2026-02-08T05:46:47.469835Z"
} | a58245 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1513
},
"timestamp": "2026-02-12T13:54:35.384Z",
"answer": 196
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0799a3 | comb_sum_binomial_row_v1_677425708_3420 | Let $d=96$. Consider all ordered pairs $(x,y)$ of positive integers such that $x+y=d$. For each such pair, form the product $xy$, and let $C$ be the maximum of all such products.
Consider all ordered pairs $(x,y)$ of positive integers such that $xy=C$. For each such pair, form the sum $x+y$, and let $S$ be the set of ... | 61,964 | graphs = [
Graph(
let={
"_d": Const(96),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_d")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B1 | [
"B1/B3/COUNT_FIB_DIVISIBLE/MAX_PRIME_BELOW"
] | 029090 | comb_sum_binomial_row_v1 | null | 8 | 0 | [
"B1",
"B3",
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 4 | 0.007 | 2026-02-08T05:41:54.746154Z | {
"verified": true,
"answer": 61964,
"timestamp": "2026-02-08T05:41:54.753048Z"
} | 99eeb3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 3172
},
"timestamp": "2026-02-12T13:58:12.880Z",
"answer": 61964
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6fd2f2 | comb_count_derangements_v1_1125832087_1354 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 10000$. For each such pair, compute $x + y$, and let $m$ be the minimum value of $x + y$ over all pairs in $S$. Let $n$ be the number of nonnegative integers $j \leq 200$ such that $\binom{m}{j} \equiv 1 \pmod{2}$. Compute the number ... | 14,833 | graphs = [
Graph(
let={
"_m": Const(10000),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(200)), Eq(Mod(value=Binom(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var... | COMB | null | COUNT | sympy | B3 | [
"B3/V8"
] | 4fad5b | comb_count_derangements_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.002 | 2026-02-08T03:41:33.478219Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T03:41:33.480355Z"
} | 4f8b76 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1741
},
"timestamp": "2026-02-10T15:25:15.450Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
},... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
1dfce3 | nt_count_primes_v1_865884756_2858 | Let $N$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all prime numbers $n$ such that $N \leq n \leq 11699$. Compute the number of elements in $S$. | 1,404 | graphs = [
Graph(
let={
"upper": Const(11699),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.285 | 2026-02-08T16:58:58.902279Z | {
"verified": true,
"answer": 1404,
"timestamp": "2026-02-08T16:58:59.187036Z"
} | c8c662 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2056
},
"timestamp": "2026-02-17T16:18:41.199Z",
"answer": 1404
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f5868 | antilemma_sum_equals_v1_1978505735_5766 | Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 81$, $1 \leq j \leq 81$, and $i + j = 83$. Let $x = |S|$. Compute the remainder when $1666x$ is divided by $66025$. | 1,230 | graphs = [
Graph(
let={
"_n": Const(83),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(81)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T19:12:41.450970Z | {
"verified": true,
"answer": 1230,
"timestamp": "2026-02-08T19:12:41.455136Z"
} | 8b342a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 817
},
"timestamp": "2026-02-18T21:34:46.317Z",
"answer": 1230
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
918a56 | nt_max_prime_below_v1_1915831931_3653 | Let $p$ be a positive integer such that there exists a positive integer $q$ satisfying $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of such integers $p$. Determine the largest prime number $n$ such that $N \leq n \leq 57600$. | 57,593 | graphs = [
Graph(
let={
"upper": Const(57600),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.387 | 2026-02-08T17:47:59.178850Z | {
"verified": true,
"answer": 57593,
"timestamp": "2026-02-08T17:48:00.566083Z"
} | 9d2bf0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 3821
},
"timestamp": "2026-02-18T08:07:02.920Z",
"answer": 57593
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
989fff | nt_sum_gcd_range_mod_v1_971394319_1724 | Let $N = \sum_{d \mid 6400} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $k = 288$ and define $$S = \sum_{n=1}^{N} \gcd(n, k).$$ Let $r$ be the remainder when $S$ is divided by $11177$. Compute $r + \phi(r + 1) + \tau(r + 1)$, where $\tau(m)$ denotes the number of positive divisors of $m$. | 14,210 | graphs = [
Graph(
let={
"N": SumOverDivisors(n=Const(value=6400), var='d', expr=EulerPhi(n=Var(name='d'))),
"k": Const(288),
"M": Const(11177),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.534 | 2026-02-08T13:52:33.860072Z | {
"verified": true,
"answer": 14210,
"timestamp": "2026-02-08T13:52:34.394356Z"
} | 928a8a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 2162
},
"timestamp": "2026-02-15T21:36:20.226Z",
"answer": 14210
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
df01b6 | modular_mod_compute_v1_124444284_7737 | Let $m = 8$ and let $n = \sum_{k=1}^{m} k$. Define $a = \sum_{k=1}^{n} k$. Find the remainder when $a$ is divided by $25600$. | 666 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Var("k")),
"a": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"m": Const(25600),
"result": Mod(value=Ref("a"), modulus=Ref("m")... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/SUM_ARITHMETIC"
] | 2a57af | modular_mod_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T09:20:24.809547Z | {
"verified": true,
"answer": 666,
"timestamp": "2026-02-08T09:20:24.811526Z"
} | 7158d5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 280
},
"timestamp": "2026-02-15T20:38:52.372Z",
"answer": 666
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
ad0629 | lte_diff_endings_v1_1520064083_2628 | Let $a = 9$, $b = 7$, $p = 2$, $K = 4$, and $N = 484825$. Let $d = a - b$, and let $v_p(d)$ be the largest integer $k$ such that $p^k$ divides $d$. Define $m = K - v_p(d)$ and let $p^m$ be the $m$-th power of $p$. Compute the greatest integer less than or equal to $N / p^m$. | 60,603 | graphs = [
Graph(
let={
"a_val": Const(9),
"b_val": Const(7),
"p_val": Const(2),
"K_val": Const(4),
"N_val": Const(484825),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val"... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 4 | null | [
"LTE_DIFF"
] | 1 | 0 | 2026-02-08T04:53:28.956915Z | {
"verified": true,
"answer": 60603,
"timestamp": "2026-02-08T04:53:28.957352Z"
} | d138fa | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 201
},
"timestamp": "2026-02-18T14:34:31.762Z",
"answer": 60603
}
] | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
b85279 | modular_mod_compute_v1_809748730_15 | Let $a = 42025$. Let $m$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 88$. Define $r$ to be the remainder when $a$ is divided by $m$. Compute the remainder when $44121 \cdot r$ is divided by $87595$. | 48,694 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": Const(42025),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(88)))), e... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T11:17:28.557015Z | {
"verified": true,
"answer": 48694,
"timestamp": "2026-02-08T11:17:28.558266Z"
} | 9071a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 841
},
"timestamp": "2026-02-14T11:34:12.142Z",
"answer": 48694
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f9a136 | geo_count_lattice_triangle_v1_865884756_6320 | Let $A$ be twice the area of the triangle with vertices at $(324, 233)$, $(200, 111)$, and $(0, 0)$. Compute $A$ using the shoelace formula. Let $B$ be the sum of the greatest common divisors of the absolute differences in coordinates along each side of the triangle: $\gcd(|324 - 0|, |233 - 0|)$, $\gcd(|200 - 324|, |11... | 5,317 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=324), Const(value=111)), Mul(Const(value=200), Sub(left=Const(value=0), right=Const(value=233))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=324)), b=Abs(arg=Const(value=233))), GCD(a=Abs(arg=Sub(left=Const(value=200), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.004 | 2026-02-08T19:08:49.428314Z | {
"verified": true,
"answer": 5317,
"timestamp": "2026-02-08T19:08:49.432621Z"
} | faaa6d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1065
},
"timestamp": "2026-02-18T21:24:20.001Z",
"answer": 5317
},
{... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
35bd41 | comb_sum_binomial_row_v1_1218484723_7595 | Let $N = 2^{10}$. Compute $$\left|\left\{ j \in \mathbb{Z} : j \ge \sum_{k=0}^{8} (-1)^k \binom{8}{k},\, j \le 98229,\, \binom{98229}{j} \text{ is odd} \right\}\right| - N€. | 7,168 | graphs = [
Graph(
let={
"n": Const(10),
"result": Pow(Const(2), Ref("n")),
"Q": Sub(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Const(0), end=Const(8), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(8), k=Var("k")))))... | COMB | null | SUM | sympy | STARS_BARS | [
"V8",
"BINOMIAL_ALTERNATING"
] | 88e903 | comb_sum_binomial_row_v1 | negation_mod | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"STARS_BARS",
"V8"
] | 3 | 0.039 | 2026-02-25T09:01:59.955450Z | {
"verified": true,
"answer": 7168,
"timestamp": "2026-02-25T09:01:59.994848Z"
} | 4b47b8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T05:28:00.258Z",
"answer": 7168
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
7687be | comb_binomial_compute_v1_1419126231_381 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 20$ such that
$$
17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 40817.
$$
Compute $\binom{14}{k}$. | 3,003 | graphs = [
Graph(
let={
"_n": Const(20),
"n": Const(14),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Eq(Sum(Mul(Const(17), ... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_binomial_compute_v1 | null | 5 | 0 | [
"POLY4_COUNT"
] | 1 | 0.003 | 2026-02-25T09:54:54.138414Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-25T09:54:54.141561Z"
} | 05303a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 893
},
"timestamp": "2026-03-30T08:18:48.788Z",
"answer": 3003
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
325e50 | comb_sum_binomial_row_v1_798873815_262 | Let $n_0 = 2$. Define $n$ to be the smallest divisor $d$ of $4199$ such that $d \geq n_0$. Let $r = 2^n$. Find the remainder when $29037 \cdot r$ is divided by $61517$. | 46,382 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(4199))))),
"result": Pow(Const(2), Ref("n")),
"Q": Mod(value=Mul(Const(29037), Ref("result")... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T02:31:57.976627Z | {
"verified": true,
"answer": 46382,
"timestamp": "2026-02-08T02:31:57.977609Z"
} | 490809 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1692
},
"timestamp": "2026-02-08T19:17:46.279Z",
"answer": 46382
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -0.92,
"mid": 0.86,
"hi": 2.4
} | ||
70c869 | nt_min_phi_inverse_v1_1978505735_8331 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 46$ and there exist positive integers $a \leq 14$ and $b \leq 6$ satisfying $t = 2a + 3b$. Let $\text{upper}$ be the number of elements in $T$. Let $k = 8$, and let $n_0$ be the smallest positive integer $n \leq \text{upper}$ such that $\phi(n) = k$, where... | 68,629 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=14)), Geq(left=Var(name='b'), right=Const(va... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.009 | 2026-02-08T20:47:57.003321Z | {
"verified": true,
"answer": 68629,
"timestamp": "2026-02-08T20:47:57.011829Z"
} | 95f05b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 3303
},
"timestamp": "2026-02-19T01:07:13.231Z",
"answer": 68629
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a86935 | antilemma_k2_v1_124444284_8227 | Define
$$
x = \sum_{k=1}^{342} \phi(k) \left\lfloor \frac{342}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute the remainder when $44121 \cdot x$ is divided by $53758$. | 26,409 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(342), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(342), Var("k"))))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(53758)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T09:36:32.017234Z | {
"verified": true,
"answer": 26409,
"timestamp": "2026-02-08T09:36:32.017756Z"
} | a74e27 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1316
},
"timestamp": "2026-02-14T05:11:32.779Z",
"answer": 26409
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a90ebe | geo_count_lattice_triangle_v1_1218484723_1031 | Let $A = \left|\{ t : \exists\, a,b \in \mathbb{Z},\ 1 \leq a \leq 11,\ 1 \leq b \leq 51,\ t = 2a + 3b + 14,\ 19 \leq t \leq 189 \}\right|$, $B = \left|\{ t_1 : \exists\, a,b \in \mathbb{Z},\ 1 \leq a \leq 571,\ 1 \leq b \leq 70,\ t_1 = 3a + 5b + 11,\ 19 \leq t_1 \leq 2074 \}\right|$, and $C = \left|\{ v : 32 \leq v \l... | 33,844 | graphs = [
Graph(
let={
"_c": Const(289),
"_m": Const(169),
"_n": Const(65866),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(... | GEOM | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM/QF_PSD_DISTINCT"
] | e187db | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"LIN_FORM",
"QF_PSD_DISTINCT"
] | 2 | 0.042 | 2026-02-25T02:45:07.248981Z | {
"verified": true,
"answer": 33844,
"timestamp": "2026-02-25T02:45:07.291284Z"
} | edb614 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 416,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T00:02:42.844Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 4.77,
"mid": 6.8,
"hi": 9.83
} | ||
a3ecc0 | sequence_lucas_compute_v1_548369836_133 | Let $m = 11901$ and $n = 67805$. Define $L$ to be the 20th Lucas number. Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq m$ and $\gcd\left(k, 1 + 2 + 3 + 4\right) = 1$. Let $C$ be the number of elements in $S$. Compute the remainder when $C - L$ is divided by $n$. | 57,439 | graphs = [
Graph(
let={
"_m": Const(11901),
"_n": Const(67805),
"n": Const(20),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Eq(G... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/C4"
] | db3d2e | sequence_lucas_compute_v1 | negation_mod | 4 | 0 | [
"C4",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T02:46:52.528023Z | {
"verified": true,
"answer": 57439,
"timestamp": "2026-02-08T02:46:52.529900Z"
} | b2bc8b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1246
},
"timestamp": "2026-02-08T19:54:07.567Z",
"answer": 57439
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -3.84,
"mid": -1.86,
"hi": 0.18
} | ||
c09739 | alg_poly3_sum_v1_1218484723_2416 | Compute the remainder when $\sum_{\substack{a=1}}^{91} \sum_{b=1}^{91} \left( -7b^3 - 18ab^2 - 12a^2b \right)$ is divided by $56020$, where the upper limit for $a$ is $\sum_{k=1}^{13} k$. | 36,828 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Summation(var="k", start=Const(1), end=Const(13), expr=Var("k"))), Geq(Var("b"), Const... | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | alg_poly3_sum_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.022 | 2026-02-25T04:12:51.620142Z | {
"verified": true,
"answer": 36828,
"timestamp": "2026-02-25T04:12:51.641999Z"
} | 71dcbe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 4903
},
"timestamp": "2026-03-29T04:37:05.307Z",
"answer": 36828
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
cfc98a | comb_count_derangements_v1_601307018_7486 | Let $n = \sum_{k=0}^{2} 2^{k}$ and let $D_n$ denote the number of derangements of $n$ elements. Compute $88804 - D_n$. | 86,950 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(0), end=Const(2), expr=Pow(Ref("_n"), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Sub(Const(88804), Ref("result")),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.005 | 2026-03-10T08:01:38.509062Z | {
"verified": true,
"answer": 86950,
"timestamp": "2026-03-10T08:01:38.514416Z"
} | 51f33c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 730
},
"timestamp": "2026-04-19T06:51:13.335Z",
"answer": 86950
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
ab0606 | nt_sum_divisors_compute_v1_1248542787_380 | Compute the sum of all positive divisors of $ 40804 $. | 72,121 | graphs = [
Graph(
let={
"n": Const(40804),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"MOBIUS_SUM",
"WILSON"
] | d9a889 | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"MOBIUS_SUM",
"WILSON"
] | 2 | 0.003 | 2026-02-08T03:05:06.098844Z | {
"verified": true,
"answer": 72121,
"timestamp": "2026-02-08T03:05:06.101724Z"
} | 318720 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 609
},
"timestamp": "2026-02-09T03:27:58.381Z",
"answer": 72121
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a7e1ba | comb_count_permutations_fixed_v1_1915831931_2398 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 2700$, $\gcd(p, q) = 1$, and $p < q$. Compute $\binom{7}{k} \cdot !(7 - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 70 | graphs = [
Graph(
let={
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=2700)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T16:46:06.273404Z | {
"verified": true,
"answer": 70,
"timestamp": "2026-02-08T16:46:06.276758Z"
} | 3c4d96 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1300
},
"timestamp": "2026-02-17T12:17:42.556Z",
"answer": 70
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
63f83f | nt_count_coprime_and_v1_784195855_4057 | Let $n = 32769$. Define $k_1$ to be the number of nonnegative integers $j \leq 32769$ such that $\binom{32769}{j}$ is odd. Let $k_2 = 9$. Let $A$ be the set of all positive integers $n \leq 24696$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. Let $r$ be the number of elements in $A$. Determine the value of the s... | 2,136 | graphs = [
Graph(
let={
"_n": Const(32769),
"upper": Const(24696),
"k1": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32769)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='non... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_coprime_and_v1 | null | 6 | 0 | [
"V8"
] | 1 | 2.777 | 2026-02-08T06:47:47.462440Z | {
"verified": true,
"answer": 2136,
"timestamp": "2026-02-08T06:47:50.239479Z"
} | 3272f2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 3210
},
"timestamp": "2026-02-13T04:56:38.000Z",
"answer": 2136
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
092795 | comb_factorial_compute_v1_1218484723_587 | Let $n$ be the minimum value of $-15a^2b -33ab^2 + 37a^3 + C \cdot b^3$ over all positive integers $a, b$ with $1 \le a, b \le 17$, where $C = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 25,\ 17a_1^4 + 68a_1b_1^3 + 68a_1^3b_1 + 102a_1^2b_1^2 + 17b_1^4 = 2720000 \}\right|$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_m": Const(17),
"_n": Const(37),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_m")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(17)))), expr=S... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/POLY3_MIN"
] | 02513d | comb_factorial_compute_v1 | null | 6 | 0 | [
"POLY3_MIN",
"POLY4_COUNT"
] | 2 | 0.006 | 2026-02-25T02:15:44.446324Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T02:15:44.452120Z"
} | 5ce569 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T23:21:29.993Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok_later"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma... | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
8c11bb | geo_count_lattice_triangle_v1_865884756_4292 | Let $A$ be the polygon with vertices at $(0, 0)$, $(128, 55)$, $(210, 222)$, and $(0, 222)$. The area of $A$ is equal to $\frac{1}{2}(a + 2 - b)$, where $a$ is twice the area of $A$ computed via a suitable formula, and $b$ is the number of lattice points on the boundary of $A$. Compute the value of $\frac{a + 2 - b}{2}... | 8,430 | graphs = [
Graph(
let={
"_n": Const(210),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=222)), Mul(Const(value=210), Sub(left=Const(value=0), right=Const(value=55))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=55))), GCD(a=Abs(arg=... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-08T17:51:58.682998Z | {
"verified": true,
"answer": 8430,
"timestamp": "2026-02-08T17:51:58.690331Z"
} | 3613b2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 5901
},
"timestamp": "2026-02-18T09:10:04.297Z",
"answer": 8430
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab0e29 | modular_min_linear_v1_1915831931_1835 | Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 18870336$. Let $b$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = 125316$. Let $m = 19117$. Determine the value of the smallest positive integer $x_2$ such that... | 4,040 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(18870336)))), expr=Sum(Var("x"), Var("y")))),
"b": MinOverSe... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_min_linear_v1 | null | 5 | 0 | [
"B3"
] | 1 | 4.175 | 2026-02-08T16:29:00.209282Z | {
"verified": true,
"answer": 4040,
"timestamp": "2026-02-08T16:29:04.384272Z"
} | dd4863 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2540
},
"timestamp": "2026-02-17T04:45:32.770Z",
"answer": 4040
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ff020d | comb_binomial_compute_v1_1874849503_275 | Let $n = 15$. Define $k$ as
$$
\sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Compute $\binom{n}{k}$. | 5,005 | graphs = [
Graph(
let={
"n": Const(15),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T12:55:12.263779Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-02-08T12:55:12.265272Z"
} | 154152 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 654
},
"timestamp": "2026-02-09T15:15:55.911Z",
"answer": 5005
},
{
"id... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
e12d8c | diophantine_fbi2_min_v1_1918700295_3956 | Let $k = 22$. Let $S$ be the set of positive integers $d$ such that $d$ divides $k$, $\frac{k}{d} \geq 2$, and $d$ is at least the number of positive integers at most $88$ that are divisible by $22$. Determine the minimum value of $d$ in $S$ that is at most $32$. Let this value be $d_{\text{min}}$. Compute the remainde... | 7,565 | graphs = [
Graph(
let={
"k": Const(22),
"upper": Const(32),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(88)), Divides(divisor=Const(2... | NT | null | EXTREMUM | sympy | C2 | [
"C2"
] | 9685eb | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.012 | 2026-02-08T09:03:47.480144Z | {
"verified": true,
"answer": 7565,
"timestamp": "2026-02-08T09:03:47.492070Z"
} | d5ebbe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 547
},
"timestamp": "2026-02-14T00:04:22.849Z",
"answer": 7565
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
c37b0e | nt_gcd_compute_v1_677425708_2703 | Let $a = 546227$ and $b = 943483$. Let $r = \gcd(a, b)$. Let $n$ be the largest prime number less than or equal to $14$. Let $Q$ be the remainder when $n - r$ is divided by $50322$. Find the value of $Q$. | 678 | graphs = [
Graph(
let={
"_n": Const(50322),
"a": Const(546227),
"b": Const(943483),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sub(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(14)),... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | nt_gcd_compute_v1 | negation_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T05:13:04.176400Z | {
"verified": true,
"answer": 678,
"timestamp": "2026-02-08T05:13:04.178054Z"
} | cc50ce | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 777
},
"timestamp": "2026-02-11T23:04:44.542Z",
"answer": 678
},
{
"id... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
d7bb8c | modular_mod_compute_v1_865884756_6610 | Let $a = -7921$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 262144$. Let $s$ be the minimum value of $x + y$ over all such pairs. Compute the remainder when $a$ is divided by $s$. | 271 | graphs = [
Graph(
let={
"a": Const(-7921),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(262144)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T19:19:43.763436Z | {
"verified": true,
"answer": 271,
"timestamp": "2026-02-08T19:19:43.766078Z"
} | 1077f9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 976
},
"timestamp": "2026-02-18T21:51:18.969Z",
"answer": 271
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0dfda3 | algebra_quadratic_discriminant_v1_717093673_1517 | Let $a = 3$, $b = 1$, and $c = 3$. Compute the discriminant $D = b^2 - 4ac$. Define
$$
\alpha = \begin{cases}
2 & \text{if } D > 0, \\
0 & \text{otherwise},
\end{cases}
\qquad
\beta = \begin{cases}
1 & \text{if } D = 0, \\
0 & \text{otherwise}.
\end{cases}
$$
Compute $\alpha + \beta$. | 0 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(1),
"c": Const(3),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Const(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"LTE_DIFF_P2",
"B3"
] | 853b4c | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"B3",
"COPRIME_PAIRS",
"LTE_DIFF_P2"
] | 3 | 0.052 | 2026-02-08T16:08:05.188866Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T16:08:05.240699Z"
} | 63523a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 183
},
"timestamp": "2026-02-16T06:58:38.526Z",
"answer": 0
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
687605 | comb_bell_compute_v1_1353956133_59 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 4610$ and $\binom{4610}{j}$ is odd. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the remainder when $44121 \cdot B_n$ is divided by $70876$. | 13,488 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4610)), Eq(Mod(value=Binom(n=Const(4610), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T11:17:10.929474Z | {
"verified": true,
"answer": 13488,
"timestamp": "2026-02-08T11:17:10.930362Z"
} | a58f27 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1512
},
"timestamp": "2026-02-24T13:15:12.422Z",
"answer": 13488
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
caf8ef | modular_count_residue_v1_1520064083_3039 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 61504$ and $n \equiv 2 \pmod{3}$. Let $B$ be the number of unordered pairs of positive integers $(p, q)$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $C$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $x... | 20,533 | graphs = [
Graph(
let={
"upper": Const(61504),
"m": Const(3),
"r": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"))))),
... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 9428c6 | modular_count_residue_v1 | mod_exp | 5 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 2.033 | 2026-02-08T05:25:43.542139Z | {
"verified": true,
"answer": 20533,
"timestamp": "2026-02-08T05:25:45.574798Z"
} | 23e8f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 811
},
"timestamp": "2026-02-12T08:40:45.132Z",
"answer": 20533
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f8bc63 | alg_poly_preperiod_count_v1_1218484723_2926 | For each integer $a$ with $0 \le a \le 29086$, define the sequence:
$$
\begin{align*}
N &= (2a^4 - 5a^3 + a^2 + 2a - 5) \bmod 17, \\
M &= (2N^4 - 5N^3 + N^2 + 2N - 5) \bmod 17, \\
R &= (2M^4 - 5M^3 + M^2 + 2M - 5) \bmod 17, \\
S &= (2R^4 - 5R^3 + R^2 + 2R - 5) \bmod 17, \\
T &= (2S^4 - 5S^3 + S^2 + 2S - 5) \bmod 17.
\e... | 11,977 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(4))), Mul(Const(-5), Pow(Var("a"), Const(3))), Pow(Var("a"), Const(2)), Mul(Const(2), Var("a")), Const(-5)), modulus=Const(17)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(4))), Mul(Const(-5), P... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.155 | 2026-02-25T04:40:51.457218Z | {
"verified": true,
"answer": 11977,
"timestamp": "2026-02-25T04:40:51.612462Z"
} | 042d42 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 346,
"completion_tokens": 9351
},
"timestamp": "2026-03-29T07:21:03.624Z",
"answer": 11977
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
3563ef | modular_mod_compute_v1_1456120455_27 | Let $a$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 102$. Compute the remainder when $a$ is divided by $11664$. | 2,601 | graphs = [
Graph(
let={
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(102)))), expr=Mul(Var("x"), Var("y")))),
"m": Const(11664),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T02:50:55.127830Z | {
"verified": true,
"answer": 2601,
"timestamp": "2026-02-08T02:50:55.129034Z"
} | 29440f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 350
},
"timestamp": "2026-02-08T19:52:43.238Z",
"answer": 2601
},
{
"id... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.16,
"mid": -6.07,
"hi": -3.82
} | ||
95a6c1 | diophantine_product_count_v1_898971024_2773 | Let $k = 360$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6400$. Let $u$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $r$ be the number of positive integers $x_1$ such that $1 \le x_1 \le u$, $x_1$ divides $360$, and $\frac{360}{x_1} \le u$. Compute $r$. | 20 | graphs = [
Graph(
let={
"k": Const(360),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6400)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"COUNT_COPRIME_GRID"
] | 2 | 0.286 | 2026-02-08T16:58:05.194670Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T16:58:05.480598Z"
} | e3de87 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1359
},
"timestamp": "2026-02-17T16:08:20.767Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e8d322 | nt_count_divisible_and_v1_1440796553_1171 | Let $d_1 = 4$. Let $d_2$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 9$. Let $U = 37260$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq U$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute $44121$ times the number of element... | 59,285 | graphs = [
Graph(
let={
"upper": Const(37260),
"d1": Const(4),
"d2": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(9)))), e... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 3 | 0 | [
"B3"
] | 1 | 1.426 | 2026-02-08T12:13:19.543037Z | {
"verified": true,
"answer": 59285,
"timestamp": "2026-02-08T12:13:20.969150Z"
} | 237ea9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 981
},
"timestamp": "2026-02-14T23:04:46.522Z",
"answer": 59285
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f3a362 | antilemma_k3_v1_1742523217_119 | Let $n = 72756$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 72,756 | graphs = [
Graph(
let={
"_n": Const(72756),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T02:53:16.030917Z | {
"verified": true,
"answer": 72756,
"timestamp": "2026-02-08T02:53:16.031322Z"
} | 68be46 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1102
},
"timestamp": "2026-02-09T13:52:23.944Z",
"answer": 72756
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST"... | {
"lo": -5.93,
"mid": -3.18,
"hi": -0.5
} | ||
c56712 | comb_count_permutations_fixed_v1_1440796553_1580 | Let $n = 9$. Let $k$ be the number of integers $t$ with $5 \leq t \leq 12$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!(n - k)$ denotes the number of derangements of $n - k$ elements. Compute the remainde... | 30,660 | graphs = [
Graph(
let={
"n": Const(9),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(nam... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T14:04:16.699016Z | {
"verified": true,
"answer": 30660,
"timestamp": "2026-02-08T14:04:16.700726Z"
} | cbc3eb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 2203
},
"timestamp": "2026-02-24T19:38:33.946Z",
"answer": 30660
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.