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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
bbd629 | alg_qf_psd_min_v1_1218484723_5431 | Let
$$C = \left|\left\{(a_2,b_2) : 1 \le a_2 \le 30,\ 1 \le b_2 \le 30,\ 5b_2^{2} + 10a_2b_2 + 5a_2^{2} = 3645\right\}\right|.$$
Define
$$L = \min\left\{36a_1b_1 + C\,a_1^{2} + 20b_1^{2} : 1 \le a_1 \le 29,\ 1 \le b_1 \le 29\right\}.$$
Let $V$ be the set of integers $v$ such that
$$v \ge L,\quad v \le 32800,$$
and ther... | 85,618 | graphs = [
Graph(
let={
"_c": Const(29),
"_m": Const(2),
"_n": Const(374),
"result": MinOverSet(set=MapOverSet(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)), ... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/QF_PSD_MIN/QF_PSD_DISTINCT"
] | 4ed755 | alg_qf_psd_min_v1 | null | 7 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_DISTINCT",
"QF_PSD_MIN"
] | 3 | 0.247 | 2026-02-25T06:59:50.248265Z | {
"verified": true,
"answer": 85618,
"timestamp": "2026-02-25T06:59:50.495019Z"
} | 780bc2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 429,
"completion_tokens": 16933
},
"timestamp": "2026-03-29T21:06:10.744Z",
"answer": 85618
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
a306b9 | nt_sum_divisors_mod_v1_655260480_2962 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 2822400$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Let $n$ be the minimum value in $T$. Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q... | 29,047 | 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(2822400)))), expr=Sum(Var("x"), Var("y")))),
"n": CountOver... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/L3B",
"B3/L3B"
] | a1b590 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"L3B"
] | 3 | 0.006 | 2026-02-08T17:05:32.061991Z | {
"verified": true,
"answer": 29047,
"timestamp": "2026-02-08T17:05:32.068042Z"
} | 29a2e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 3200
},
"timestamp": "2026-02-17T19:38:06.866Z",
"answer": 29047
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3B",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
10e196 | antilemma_k2_v1_1470522791_929 | Let $x = \sum_{k=1}^{351} \phi(k) \left\lfloor \frac{351}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $x + 2^{x \bmod 15} \bmod 95336$. | 61,840 | graphs = [
Graph(
let={
"_n": Const(351),
"x": Summation(var="k", start=Const(1), end=Const(351), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(15))), modulus=Const(95336))),
... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T13:18:54.790607Z | {
"verified": true,
"answer": 61840,
"timestamp": "2026-02-08T13:18:54.791720Z"
} | 5c4924 | 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": 983
},
"timestamp": "2026-02-15T13:11:03.127Z",
"answer": 61840
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
22b5f5 | diophantine_product_count_v1_168721529_661 | Let $p = 97$, $q = 37$, and $r = 31$. Define $n_1 = pqr$. Let $t = \mu(n_1)^2$, where $\mu$ denotes the M\"obius function, and let $n = t$. Let $m$ be the number of distinct prime factors of $n$. Define $k = 420$ and $u = 328 + m$. Compute the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$... | 22 | graphs = [
Graph(
let={
"p": Const(97),
"q": Const(37),
"r": Const(31),
"n1": Mul(Ref("p"), Ref("q"), Ref("r")),
"t": Pow(MoebiusMu(n=Ref(name='n1')), Const(2)),
"n": Ref("t"),
"m": SmallOmega(n=Ref(name='n')),
"... | NT | null | COUNT | sympy | MOBIUS_SQUAREFREE | [
"MOBIUS_SQUAREFREE",
"OMEGA_ZERO"
] | 55bf55 | diophantine_product_count_v1 | null | 4 | 2 | [
"MOBIUS_SQUAREFREE",
"OMEGA_ZERO"
] | 2 | 0.012 | 2026-02-08T13:10:46.298927Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T13:10:46.311001Z"
} | 2924c1 | 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": 4001
},
"timestamp": "2026-02-09T07:37:10.730Z",
"answer": 22
},
{
"id"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok"
},
{
"lemma": "OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"l... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
b7c6d0 | antilemma_sum_equals_v1_655260480_5417 | Let $m = 37249$ and define $n = 7 \times 8$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i, j \leq 54$ and $i + j = n$. Let $Q = m - x$. Find the value of $Q$. | 37,196 | graphs = [
Graph(
let={
"_m": Const(37249),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(8)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.006 | 2026-02-08T18:27:49.465468Z | {
"verified": true,
"answer": 37196,
"timestamp": "2026-02-08T18:27:49.471642Z"
} | 54f9bf | 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": 762
},
"timestamp": "2026-02-18T17:09:25.260Z",
"answer": 37196
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
0641a2 | sequence_count_fib_divisible_v1_798873815_75 | Let $S$ be the set of all real numbers $x$ such that $x^2 - 492x = 0$. Define $U$ to be the sum of all elements in $S$. Let $d = 7$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq U$ and the $n$th Fibonacci number is divisible by $d$. | 61 | graphs = [
Graph(
let={
"upper": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-492), Var("x"))), Const(0)))),
"d": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(V... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.021 | 2026-02-08T02:25:44.752969Z | {
"verified": true,
"answer": 61,
"timestamp": "2026-02-08T02:25:44.774223Z"
} | ff137e | 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": 3439
},
"timestamp": "2026-02-23T13:34:31.517Z",
"answer": 61
},
{
"id"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -1.87,
"mid": 0.03,
"hi": 1.69
} | ||
f5ccbf | antilemma_k2_v1_1918700295_2585 | Let $x$ be the sum of the roots of the equation $t^2 - 420t - 52000 = 0$. Compute
$$
\sum_{k=1}^{x} \phi(k) \left\lfloor \frac{420}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 88,410 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-420), Var("x")), Const(-52000)), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(420), Var("... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T08:00:16.643084Z | {
"verified": true,
"answer": 88410,
"timestamp": "2026-02-08T08:00:16.644004Z"
} | c2b7b4 | 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": 496
},
"timestamp": "2026-02-13T14:48:30.030Z",
"answer": 88410
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4a98ef | comb_binomial_compute_v1_601307018_5985 | Let $N = \binom{16}{7}$. Compute the number of positive integers $x \le 48475$ satisfying $x^2 - 91936x + 2107473255 \le 0$. Multiply this count by $N$, and find the remainder when the result is divided by $50382$. | 16,994 | graphs = [
Graph(
let={
"n": Const(16),
"k": Const(7),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Mul(CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(48475)), Leq(Sum(Mul(Const(1), Pow(Var("x"... | COMB | null | COMPUTE | sympy | QUADRATIC_INEQ | [
"QUADRATIC_INEQ"
] | d7447b | comb_binomial_compute_v1 | affine_mod | 4 | 0 | [
"QUADRATIC_INEQ"
] | 1 | 0.003 | 2026-03-10T06:33:43.854079Z | {
"verified": true,
"answer": 16994,
"timestamp": "2026-03-10T06:33:43.857071Z"
} | c523a3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1901
},
"timestamp": "2026-04-19T03:18:30.698Z",
"answer": 16994
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QUADRATIC_INEQ",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM... | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
3b0bbb | geo_visible_lattice_v1_124444284_6454 | Let $n = 180$. Let $L$ be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $c = 44199$ and define $Q$ to be the remainder when $c \cdot L$ is divided by $56018$. Compute $Q$. | 7,421 | graphs = [
Graph(
let={
"n": Const(180),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(44199),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(56018)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 3.178 | 2026-02-08T08:27:56.656201Z | {
"verified": true,
"answer": 7421,
"timestamp": "2026-02-08T08:27:59.833965Z"
} | 8e9cc0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T09:37:02.097Z",
"answer": 21828
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
88a82e | nt_sum_divisors_range_v1_717093673_644 | Let $n$ be a positive integer. Define $S$ to be the set of all prime numbers $n$ such that $2 \leq n \leq 5692$. Let $M$ be the largest element of $S$. Now consider the set of all positive integers $n_1$ such that $1 \leq n_1 \leq M$. For each such $n_1$, let $d(n_1)$ denote the number of positive divisors of $n_1$. Co... | 50,073 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(5692)), IsPrime(Var("n"))))),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_divisors_range_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.261 | 2026-02-08T15:35:00.660856Z | {
"verified": true,
"answer": 50073,
"timestamp": "2026-02-08T15:35:00.922291Z"
} | 229145 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 2992
},
"timestamp": "2026-02-16T10:32:03.904Z",
"answer": 50073
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0b754b | nt_count_coprime_and_v1_1431428450_917 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. For each such pair, compute $xy$, and let $k_1$ be the maximum value of $xy$ over all such pairs. Let $k_2 = 11$. Determine the number of positive integers $n \leq 38581$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. Let... | 47,102 | graphs = [
Graph(
let={
"upper": Const(38581),
"k1": 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")))... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_coprime_and_v1 | null | 4 | 0 | [
"B1"
] | 1 | 4.669 | 2026-02-08T13:47:04.274744Z | {
"verified": true,
"answer": 47102,
"timestamp": "2026-02-08T13:47:08.944022Z"
} | 88f3b0 | 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": 1559
},
"timestamp": "2026-02-15T20:32:42.478Z",
"answer": 47102
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ac9e22 | sequence_lucas_compute_v1_601307018_7824 | For each integer $a$ with $0 \le a \le 528$, define $R = (a^5 + 5a^4 + 5a^3 + 4a^2 - 5a + 2) \bmod 529$. Then define $S = (R^5 + 5R^4 + 5R^3 + 4R^2 - 5R + 2) \bmod d$, where $d = \min\{ |x - y| : x>0,\ y>0,\ xy = 578870 \}$. Let $n$ be the number of values of $a$ such that $S = a$ and $R \ne a$. Compute $L_n$, the $n$-... | 39,603 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(528)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))),
"result": Lucas(arg=Ref(nam... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF/POLY_ORBIT_HENSEL"
] | 91f215 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B3_DIFF",
"POLY_ORBIT_HENSEL"
] | 2 | 0.011 | 2026-03-10T08:23:00.817782Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-03-10T08:23:00.828545Z"
} | f9364a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 12668
},
"timestamp": "2026-04-19T07:35:41.867Z",
"answer": 39603
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
ec79b2_n | modular_modexp_compute_v1_601307018_3142 | A cryptographic protocol uses a key derived from $29^{729}$ modulo $77284$. What is the value of this key? | 23,257 | NT | null | COMPUTE | sympy | B1 | [
"POLY_ORBIT_LEGENDRE/MIN_PRIME_FACTOR",
"B3"
] | 450c60 | modular_modexp_compute_v1 | null | 3 | null | [
"B1",
"B3",
"MIN_PRIME_FACTOR",
"POLY_ORBIT_LEGENDRE"
] | 4 | 0.32 | 2026-03-10T03:43:26.258931Z | null | d35185 | ec79b2 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 14759
},
"timestamp": "2026-03-29T17:11:48.668Z",
"answer": 23257
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"st... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
a9fadf | nt_sum_totient_over_divisors_v1_1125832087_896 | Let $n = 83385$. Define $S$ as the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 3$, $1 \leq b \leq 3$, $5 \leq t \leq 15$, and $t = 3a + 2b$. Let $N$ be the number of elements in $S$. Let $R = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $D... | 321 | graphs = [
Graph(
let={
"n": Const(83385),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 341932 | nt_sum_totient_over_divisors_v1 | digits_weighted_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:21:24.569419Z | {
"verified": true,
"answer": 321,
"timestamp": "2026-02-08T03:21:24.572331Z"
} | f6476f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 318,
"completion_tokens": 1185
},
"timestamp": "2026-02-10T14:02:36.277Z",
"answer": 321
},
{
"id... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
b9672b | alg_poly4_min_v1_1419126231_27 | Let $M$ be the number of even positive integers $n$ with $1 \le n \le 1028$ such that $\gcd(n, 21) = 1$. Find the minimum value of $14960a^4 + 14960b^4 + 21120a^3b -21120ab^{\sum_{k=1}^{2} \varphi(k) \cdot \lfloor 2/k \rfloor} + 42240a^2b^2$ over all positive integers $a$, $b$ with $1 \le a \le 294$ and $1 \le b \le M$... | 72,160 | graphs = [
Graph(
let={
"_m": Const(21120),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1028)), Divides(divisor=Const(2), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"result": MinOverS... | NT | null | COMPUTE | sympy | L3B | [
"C5/K2"
] | ba793c | alg_poly4_min_v1 | null | 6 | 0 | [
"C5",
"K2",
"L3B"
] | 3 | 4.422 | 2026-02-25T09:33:30.819807Z | {
"verified": true,
"answer": 72160,
"timestamp": "2026-02-25T09:33:35.241983Z"
} | 3cee81 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 5875
},
"timestamp": "2026-03-30T06:34:22.000Z",
"answer": 72160
},
{
"... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
6895db | sequence_fibonacci_compute_v1_124444284_9696 | Let $n$ be the number of integers $t$ with $16 \leq t \leq 70$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 5$, $1 \leq b \leq 4$, and $t = 6a + 10b$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $44121... | 30,485 | graphs = [
Graph(
let={
"_n": Const(51368),
"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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T12:37:44.401763Z | {
"verified": true,
"answer": 30485,
"timestamp": "2026-02-08T12:37:44.404159Z"
} | e52bfa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1977
},
"timestamp": "2026-02-15T02:44:35.430Z",
"answer": 30485
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
698b09 | lin_form_endings_v1_784195855_9579 | Let $T$ be the set of all integers $t$ such that $28 \leq t \leq 184$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 10$, and $t = 16a + 12b$. Let $r$ be the number of elements in $T$. Let $k = 5873$ and let $s = k \cdot r$. Let $x$ be the remainder when $s$ is divided by $62619$. ... | 11,825 | 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=4)), Geq(left=Var(name='b'), right=C... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:53:56.538173Z | {
"verified": true,
"answer": 11825,
"timestamp": "2026-02-08T16:53:56.539350Z"
} | 3097fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 3257
},
"timestamp": "2026-02-17T15:32:33.309Z",
"answer": 11825
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
5a5de8 | nt_count_with_divisor_count_v1_397696148_2570 | Let $A$ be the number of positive integers $n \le 11025$ such that $n$ has exactly $15$ positive divisors.
Let $B$ be the sum of all real solutions $x$ to the equation $x^2 - 9x - 136 = 0$.
Compute $A^2 + 4A + B$. | 294 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(11025),
"div_count": Const(15),
"result": CountOverSet(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"))))),
... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 833c91 | nt_count_with_divisor_count_v1 | quadratic_mod | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.455 | 2026-02-08T13:24:58.411386Z | {
"verified": true,
"answer": 294,
"timestamp": "2026-02-08T13:24:58.866801Z"
} | c96fcf | 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": 1523
},
"timestamp": "2026-02-15T15:22:17.861Z",
"answer": 294
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
177740 | sequence_lucas_compute_v1_784195855_5832 | Let $m = 24$ and define $n = \sum_{k=1}^{24} \phi(k) \left\lfloor \frac{24}{k} \right\rfloor$. Let $n'$ be the number of positive integers $n''$ such that $1 \leq n'' \leq n$ and $10$ divides the Fibonacci number $F_{n''}$. Compute the smallest positive integer $k$ such that $F_k \equiv 0 \pmod{L_{n'} + 2}$, where $L_{... | 2,460 | graphs = [
Graph(
let={
"_m": Const(24),
"_n": Summation(var="k", start=Const(1), end=Const(24), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_m"), Var("k"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n... | NT | null | COMPUTE | sympy | K2 | [
"K2/COUNT_FIB_DIVISIBLE"
] | b8a166 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K2"
] | 2 | 0.002 | 2026-02-08T08:08:43.597497Z | {
"verified": true,
"answer": 2460,
"timestamp": "2026-02-08T08:08:43.599672Z"
} | 764d58 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 3488
},
"timestamp": "2026-02-13T15:17:14.446Z",
"answer": 2460
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
8444b2 | nt_min_with_divisor_count_v1_971394319_1560 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6718464$. Let $U$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $d = 2$. Compute the smallest positive integer $n$ such that $1 \leq n \leq U$ and $n$ has exactly $d$ positive divisors. | 2 | 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(6718464)))), expr=Sum(Var("x"), Var("y")))),
"div_count"... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"B3"
] | 0cd20d | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 8.451 | 2026-02-08T13:44:28.368921Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T13:44:36.820380Z"
} | cef843 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1454
},
"timestamp": "2026-02-15T20:21:37.237Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
29df4d | modular_sum_quadratic_residues_v1_1820931509_564 | Let $p$ be the largest prime number at most $319$. Let $r = \frac{p(p-1)}{4}$. Find the remainder when $44121 \cdot r$ is divided by $54094$. | 52,253 | graphs = [
Graph(
let={
"_n": Const(44121),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(319)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=M... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T11:46:31.806706Z | {
"verified": true,
"answer": 52253,
"timestamp": "2026-02-08T11:46:31.808887Z"
} | b8a549 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 1008
},
"timestamp": "2026-02-14T18:41:50.675Z",
"answer": 52253
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
167cbe | antilemma_coprime_grid_v1_865884756_192 | Let $c = \sum_{d \mid \gcd(17,19)} \mu(d)$, where $\mu$ denotes the Möbius function. Determine the number of ordered pairs $(i,j)$ with $1 \leq i \leq 35$ and $1 \leq j \leq 47$ such that $\gcd(i,j) = \varphi(c)$, where $\varphi$ is Euler's totient function. Compute this number. | 1,034 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=SumOverDivisors(n=GCD(a=Const(value=17), b=Const(value=19)), var='d', expr=MoebiusMu(n=Var(name='d'))))), domain=CartesianProduct(left=Integer... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 2c7d49 | antilemma_coprime_grid_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | 3 | 0.002 | 2026-02-08T15:15:23.145567Z | {
"verified": true,
"answer": 1034,
"timestamp": "2026-02-08T15:15:23.147835Z"
} | 16d8a0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 4925
},
"timestamp": "2026-02-10T05:23:55.999Z",
"answer": 1034
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"s... | {
"lo": -10,
"mid": -1.96,
"hi": 6.09
} | ||
4a6786 | algebra_poly_eval_v1_153355830_136 | Let $a$ be the number of integers $t$ with $7 \leq t \leq 24$ for which there exist positive integers $a'$ and $b'$ such that $1 \leq a' \leq 4$, $1 \leq b' \leq 3$, and $t = 3a' + 4b'$. Define $r = 6a^2 - 7a - 4$. Compute the remainder when $22891 \cdot r$ is divided by 53089. | 31,690 | graphs = [
Graph(
let={
"_n": Const(53089),
"a": 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=4)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T02:54:43.451639Z | {
"verified": true,
"answer": 31690,
"timestamp": "2026-02-08T02:54:43.454457Z"
} | ef8082 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2045
},
"timestamp": "2026-02-10T11:49:44.917Z",
"answer": 31690
},
{
"... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 3.46,
"hi": 4.91
} | ||
15ebec | comb_factorial_compute_v1_124444284_3592 | Let $n = 32904$. Define $k$ to be the number of integers $j$ with $0 \le j \le n$ such that the binomial coefficient $\binom{n}{j}$ is odd. Compute the value of $k!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(32904),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32904)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 3 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T05:27:59.646010Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T05:27:59.646791Z"
} | 659a72 | 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": 1715
},
"timestamp": "2026-02-24T03:48:10.782Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
7790bc | sequence_fibonacci_compute_v1_1248542787_614 | Let $n$ be the number of integers $t$ such that $33 \leq t \leq 123$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 4$, and $t = 9a + 12b + 12$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 75,025 | graphs = [
Graph(
let={
"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=7)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:16:00.187841Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T03:16:00.188784Z"
} | 70133a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 1910
},
"timestamp": "2026-02-09T06:14:04.384Z",
"answer": 75025
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
9693d2 | alg_qf_psd_sum_v1_1419126231_832 | Let $R$ be the minimum value of $41a^2 + 5b^2 - 28ab$ over all positive integers $a, b$ with $1 \le a, b \le 26$. Let
$$
S = \min_{\substack{1\le a_3\le 8\\1\le b_3\le 8}} \left(7a_3^3 + 18a_3^2 b_3 - 6a_3 b_3^2 + 9b_3^3\right),
$$
$$
T = \left|\left\{ (a_2, b_2) : 1 \le a_2, b_2 \le 35,\ 17a_2^4 + 68a_2^3 b_2 + 102a_2... | 781 | graphs = [
Graph(
let={
"_c": Const(9),
"_m": Const(9),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(26)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(26)))), expr=Su... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN/POLY3_MIN",
"POLY4_COUNT"
] | 49b09a | alg_qf_psd_sum_v1 | null | 6 | 0 | [
"POLY3_MIN",
"POLY4_COUNT",
"QF_PSD_MIN"
] | 3 | 0.118 | 2026-02-25T10:18:57.223883Z | {
"verified": true,
"answer": 781,
"timestamp": "2026-02-25T10:18:57.341422Z"
} | e928b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 440,
"completion_tokens": 8870
},
"timestamp": "2026-03-30T10:09:25.949Z",
"answer": 181
},
{
... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok_later"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
a4cb92 | sequence_count_fib_divisible_v1_655260480_1061 | Let $n$ be a positive integer such that $1 \leq n \leq 5983$ and $$
n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}.
$$
Let $A$ be the number of such integers $n$.
Let $B$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq A$ and $14$ divides the $n_1$-th Fibonacci number.
Compute the small... | 12 | graphs = [
Graph(
let={
"_n": Const(5983),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.035 | 2026-02-08T15:52:56.856441Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T15:52:56.891192Z"
} | f639dc | 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": 2403
},
"timestamp": "2026-02-16T15:14:58.365Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dcf72c | nt_num_divisors_compute_v1_1125832087_2099 | Let $m = \sum_{k=1}^{8} \phi(k) \left\lfloor \frac{8}{k} \right\rfloor$, and let $n = \sum_{k=1}^{m} \phi(k) \left\lfloor \frac{36}{k} \right\rfloor$. Let $d(n)$ denote the number of positive divisors of $n$. Find the remainder when $61369 \cdot d(n)$ is divided by 51935. | 9,338 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(36),
"n": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(8), Var("k"))))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var(... | NT | null | COMPUTE | sympy | K2 | [
"K2/K2"
] | ddede2 | nt_num_divisors_compute_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T04:21:07.284884Z | {
"verified": true,
"answer": 9338,
"timestamp": "2026-02-08T04:21:07.286838Z"
} | c6db48 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1352
},
"timestamp": "2026-02-10T16:22:00.606Z",
"answer": 9338
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
2daac6 | lte_diff_endings_v1_151522320_1439 | Let $a = 31$, $b = 7$, and $N = 243052$. Let $v_2(k)$ denote the largest integer $e$ such that $2^e$ divides $k$. Define $m = 5 - v_2(a - b)$. Compute the largest integer $x$ such that $x \le \frac{N}{2^m}$. | 60,763 | graphs = [
Graph(
let={
"a_val": Const(31),
"b_val": Const(7),
"p_val": Const(2),
"K_val": Const(5),
"N_val": Const(243052),
"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 | 0.001 | 2026-02-08T04:00:21.766988Z | {
"verified": true,
"answer": 60763,
"timestamp": "2026-02-08T04:00:21.768106Z"
} | 17fc7e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 473
},
"timestamp": "2026-02-18T07:56:54.379Z",
"answer": 60763
}
] | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
5cc418 | modular_count_residue_v1_798873815_338 | Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq 40320$ and $n$ is divisible by 4. Let $s = \sum_{d \mid \gcd(17,19)} \mu(d)$, where $\mu$ is the M\"obius function. Compute
$$
\sum_{n=s}^{|\text{result}|} \tau(n),
$$
where $\tau(n)$ denotes the number of positive divisors of $n$. | 94,514 | graphs = [
Graph(
let={
"upper": Const(40320),
"m": Const(4),
"r": Const(0),
"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 | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | modular_count_residue_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 1.269 | 2026-02-08T02:35:57.554208Z | {
"verified": true,
"answer": 94514,
"timestamp": "2026-02-08T02:35:58.822966Z"
} | 44e112 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 4457
},
"timestamp": "2026-02-08T19:23:29.781Z",
"answer": 94414
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 3.26,
"mid": 5.68,
"hi": 8.81
} | ||
c954b5 | nt_sum_totient_over_divisors_v1_1520064083_1163 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1478656$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Let $R = \sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ of $n$, and $\phi$ denotes Euler's totient function. Compute the remainder ... | 61,412 | graphs = [
Graph(
let={
"_n": Const(16231),
"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(1478656)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T03:49:03.264391Z | {
"verified": true,
"answer": 61412,
"timestamp": "2026-02-08T03:49:03.269159Z"
} | 177c3b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 2249
},
"timestamp": "2026-02-10T15:47:16.829Z",
"answer": 61412
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
47cc9e | antilemma_sum_equals_v1_677425708_4159 | Let $m = 36$. Determine the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Call this number $n$. Now consider the set of all ordered pairs $(i, j)$ with $1 \leq i \leq 18$ and $1 \leq j \leq 18$ such that $i + j = n$. Compute the remainder when $12229$ times the number of such ... | 32,607 | graphs = [
Graph(
let={
"_m": Const(36),
"_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")), R... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.01 | 2026-02-08T06:28:35.438386Z | {
"verified": true,
"answer": 32607,
"timestamp": "2026-02-08T06:28:35.447937Z"
} | 10e837 | 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": 1227
},
"timestamp": "2026-02-24T06:16:22.905Z",
"answer": 32607
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
7b26a8 | nt_count_coprime_and_v1_1742523217_2633 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 86316$, $\gcd(n, 4) = 1$, and $\gcd(n, 9) = 1$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 93025$. Define $c$ to be the minimum value of $x + y$ over all pairs $(x, y) \in T$. Compute the remainder when $c - |S|$ ... | 53,831 | graphs = [
Graph(
let={
"_n": Const(81993),
"upper": Const(86316),
"k1": Const(4),
"k2": Const(9),
"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... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | nt_count_coprime_and_v1 | negation_mod | 6 | 0 | [
"B3"
] | 1 | 8.711 | 2026-02-08T04:53:27.049017Z | {
"verified": true,
"answer": 53831,
"timestamp": "2026-02-08T04:53:35.760182Z"
} | 4969c5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1282
},
"timestamp": "2026-02-11T22:20:19.672Z",
"answer": 53831
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
845999 | diophantine_fbi2_min_v1_784195855_1322 | Let $m = 2$ and $n = 61920$. Define $T$ as the set of all integers $t$ such that $7 \leq t \leq 85$ and there exist positive integers $a \in [1, 5]$, $b \in [1, 15]$ satisfying $t = 2a + 5b$. Let $c$ be the number of elements in $T$. Define $S$ as the set of all integers $d$ such that $d \geq 2$ and $d$ divides $c$. Le... | 3 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(61920),
"k": Const(33),
"upper": Const(43),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Co... | NT | null | EXTREMUM | sympy | L3C | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"L3C",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.03 | 2026-02-08T04:57:49.860191Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T04:57:49.890084Z"
} | b41d0e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 335,
"completion_tokens": 2786
},
"timestamp": "2026-02-11T22:34:30.817Z",
"answer": 3
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTO... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
0ce206 | algebra_poly_eval_v1_2051736721_611 | Let $m = 65728$. Let $n$ be the smallest divisor of $6125$ that is at least $2$. Define $x$ to be the number of nonnegative integers $j$ such that $0 \le j \le m$ and $\binom{65728}{j}$ is odd. Compute $x^3 - 5x^2 + nx + 8$. | 240 | graphs = [
Graph(
let={
"_m": Const(65728),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(6125))))),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), L... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/V8"
] | 31f1b8 | algebra_poly_eval_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"V8"
] | 2 | 0.005 | 2026-02-08T15:33:48.455323Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T15:33:48.459904Z"
} | d3d772 | 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": 1443
},
"timestamp": "2026-02-16T09:07:29.982Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
34d3b7 | nt_count_divisible_and_v1_1470522791_1118 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 36$. Let $d_1$ be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $d_2 = 18$. Define $N$ to be the number of positive integers $n$ such that $1 \leq n \leq 71712$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. ... | 1,992 | graphs = [
Graph(
let={
"upper": Const(71712),
"d1": 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(36)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 2.424 | 2026-02-08T13:26:20.392357Z | {
"verified": true,
"answer": 1992,
"timestamp": "2026-02-08T13:26:22.816329Z"
} | 853b65 | 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": 834
},
"timestamp": "2026-02-15T15:38:38.821Z",
"answer": 1992
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
0e5c9e | algebra_poly_eval_v1_601307018_872 | Let $x$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that
$$
64a^3 + 144a^2b + 27b^3 + C \cdot ab^2 = 1092727,
$$
where $C = \left|\left\{ v : 36 \le v \le 4736 \text{ and } \exists\, a,b \in \{1,\dots,11\} \text{ such that } 17b^2 + 41a^2 - 22ab = v \right\}\right|$. Let $... | 2,323 | graphs = [
Graph(
let={
"_m": Const(36),
"_n": Const(38),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(64),... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"QF_PSD_DISTINCT/POLY3_COUNT"
] | 5dc0d1 | algebra_poly_eval_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 3 | 17.762 | 2026-03-10T01:29:16.189844Z | {
"verified": true,
"answer": 2323,
"timestamp": "2026-03-10T01:29:33.951660Z"
} | 0b1d31 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 303,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T00:30:41.099Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 1.27,
"mid": 3.84,
"hi": 5.91
} | ||
fdbb48 | sequence_count_fib_divisible_v1_238844314_793 | Let $ S $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq 527 $ and $ 4 $ divides the $ n $-th Fibonacci number. Let $ r $ be the number of elements in $ S $. Compute $ 34225 - r $. | 34,138 | graphs = [
Graph(
let={
"upper": Const(527),
"d": Const(4),
"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')))))),
"Q": Sub(... | NT | null | COUNT | sympy | C3 | [
"C3/MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | aabfb0 | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"C3",
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | 3 | 0.076 | 2026-02-08T13:37:22.049595Z | {
"verified": true,
"answer": 34138,
"timestamp": "2026-02-08T13:37:22.125208Z"
} | 07fcbb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 640
},
"timestamp": "2026-02-15T18:35:27.901Z",
"answer": 34138
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
ad6ffc | comb_count_partitions_v1_1978505735_1685 | Let $n$ be the number of integers $t$ such that $16 \leq t \leq 108$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 13$, $1 \leq b \leq 3$, and $t = 6a + 10b$. Define $p(n)$ to be the number of integer partitions of $n$. Compute $p(n)$. | 31,185 | graphs = [
Graph(
let={
"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=13)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T16:21:17.236456Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T16:21:17.244343Z"
} | 05a702 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1599
},
"timestamp": "2026-02-24T20:36:58.255Z",
"answer": 31185
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
9431a4 | geo_count_lattice_rect_v1_655260480_5 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 81$ and $0 \leq y \leq 165$. | 13,612 | graphs = [
Graph(
let={
"a": Const(81),
"b": Const(165),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T15:07:46.144907Z | {
"verified": true,
"answer": 13612,
"timestamp": "2026-02-08T15:07:46.146613Z"
} | 2c4f1c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 226
},
"timestamp": "2026-02-24T19:54:17.831Z",
"answer": 13612
},
{
"i... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.29
} | ||||
a1aee7 | nt_count_coprime_and_v1_48377204_2637 | Let $u = 16030$. Let $k_1$ be the sum of all real solutions $x$ to the equation $x^2 - 11x - 840 = 0$. Let $k_2 = 13$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 13,452 | graphs = [
Graph(
let={
"upper": Const(16030),
"k1": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-11), Var("x")), Const(-840)), Const(0)))),
"k2": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n")... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_coprime_and_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 3.249 | 2026-02-08T16:52:01.225043Z | {
"verified": true,
"answer": 13452,
"timestamp": "2026-02-08T16:52:04.474338Z"
} | 61fa94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 845
},
"timestamp": "2026-02-17T14:32:23.927Z",
"answer": 13452
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2e2c12 | modular_min_linear_v1_1742523217_1165 | Let $a = 39949$, $b = 38934$, and $m = 43133$. Define $r$ to be the smallest positive integer $x$ such that $1 \leq x \leq m$ and
$$
ax \equiv b \pmod{m}.
$$
Compute the remainder when
$$
\sum_{k=1}^{8} \phi(k) \left\lfloor \frac{8}{k} \right\rfloor - r
$$
is divided by $50180$. | 19,477 | graphs = [
Graph(
let={
"a": Const(39949),
"b": Const(38934),
"m": Const(43133),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Ref("b... | NT | null | EXTREMUM | sympy | K2 | [
"K2"
] | 9468ae | modular_min_linear_v1 | negation_mod | 6 | 0 | [
"K2"
] | 1 | 2.597 | 2026-02-08T03:29:31.584371Z | {
"verified": true,
"answer": 19477,
"timestamp": "2026-02-08T03:29:34.181620Z"
} | 11859c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 2357
},
"timestamp": "2026-02-09T11:59:41.371Z",
"answer": 19477
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3451f2 | nt_count_divisors_in_range_v1_1978505735_6292 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 75$ and $1 \leq j \leq 164$ such that $\gcd(i,j) = 1$. Let $\text{result}$ be the number of positive divisors $d$ of $n$ such that $1 \leq d \leq 287$. Compute $Q = \sum_{n_1=1}^{\text{result}} \tau(n_1)$, where $\tau(n_1)$ is the n... | 188 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(75)), right=IntegerRange(start=Const(1), end=Const(164))))),
"... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.006 | 2026-02-08T19:32:33.716845Z | {
"verified": true,
"answer": 188,
"timestamp": "2026-02-08T19:32:33.722633Z"
} | 74de4b | 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": 6322
},
"timestamp": "2026-02-18T22:38:48.715Z",
"answer": 188
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7b76e1_n | alg_poly4_count_v1_1218484723_2101 | A music sequencer uses patterns where step size $a$ can be any integer from 1 to $A$, and tempo multiplier $b$ ranges from 1 to 385. The value $A$ equals the number of distinct beat offsets achievable as $15a + 6b$ within a performance window from beat 21 to 1185, with $a \le 11$, $b \le 170$. A configuration is valid ... | 385 | ALG | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"LIN_FORM"
] | 7b2633 | alg_poly4_count_v1 | null | 5 | null | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 2 | 9.42 | 2026-02-25T03:48:25.842360Z | null | b9cb34 | 7b76e1 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 4440
},
"timestamp": "2026-03-30T17:50:13.283Z",
"answer": 385
},
{
"id... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
d1db55 | comb_catalan_compute_v1_53965629_64 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 11$, $1 \le i \le 10$, and $1 \le j \le 11$. Define $a = C_n$, where $C_n$ denotes the $n$-th Catalan number. Let
$$
b = \varphi\left(|a| + \binom{7}{7}\right), \quad c = \tau\left(|a| + \binom{9}{9}\right),
$$
where $\varphi(n)$ den... | 26,964 | graphs = [
Graph(
let={
"_n": Const(11),
"n": 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(10)), right=IntegerRange(start=Const(1), end=Con... | COMB | NT | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_N"
] | eb8b36 | comb_catalan_compute_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_N"
] | 2 | 0.025 | 2026-02-08T11:15:48.256986Z | {
"verified": true,
"answer": 26964,
"timestamp": "2026-02-08T11:15:48.281941Z"
} | 3cf2f3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 1880
},
"timestamp": "2026-02-09T11:32:38.455Z",
"answer": 26964
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
745882 | comb_sum_binomial_row_v1_1742523217_1291 | Let $n$ be the sum of all integers $k$ from $\sum_{d \mid \gcd(7,11)} \mu(d)$ to $5$, inclusive. Let $r$ be the value of $\left( \sum_{d \mid 2} \phi(d) \right)^n$. Compute $86436 - r$. | 53,668 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=SumOverDivisors(n=GCD(a=Const(value=7), b=Const(value=11)), var='d', expr=MoebiusMu(n=Var(name='d'))), end=Const(5), expr=Var("k")),
"result": Pow(SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPh... | NT | null | SUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"SUM_ARITHMETIC",
"K3"
] | d07224 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"K3",
"MOBIUS_COPRIME",
"SUM_ARITHMETIC"
] | 3 | 0.002 | 2026-02-08T03:35:51.143135Z | {
"verified": true,
"answer": 53668,
"timestamp": "2026-02-08T03:35:51.145616Z"
} | fe0c9b | 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": 464
},
"timestamp": "2026-02-10T06:13:28.533Z",
"answer": 53668
},
{
"i... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
925166 | antilemma_sum_equals_v1_124444284_9077 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 53$, $1 \leq j \leq 54$, and $i + j = 54$. Compute $x$. | 53 | graphs = [
Graph(
let={
"_n": Const(54),
"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(53)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.055 | 2026-02-08T12:11:22.411848Z | {
"verified": true,
"answer": 53,
"timestamp": "2026-02-08T12:11:22.467006Z"
} | 3ac8aa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 252
},
"timestamp": "2026-02-24T15:17:23.430Z",
"answer": 53
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
24a47d | antilemma_k3_v1_168721529_1395 | Let $n = 50672$. Compute the remainder when $13689 - \sum_{d \mid n} \phi(d)$ is divided by $84830$, where $\phi$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $n$. | 47,847 | graphs = [
Graph(
let={
"_n": Const(50672),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(13689), Ref("x")), modulus=Const(84830)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:40:52.065718Z | {
"verified": true,
"answer": 47847,
"timestamp": "2026-02-08T13:40:52.066513Z"
} | ac9e9a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 934
},
"timestamp": "2026-02-09T16:27:06.209Z",
"answer": 47847
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
e1e306 | lin_form_endings_v1_971394319_1986 | Let $a = 21$, $b = 6$, $A = 41$, and $B = 29$. Let $g = \gcd(a, b)$, and define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. The size of a certain set $T$ is given by $|T| = a'A + b'B - a'b'$. The total number of elements under consideration is $aA + bB - a - b + 1$. ... | 66,510 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(6),
"A_val": Const(41),
"B_val": Const(29),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T14:04:33.183486Z | {
"verified": true,
"answer": 66510,
"timestamp": "2026-02-08T14:04:33.184316Z"
} | 685fd3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1241
},
"timestamp": "2026-02-15T23:41:36.110Z",
"answer": 66510
},
... | 1 | [
{
"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": "V8_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
069813 | comb_binomial_compute_v1_1218484723_4253 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $64a^3 + 108a^2b + 144ab^2 + 27b^3 = 970299$. Compute $\binom{12}{k}$. | 792 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(12),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(108), ... | COMB | null | COMPUTE | sympy | SUM_GEOM | [
"POLY3_COUNT"
] | 355dbe | comb_binomial_compute_v1 | null | 5 | 0 | [
"POLY3_COUNT",
"SUM_GEOM"
] | 2 | 0.017 | 2026-02-25T05:53:53.712555Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-25T05:53:53.730046Z"
} | 753478 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T14:36:03.519Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V8",
"... | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
0a574f | comb_count_partitions_v1_1520064083_6349 | Let $S$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 11$, $1 \le b \le 4$, $15 \le t \le 66$, and $t = 3a + 7b + 5$. Let $n$ be the number of elements in $S$. Let $p(n)$ denote the number of ways to write $n$ as a sum of positive integers, disregarding order. Comp... | 37,338 | graphs = [
Graph(
let={
"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=11)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:01:56.354051Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T08:01:56.355484Z"
} | 22d3cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T08:50:57.142Z",
"answer": 31185
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
44aca4 | modular_min_modexp_v1_1874849503_3 | Let $T$ be the set of all positive integers $t$ such that $7 \leq t \leq 867$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 159$, $1 \leq b \leq 36$, and $t = 5a + 2b$. Let $m = |T|$. Determine the smallest positive integer $x$ such that $1 \leq x \leq 428$ and $$13^x \equiv 623 \pmod{m}.$$ Compute the... | 51 | graphs = [
Graph(
let={
"a": Const(13),
"b": Const(623),
"m": 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=Con... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM"
] | 7b2633 | modular_min_modexp_v1 | null | 7 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.17 | 2026-02-08T12:45:48.090943Z | {
"verified": true,
"answer": 51,
"timestamp": "2026-02-08T12:45:48.260777Z"
} | 4cee67 | 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": 4529
},
"timestamp": "2026-02-10T01:30:48.661Z",
"answer": 51
},
{
"id... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
d747ab | geo_count_lattice_rect_v1_458359167_1563 | Compute the number of lattice points $(x, y)$ such that $0 \le x \le 121$ and $0 \le y \le 91$. | 11,224 | graphs = [
Graph(
let={
"a": Const(121),
"b": Const(91),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T04:45:26.153264Z | {
"verified": true,
"answer": 11224,
"timestamp": "2026-02-08T04:45:26.154712Z"
} | acf5b8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 271
},
"timestamp": "2026-02-24T01:41:05.241Z",
"answer": 11224
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||||
ee51aa | nt_count_with_divisor_count_v1_349078426_742 | Let $n = 2$. Let $d_0$ be the smallest divisor of $11011$ that is at least $n$. Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq 69696$ and the number of positive divisors of $k$ is equal to $d_0$. Let $c = 24947$. Compute $c \cdot |S|$. | 74,841 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(69696),
"div_count": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(11011))))),
"result": CountOverSet(set=SolutionsSet(var=Var("... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.773 | 2026-02-08T13:15:59.350291Z | {
"verified": true,
"answer": 74841,
"timestamp": "2026-02-08T13:16:03.123779Z"
} | 7b1c26 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 1584
},
"timestamp": "2026-02-15T11:32:33.718Z",
"answer": 74841
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a7de30 | nt_max_prime_below_v1_677425708_1494 | Let $t$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all prime numbers $n$ such that $t \leq n \leq 29241$. Determine the value of the largest element in $S$. | 29,231 | graphs = [
Graph(
let={
"upper": Const(29241),
"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 | 0.663 | 2026-02-08T04:13:43.223029Z | {
"verified": true,
"answer": 29231,
"timestamp": "2026-02-08T04:13:43.886433Z"
} | c5e3f7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 5205
},
"timestamp": "2026-02-10T15:59:37.352Z",
"answer": 29231
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
c9111f | geo_count_lattice_triangle_v1_2051736721_890 | Let $A$ be the absolute value of $120 \cdot 128 + 210 \cdot (0 - 55)$. Let $B$ be the sum of $\gcd(120, \left| \sum_{k=1}^{10} k \right|)$, $\gcd(|210 - 120|, |128 - 55|)$, and $\gcd(|0 - 210|, |0 - 128|)$. Compute $\frac{A + 2 - B}{2}$. | 1,902 | graphs = [
Graph(
let={
"_n": Const(210),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=128)), Mul(Const(value=210), Sub(left=Const(value=0), right=Const(value=55))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Summation(expr=Var(name='k'), var... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.009 | 2026-02-08T15:44:02.923811Z | {
"verified": true,
"answer": 1902,
"timestamp": "2026-02-08T15:44:02.932723Z"
} | cf1e03 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 520
},
"timestamp": "2026-02-16T06:17:55.914Z",
"answer": 1901
},
{
"id": 11,... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
7cdda8 | nt_sum_divisors_mod_v1_1520064083_9726 | Let $n$ be the number of positive integers at most $35272$ that are divisible by 8 and relatively prime to 21. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $\sigma(n) \bmod 10891 + 2$. | 150 | graphs = [
Graph(
let={
"_n": Const(21),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(35272)), Divides(divisor=Const(8), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"M": Const(10891),
... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.004 | 2026-02-08T10:59:22.652673Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T10:59:22.656400Z"
} | 11d33a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 2581
},
"timestamp": "2026-02-14T09:48:35.734Z",
"answer": 150
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
49384c | diophantine_fbi2_min_v1_1520064083_8313 | Let $d_0$ be the smallest integer $d$ such that $4 \leq d \leq 43$, $d$ divides $33$, and $\frac{33}{d} \geq 3$. Let $N$ be the number of integers $t$ such that $10 \leq t \leq 217$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 19$, $1 \leq b \leq 28$, and $t = 7a + 3b$. Compute $N - d_0$. | 185 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(33),
"upper": Const(43),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), ... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | diophantine_fbi2_min_v1 | negation_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T10:08:10.000728Z | {
"verified": true,
"answer": 185,
"timestamp": "2026-02-08T10:08:10.005843Z"
} | 960e4d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 4906
},
"timestamp": "2026-02-14T06:31:37.531Z",
"answer": 185
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
595cda | nt_count_gcd_equals_v1_1125832087_2251 | Let $n = 82544$. Define $d$ to be the number of nonnegative integers $j$ such that $0 \leq j \leq 82544$ and $\binom{82544}{j}$ is odd. Let $k = 64$ and $\text{upper} = 11449$. Compute the number of positive integers $n$ such that $1 \leq n \leq 11449$ and $\gcd(n, 64) = d$. | 178 | graphs = [
Graph(
let={
"_n": Const(82544),
"upper": Const(11449),
"k": Const(64),
"d": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(82544)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"V8"
] | 1 | 1.039 | 2026-02-08T04:25:43.740013Z | {
"verified": true,
"answer": 178,
"timestamp": "2026-02-08T04:25:44.779286Z"
} | 9b2989 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 892
},
"timestamp": "2026-02-10T16:46:17.622Z",
"answer": 178
},
{
"id... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
5f4508 | antilemma_k2_v1_151522320_1098 | Let $m = 11$ and $n = 11$. Compute $$
\sum_{k=1}^{A} \varphi(k) \left\lfloor \frac{B}{k} \right\rfloor,
$$ where $A = \sum_{k=1}^{11} \varphi(k) \left\lfloor \frac{11}{k} \right\rfloor$ and $B = \sum_{k=1}^{11} k$. | 2,211 | graphs = [
Graph(
let={
"_m": Const(11),
"_n": Const(11),
"x": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Const(11), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_m"), Var("k"))))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var... | NT | COMB | COMPUTE | sympy | K13 | [
"SUM_ARITHMETIC/K2",
"K2/K2",
"K2"
] | 816e12 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.003 | 2026-02-08T03:48:07.146966Z | {
"verified": true,
"answer": 2211,
"timestamp": "2026-02-08T03:48:07.150404Z"
} | 0d1a92 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 5999
},
"timestamp": "2026-02-10T15:48:42.431Z",
"answer": 2211
},
{
"i... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
d2b199 | sequence_fibonacci_compute_v1_124444284_3577 | Let $n$ be the number of integers $t$ such that $13 \leq t \leq 34$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 7$, and $t = 3a + 2b + 8$. Compute the $n$-th Fibonacci number. | 6,765 | graphs = [
Graph(
let={
"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=4)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:27:44.081505Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T05:27:44.082308Z"
} | 1450d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1991
},
"timestamp": "2026-02-12T09:36:16.578Z",
"answer": 6765
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f9772b | antilemma_cartesian_v1_898971024_237 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 16 and $b$ is an integer from 1 to 23. Compute $$ x + \phi\left(|x| + \binom{5}{5}\right) + \tau\left(|x| + 0!\right), $$ where $\phi(n)$ denotes Euler's totient function and $\tau(n)$ denotes the number of positive divisors of $n$. Comput... | 614 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(23)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Binom(n=Const(5), k=Const(5)))), NumDivisors(n=Sum(Abs(arg=R... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0",
"ONE_BINOM_N"
] | 7decc2 | antilemma_cartesian_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_N",
"ONE_FACTORIAL_0"
] | 3 | 0.002 | 2026-02-08T15:18:25.898632Z | {
"verified": true,
"answer": 614,
"timestamp": "2026-02-08T15:18:25.900820Z"
} | e5b93b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 908
},
"timestamp": "2026-02-24T20:24:12.441Z",
"answer": 614
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "ONE_FACTORIAL... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
d836e2 | nt_euler_phi_compute_v1_349078426_1339 | Let $n = 80000$. Define $\phi(n)$ to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Let $c$ be the number of integers $n$ with $1 \leq n \leq 100$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $Q$ be the sum of $\left(i+1\right)^2$ times the $i... | 127 | graphs = [
Graph(
let={
"n": Const(80000),
"result": EulerPhi(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(100)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | e41f22 | nt_euler_phi_compute_v1 | digits_weighted_mod | 4 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T13:33:40.209038Z | {
"verified": true,
"answer": 127,
"timestamp": "2026-02-08T13:33:40.211330Z"
} | e8b807 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1615
},
"timestamp": "2026-02-15T17:54:01.911Z",
"answer": 127
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ba7b42 | nt_sum_totient_over_divisors_v1_898971024_1409 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 5635876$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 4,748 | 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(5635876)))), expr=Sum(Var("x"), Var("y")))),
"result": SumOv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T16:06:19.377179Z | {
"verified": true,
"answer": 4748,
"timestamp": "2026-02-08T16:06:19.382089Z"
} | 590a20 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1097
},
"timestamp": "2026-02-16T21:51:11.820Z",
"answer": 4748
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ad9ef5 | geo_count_lattice_rect_v1_124444284_7582 | Let $a = 300$ and $b = 177$. Define $\mathcal{R}$ to be the set of all lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $N$ be the number of points in $\mathcal{R}$. Compute the remainder when $82153 \cdot N$ is divided by $51842$. | 266 | graphs = [
Graph(
let={
"a": Const(300),
"b": Const(177),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(82153), Ref("result")), modulus=Const(51842)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 5 | 0 | null | null | 0.002 | 2026-02-08T09:11:47.264746Z | {
"verified": true,
"answer": 266,
"timestamp": "2026-02-08T09:11:47.266739Z"
} | 211ec9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1568
},
"timestamp": "2026-02-24T10:52:41.743Z",
"answer": 266
},
{
"id... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
ccd2e7 | nt_count_digit_sum_v1_124444284_1655 | Let $N = 5184$. Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = N$. For each such pair, compute $x + y$, and let $T$ be the set of all such sums. Let $s$ be the minimum value in $T$. Now, let $U$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = s$. For ... | 4,030 | graphs = [
Graph(
let={
"_n": Const(5184),
"upper": Const(70756),
"target_sum": 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")), Min... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | nt_count_digit_sum_v1 | null | 7 | 0 | [
"B3"
] | 1 | 3.72 | 2026-02-08T04:04:26.823962Z | {
"verified": true,
"answer": 4030,
"timestamp": "2026-02-08T04:04:30.544222Z"
} | f4bd29 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 6066
},
"timestamp": "2026-02-10T15:21:51.798Z",
"answer": 4030
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
84ffbd | diophantine_fbi2_count_v1_2051736721_4464 | Compute the number of positive integers $d$ such that $6 \leq d \leq 133$, $d$ divides 360, and $4 \leq \frac{360}{d} \leq 131$. | 16 | graphs = [
Graph(
let={
"_n": Const(6),
"k": Const(360),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(133)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(4)), Leq(Div(... | NT | null | COUNT | sympy | B3 | [
"K2"
] | 6897ab | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3",
"K2"
] | 2 | 4.012 | 2026-02-08T18:00:15.364945Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T18:00:19.376499Z"
} | ad93ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 1342
},
"timestamp": "2026-02-18T11:32:05.107Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8137ff | diophantine_product_count_v1_971394319_1029 | Let $n = 14641$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = n$. Determine the number of positive integers $x$ such that $1 \le x \le s$, $x$ divides $840$, and $\frac{840}{x} \le s$. | 26 | graphs = [
Graph(
let={
"_n": Const(14641),
"k": Const(840),
"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 | 6 | 0 | [
"B3"
] | 1 | 0.011 | 2026-02-08T13:26:46.979551Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T13:26:46.990062Z"
} | eb8bd6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 2755
},
"timestamp": "2026-02-15T15:52:21.973Z",
"answer": 26
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ed4eef | comb_factorial_compute_v1_1218484723_3969 | Let $C$ be the number of integers $t$ in $[24, 2079]$ that can be expressed as $t = 3a + 5b + 16$ for some integers $a, b$ with $1 \le a \le 481$, $1 \le b \le 124$. Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 40$ such that $2b^2 - 4ab + 2a^2 = C$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Leq(Var("a"), Var("b"))... | COMB | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"LIN_FORM/QF_PSD_ORBIT"
] | d77f66 | comb_factorial_compute_v1 | null | 5 | 0 | [
"LIN_FORM",
"POLY_ORBIT_COUNT",
"QF_PSD_ORBIT"
] | 3 | 9.416 | 2026-02-25T05:34:49.007934Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T05:34:58.423626Z"
} | 435ef2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 26674
},
"timestamp": "2026-03-29T13:12:04.907Z",
"answer": 40320
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
7d1966 | nt_count_divisible_v1_677425708_341 | Let $a$ and $b$ be positive integers such that $\gcd(a, b) = 1$. Define $\mu(n)$ to be the Möbius function. Compute the number of positive integers $n$ such that $n \leq 66795$, $n$ is divisible by 21, and $$n \geq \sum_{d \mid \gcd(13,17)} \mu(d).$$ Determine the value of this count. | 3,180 | graphs = [
Graph(
let={
"upper": Const(66795),
"divisor": Const(21),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=13), b=Const(value=17)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Re... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_divisible_v1 | null | 2 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 2.091 | 2026-02-08T03:13:52.288243Z | {
"verified": true,
"answer": 3180,
"timestamp": "2026-02-08T03:13:54.379529Z"
} | 55df50 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 540
},
"timestamp": "2026-02-08T20:27:51.409Z",
"answer": 3180
},
{
"id... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"statu... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
f4c6ed | geo_count_lattice_rect_v1_238844314_204 | Let $a = 49$ and $b = 87$. Define $L$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Compute $12321 - L$. | 7,921 | graphs = [
Graph(
let={
"a": Const(49),
"b": Const(87),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Sub(Const(12321), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T13:10:23.783477Z | {
"verified": true,
"answer": 7921,
"timestamp": "2026-02-08T13:10:23.785412Z"
} | 594772 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 318
},
"timestamp": "2026-02-24T17:20:08.169Z",
"answer": 7921
},
{
"id... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
2afb53 | nt_sum_divisors_mod_v1_1742523217_4448 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 396900$. Define $n$ as the minimum value of $x + y$ over all such pairs. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Define $M = 11119$ and let $r$ be the remainder when $\sigma(n)$ is divided by $M$. Compute the v... | 55,698 | 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(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11119... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T07:17:45.131305Z | {
"verified": true,
"answer": 55698,
"timestamp": "2026-02-08T07:17:45.134280Z"
} | 8a746b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2658
},
"timestamp": "2026-02-13T09:20:48.311Z",
"answer": 55698
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3b4028 | antilemma_k2_v1_784195855_7999 | Let $x = \sum_{k=1}^{286} \phi(k) \left\lfloor \frac{286}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the remainder when $44121x$ is divided by $67510$. Compute $Q$. | 16,741 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(286), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(286), Var("k"))))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(67510)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T09:39:36.184186Z | {
"verified": true,
"answer": 16741,
"timestamp": "2026-02-08T09:39:36.184886Z"
} | 7b674b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 2327
},
"timestamp": "2026-02-14T08:28:30.181Z",
"answer": 16741
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a94327 | nt_count_coprime_v1_397696148_509 | Let $k$ be the largest prime number less than or equal to 21. Let $U = 68121$. Determine the number of positive integers $n$ such that $1 \leq n \leq U$ and $\gcd(n, k) = 1$. | 64,536 | graphs = [
Graph(
let={
"_n": Const(21),
"upper": Const(68121),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 5.806 | 2026-02-08T11:31:42.962250Z | {
"verified": true,
"answer": 64536,
"timestamp": "2026-02-08T11:31:48.767778Z"
} | 12d659 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 547
},
"timestamp": "2026-02-14T15:17:10.652Z",
"answer": 64536
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
26ebaf | v1_endings_v1_1874849503_380 | Let $n = 30044$ and $p = 3$. Define $n!$ to be the factorial of $n$. Let $x$ be the largest integer $k$ such that $3^k$ divides $n!$. Compute $x$. | 15,016 | graphs = [
Graph(
let={
"n_val": Const(30044),
"p_val": Const(3),
"n_fact": Factorial(Ref("n_val")),
"x": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 3 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T13:00:12.205273Z | {
"verified": true,
"answer": 15016,
"timestamp": "2026-02-08T13:00:12.205978Z"
} | e2e970 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1397
},
"timestamp": "2026-02-09T16:19:20.763Z",
"answer": 15016
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
e55661 | diophantine_fbi2_count_v1_2051736721_780 | Let $A$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 16402500$. Let $\sigma$ be the sum $x_1 + y_1$ for each pair in $A$, and let $k_0$ be the minimum value of $\sigma$ over all such pairs. Now, let $B$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy... | 11 | graphs = [
Graph(
let={
"_n": Const(172),
"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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=T... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"B3/B3"
] | 8ffef9 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.085 | 2026-02-08T15:40:06.484412Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T15:40:06.568942Z"
} | f1ca57 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 2971
},
"timestamp": "2026-02-16T11:12:12.343Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b6eef1 | comb_count_surjections_v1_1520064083_1686 | Let $ n $ be the number of ordered triples $ (x_1, x_2, x_3) $ of positive odd integers that satisfy $ x_1 + x_2 + x_3 = 7 $. Let $ k = 2 $. Let $ r = k! \cdot S(n, k) $, where $ S(n, k) $ denotes the Stirling number of the second kind. Compute $ 50176 - r $. | 50,114 | graphs = [
Graph(
let={
"_n": Const(50176),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T04:12:40.743913Z | {
"verified": true,
"answer": 50114,
"timestamp": "2026-02-08T04:12:40.746808Z"
} | 884e7a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 2057
},
"timestamp": "2026-02-23T23:47:16.088Z",
"answer": 50114
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
719128 | comb_count_surjections_v1_1742523217_2766 | Let $n$ be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 7$, $1 \leq j \leq 7$, and $i + j = 7$. Let $k$ be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 2$, $1 \leq j \leq 3$, and $i + j = 4$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling numb... | 24,902 | graphs = [
Graph(
let={
"_n": Const(24964),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.022 | 2026-02-08T05:20:05.536156Z | {
"verified": true,
"answer": 24902,
"timestamp": "2026-02-08T05:20:05.558216Z"
} | 662dd4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 755
},
"timestamp": "2026-02-24T03:08:17.655Z",
"answer": 24902
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
4825ba | nt_count_coprime_v1_1520064083_711 | Let $k = 11$. Find the number of positive integers $n$ at most 40000 such that $\gcd(n, k) = \phi(2)$. | 36,364 | graphs = [
Graph(
let={
"upper": Const(40000),
"k": Const(11),
"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")), EulerPhi(n=Const(2)))))),
},
goal=Ref("... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_count_coprime_v1 | null | 3 | 0 | [
"ONE_PHI_2"
] | 1 | 5.736 | 2026-02-08T03:34:07.622584Z | {
"verified": true,
"answer": 36364,
"timestamp": "2026-02-08T03:34:13.359037Z"
} | eab33f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 434
},
"timestamp": "2026-02-18T03:00:16.367Z",
"answer": 36364
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
8be783 | antilemma_k2_v1_655260480_5802 | Let $ x = \sum_{k=1}^{235} \phi(k) \left\lfloor \frac{235}{k} \right\rfloor $, where $ \phi(k) $ denotes Euler's totient function. Let $ Q $ be the remainder when $ 32 - x $ is divided by $ 68771 $. Compute $ Q $. | 41,073 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(235), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(235), Var("k"))))),
"Q": Mod(value=Sub(Const(32), Ref("x")), modulus=Const(68771)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2"
] | 2 | 0.003 | 2026-02-08T18:40:09.994455Z | {
"verified": true,
"answer": 41073,
"timestamp": "2026-02-08T18:40:09.997431Z"
} | a0f54a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1620
},
"timestamp": "2026-02-18T18:30:02.911Z",
"answer": 41073
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c877e5 | modular_mod_compute_v1_798873815_232 | Let $n = 4046$. Define $S$ as the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Let $m$ be the number of elements in $S$. Compute the remainder when $61504$ is divided by $m$. Determine the value of this remainder. | 814 | graphs = [
Graph(
let={
"_n": Const(4046),
"a": Const(61504),
"m": 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')),... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_mod_compute_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T02:31:30.693932Z | {
"verified": true,
"answer": 814,
"timestamp": "2026-02-08T02:31:30.696047Z"
} | f36a9f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1327
},
"timestamp": "2026-02-08T19:13:02.802Z",
"answer": 814
},
{
"id... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -4.71,
"mid": -2.86,
"hi": -0.92
} | ||
328f9d | nt_count_digit_sum_v1_1915831931_1212 | Let $T$ be the set of integers $t$ such that $7 \leq t \leq 34$ and there exist positive integers $a \leq 6$ and $b \leq 4$ for which $t = 3a + 4b$. Let $s$ be the number of elements in $T$.
Let $N$ be the number of positive integers $n$, with $1 \leq n \leq 99999$, such that the sum of the decimal digits of $n$ is eq... | 6,000 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": 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=6)),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 4.946 | 2026-02-08T15:56:55.970558Z | {
"verified": true,
"answer": 6000,
"timestamp": "2026-02-08T15:57:00.916603Z"
} | 279798 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 2204
},
"timestamp": "2026-02-16T17:23:58.487Z",
"answer": 6000
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4e668c | nt_sum_divisors_mod_v1_1520064083_4461 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 396900$. Define $n$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10973$. | 4,368 | 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(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10973... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T06:17:29.436143Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T06:17:29.437936Z"
} | 947821 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 2433
},
"timestamp": "2026-02-12T22:11:58.976Z",
"answer": 4368
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e160c5 | nt_count_divisors_in_range_v1_2051736721_1707 | Let $n = 20160$. Let $a$ be the number of positive integers $k$ such that $1 \leq k \leq 2064$ and $43$ divides $k$. Let $b = 1012$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 43 | graphs = [
Graph(
let={
"n": Const(20160),
"a": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(2064)), Divides(divisor=Const(43), dividend=Var("k"))), domain='positive_integers')),
"b": Const(1012),
"resu... | NT | null | COUNT | sympy | LIN_FORM | [
"C2"
] | 9685eb | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 0.413 | 2026-02-08T16:10:28.850113Z | {
"verified": true,
"answer": 43,
"timestamp": "2026-02-08T16:10:29.263058Z"
} | 233b64 | 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": 2533
},
"timestamp": "2026-02-16T22:36:44.683Z",
"answer": 43
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ad1271 | nt_sum_gcd_range_mod_v1_677425708_556 | Let $n = 2520$. Define $k$ to be the number of positive integers from $1$ to $n$ inclusive that are divisible by $10$. Let $N = 1296$ and compute the sum $$\sum_{i=1}^{N} \gcd(i, k).$$ Find the remainder when this sum is divided by $11399$. | 11,154 | graphs = [
Graph(
let={
"_n": Const(2520),
"N": Const(1296),
"k": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Const(10), dividend=Var("k"))), domain='positive_integers')),
"M": Co... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"C2"
] | 1 | 0.334 | 2026-02-08T03:35:52.942862Z | {
"verified": true,
"answer": 11154,
"timestamp": "2026-02-08T03:35:53.276822Z"
} | cf49fa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 3865
},
"timestamp": "2026-02-08T20:45:25.925Z",
"answer": 11154
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
43c17c | antilemma_sum_equals_v1_458359167_4881 | Let $n$ be the number of outcomes when two standard 6-sided dice are rolled. Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 35$, $1 \leq j \leq 36$, and $i + j = n$. | 35 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.022 | 2026-02-08T12:06:56.345371Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T12:06:56.366967Z"
} | 9eca3e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 701
},
"timestamp": "2026-02-24T15:12:56.418Z",
"answer": 35
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
4bb2d6 | geo_count_lattice_triangle_v1_784195855_5014 | Consider the triangle with vertices at $(120, 23)$, $(196, 144)$, and $(0, 0)$. Let $A$ be twice the area of this triangle. Let $B$ be the number of lattice points on the boundary of the triangle, computed as the sum of the greatest common divisors of the absolute differences in coordinates along each edge. Specificall... | 3,804 | graphs = [
Graph(
let={
"_n": Const(28),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=144)), Mul(Const(value=196), Sub(left=Const(value=0), right=Const(value=23))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=23))), GCD(a=Abs(arg=S... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.005 | 2026-02-08T07:34:13.466951Z | {
"verified": true,
"answer": 3804,
"timestamp": "2026-02-08T07:34:13.472068Z"
} | ecbb41 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2068
},
"timestamp": "2026-02-13T11:16:10.120Z",
"answer": 3804
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
008b29 | nt_count_gcd_equals_v1_1915831931_3540 | Let $k$ be the number of positive integers $n \leq 2100$ such that the $n$-th Fibonacci number is divisible by $12$. Let $d$ be the sum of $\phi(d_1)$ over all positive divisors $d_1$ of $175$, where $\phi$ denotes Euler's totient function. Let $r$ be the number of positive integers $n_1 \leq 34225$ such that $\gcd(n_1... | 45,455 | graphs = [
Graph(
let={
"_n": Const(50342),
"upper": Const(34225),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2100)), Divides(divisor=Const(12), dividend=Fibonacci(arg=Var(name='n')))))),
"d": Su... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"K3"
] | 1c15c3 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K3"
] | 2 | 2.987 | 2026-02-08T17:43:12.903915Z | {
"verified": true,
"answer": 45455,
"timestamp": "2026-02-08T17:43:15.890582Z"
} | e9f7da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 1426
},
"timestamp": "2026-02-18T07:04:08.473Z",
"answer": 45455
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7e5941 | comb_catalan_compute_v1_865884756_5480 | Let $n$ be the number of ordered pairs $(i,j)$ of integers such that $1 \le i \le 12$, $1 \le j \le 12$, and $i + j = 14$. Define $Q$ to be the remainder when $35759$ times the $n$-th Catalan number is divided by $62336$. Compute $Q$. | 33,982 | graphs = [
Graph(
let={
"_n": Const(62336),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(14)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T18:37:58.035550Z | {
"verified": true,
"answer": 33982,
"timestamp": "2026-02-08T18:37:58.046261Z"
} | 69b94d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 2644
},
"timestamp": "2026-02-18T18:10:24.878Z",
"answer": 33982
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
5d0b9f | nt_sum_gcd_range_mod_v1_397696148_363 | Let $N$ be the number of ordered pairs $(a,b)$ where $a$ is an integer with $1 \le a \le 3$ and $b$ is an integer with $1 \le b \le 673$. Let $k = 336$. Compute $$\sum_{n=1}^{N} \gcd(n, k).$$ Then find the remainder when this sum is divided by $10457$. Determine the value of this remainder. | 8,269 | graphs = [
Graph(
let={
"N": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(673)))),
"k": Const(336),
"M": Const(10457),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), ex... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.096 | 2026-02-08T11:27:09.622354Z | {
"verified": true,
"answer": 8269,
"timestamp": "2026-02-08T11:27:09.718228Z"
} | 9b2347 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 2755
},
"timestamp": "2026-02-14T14:16:59.263Z",
"answer": 8269
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bb7e16 | nt_count_with_divisor_count_v1_153355830_1886 | Let $n = 4$ and define $d = \sum_{k=1}^{n} k$. Let $S$ be the set of all positive integers $m \leq 15376$ such that the number of positive divisors of $m$ is exactly $d$. Determine the number of elements in $S$. | 214 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(15376),
"div_count": 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_with_divisor_count_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 1.44 | 2026-02-08T06:45:12.254462Z | {
"verified": true,
"answer": 214,
"timestamp": "2026-02-08T06:45:13.694152Z"
} | 384b8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 2328
},
"timestamp": "2026-02-13T04:35:10.045Z",
"answer": 214
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
8fde67 | alg_linear_system_2x2_v1_1419126231_160 | Let $\det = (-1)(-6) - (-10)\cdot\left|\{(a,b) : 1\le a,b\le 15,\ 16b^2 = 256\}\right|$, $M = (-45173)(-6) - (-500246)(15)$, and $R = (-1)(-500246) - (-10)(-45173)$. Let $S = \frac{M}{\det} + \frac{R}{\det}$. Find the remainder when $44121S$ is divided by $99697$. | 48,508 | graphs = [
Graph(
let={
"_n": Const(15),
"num_x": Sub(Mul(Const(-45173), Const(-6)), Mul(Const(-500246), Const(15))),
"num_y": Sub(Mul(Const(-1), Const(-500246)), Mul(Const(-10), Const(-45173))),
"det": Sub(Mul(Const(-1), Const(-6)), Mul(Const(-10), CountOverS... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | alg_linear_system_2x2_v1 | null | 5 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.003 | 2026-02-25T09:44:24.680935Z | {
"verified": true,
"answer": 48508,
"timestamp": "2026-02-25T09:44:24.683839Z"
} | 9f39fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 1739
},
"timestamp": "2026-03-30T07:19:09.052Z",
"answer": 48508
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
810ac8 | nt_sum_divisors_mod_v1_124444284_8 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 176400$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Find the remainder when $\sigma(n)$ is divided by $10657$. | 2,880 | 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(176400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10657... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T02:52:53.856514Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T02:52:53.858676Z"
} | 8c07e6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 829
},
"timestamp": "2026-02-08T19:57:51.942Z",
"answer": 2880
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -2.26,
"mid": 0.02,
"hi": 1.88
} | ||
40e55a | nt_sum_gcd_range_mod_v1_1742523217_114 | Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 6072785318175738493981650$. Let $k = 120$ and $M = 10069$. Define $s = \sum_{n=1}^{N} \gcd(n, k)$. Let $r$ be the remainder when $s$ is divided by $M$. Compute the remainder when $... | 12,395 | graphs = [
Graph(
let={
"_n": Const(86234),
"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=6072785318175738493981650)), Eq(left=GCD(a=Va... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"ONE_PHI_1"
] | 81fa00 | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_1"
] | 2 | 0.094 | 2026-02-08T02:53:14.318641Z | {
"verified": true,
"answer": 12395,
"timestamp": "2026-02-08T02:53:14.412545Z"
} | bedb3e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 420
},
"timestamp": "2026-02-17T15:41:59.599Z",
"answer": 796
}
] | 0 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"s... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
325ca1 | sequence_fibonacci_compute_v1_2051736721_5586 | Let $T$ be the set of all integers $t$ with $5 \leq t \leq 30$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 9$, $1 \leq b \leq 4$, and $t = 2a + 3b$. Let $n$ be the number of elements in $T$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 ... | 46,368 | graphs = [
Graph(
let={
"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=9)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T18:40:40.741720Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T18:40:40.742594Z"
} | 1f144b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 2246
},
"timestamp": "2026-02-18T18:36:05.097Z",
"answer": 46368
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
06b80e | sequence_lucas_compute_v1_601307018_1175 | Let $n$ be the number of elements in the set $\{1, 2, 3\} \times \{1, 2, 3, 4, 5, 6, 7\}$. Let $N = L_n$, where $L_n$ denotes the $n$-th Lucas number. Compute $N$. | 24,476 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(7)))),
"result": Lucas(arg=Ref(name='n')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | ALG | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | sequence_lucas_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.013 | 2026-03-10T01:49:11.783869Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-03-10T01:49:11.796994Z"
} | cb20a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 883
},
"timestamp": "2026-03-29T01:28:49.193Z",
"answer": 24476
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -6.52,
"mid": -3.37,
"hi": -0.99
} | ||
7cdbb9_n | comb_count_partitions_v1_1218484723_3404 | Two athletes split a total of 4626 training minutes, each taking an odd number of minutes. Let $N$ be the number of such splits. A digital lock uses a function $f(a) = (3a^3 + a + 5) \bmod 1849$ to cycle through codes. A code $a$ is *cyclic of order 3* if applying $f$ three times returns to $a$, but not before. Let $n$... | 48,998 | COMB | null | COUNT | sympy | COMB1 | [
"COMB1",
"POLY_ORBIT_HENSEL"
] | 74eaa4 | comb_count_partitions_v1 | affine_mod | 7 | null | [
"COMB1",
"POLY_ORBIT_HENSEL"
] | 2 | 0.004 | 2026-02-25T05:07:28.705582Z | null | 20ed1d | 7cdbb9 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 29600
},
"timestamp": "2026-03-31T05:36:26.492Z",
"answer": 48998
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V8",
"status"... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
fd4109 | nt_num_divisors_compute_v1_1915831931_2733 | Let $n = 18225$. Compute the number of positive divisors of $n$. | 21 | graphs = [
Graph(
let={
"n": Const(18225),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/WILSON",
"MOBIUS_SUM"
] | 5f48ab | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"LIN_FORM",
"MOBIUS_SUM",
"WILSON"
] | 3 | 0.015 | 2026-02-08T17:04:51.250715Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T17:04:51.265866Z"
} | c97681 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 297
},
"timestamp": "2026-02-16T08:59:20.169Z",
"answer": 30
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
30e68e | nt_max_prime_below_v1_1520064083_844 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 6$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $T$ be the set of all prime numbers $n$ such that $|S| \leq n \leq 10739$. Compute the largest element of $T$. | 10,739 | graphs = [
Graph(
let={
"upper": Const(10739),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=V... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_max_prime_below_v1 | null | 4 | 0 | [
"L3C"
] | 1 | 0.255 | 2026-02-08T03:37:46.957755Z | {
"verified": true,
"answer": 10739,
"timestamp": "2026-02-08T03:37:47.212512Z"
} | 301bc7 | 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": 1481
},
"timestamp": "2026-02-10T15:07:31.258Z",
"answer": 10739
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
d80ccd | comb_count_surjections_v1_865884756_6818 | Let $n = 7$ and $k = 3$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 1,806 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.008 | 2026-02-08T19:24:35.938859Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T19:24:35.946423Z"
} | dd6add | 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": 1564
},
"timestamp": "2026-02-18T22:17:43.850Z",
"answer": 1806
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} |
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