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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3b0561 | comb_factorial_compute_v1_124444284_2736 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 4630500$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"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=4630500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T04:54:38.485193Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T04:54:38.486595Z"
} | 59c396 | 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": 1195
},
"timestamp": "2026-02-11T22:42:28.465Z",
"answer": 40320
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "n... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
42252c | antilemma_k3_v1_458359167_2353 | Let $n = 81505$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Compute $x$. | 81,505 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=81505), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T05:20:01.600045Z | {
"verified": true,
"answer": 81505,
"timestamp": "2026-02-08T05:20:01.600419Z"
} | 2eb49e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 2024
},
"timestamp": "2026-02-12T07:58:08.894Z",
"answer": 81505
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "n... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
40c550 | nt_count_coprime_v1_1439011603_1704 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $x \cdot y = 100$. Let $\mathcal{S}$ be the set of all positive integers $n$ such that $1 \leq n \leq 55440$ and $\gcd(n, k) = 1$. Compute the number of elements in $\mathcal{S}$. | 22,176 | graphs = [
Graph(
let={
"_n": Const(100),
"upper": Const(55440),
"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")), Ref("_n")))),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 4.279 | 2026-02-08T16:13:41.591046Z | {
"verified": true,
"answer": 22176,
"timestamp": "2026-02-08T16:13:45.870316Z"
} | c32006 | 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": 784
},
"timestamp": "2026-02-16T22:58:50.949Z",
"answer": 22176
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
289fb9 | comb_count_surjections_v1_601307018_1828 | Let $n = \sum_{k=0}^{2} 2^k$. Compute $4! \cdot S(n, 4)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 8,400 | graphs = [
Graph(
let={
"n": Summation(var="k1", start=Const(0), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_GEOM"
] | 04214c | comb_count_surjections_v1 | null | 3 | 0 | [
"POLY_ORBIT_LEGENDRE",
"SUM_GEOM"
] | 2 | 0.08 | 2026-03-10T02:34:06.266430Z | {
"verified": true,
"answer": 8400,
"timestamp": "2026-03-10T02:34:06.346288Z"
} | eef0e4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1069
},
"timestamp": "2026-03-29T03:30:55.006Z",
"answer": 8400
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -4.26,
"mid": -1.81,
"hi": 1.21
} | ||
92e586 | comb_count_permutations_fixed_v1_601307018_3692 | Let $D_n$ denote the number of derangements of $n$ elements. Define
$$k = \binom{6}{0} - \binom{\sum_{k1=1}^{4} k1}{0}.$$
Let $n$ be the number of elements of the Cartesian product $\{1, 1+1, \ldots, 2\} \times \{1, 1+1, \ldots, 3\}$. Compute
$$\binom{n}{k} \cdot D_{n - k}.$$ | 265 | graphs = [
Graph(
let={
"_n": Const(4),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(3)))),
"k": Sub(Binom(n=Const(6), k=Const(0)), Binom(n=Summation(var="k1", start=Const(1), end=Ref(... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_ARITHMETIC/ONE_BINOM_0/ZERO_BINOM_0",
"COUNT_CARTESIAN"
] | 33b2cf | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_0",
"POLY_ORBIT_LEGENDRE",
"SUM_ARITHMETIC",
"ZERO_BINOM_0"
] | 5 | 0.166 | 2026-03-10T04:18:09.825689Z | {
"verified": true,
"answer": 265,
"timestamp": "2026-03-10T04:18:09.992161Z"
} | 776296 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1049
},
"timestamp": "2026-04-19T01:02:30.831Z",
"answer": 265
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok_later"
},
{
"lemma": "SUM_... | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
067bd0 | sequence_lucas_compute_v1_2051736721_2958 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 121$. Let $L_n$ denote the $n$-th Lucas number. Compute the remainder when $3007 \cdot L_n$ is divided by $56204$. | 46,149 | graphs = [
Graph(
let={
"_n": Const(3007),
"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(121)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_lucas_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T17:02:05.570395Z | {
"verified": true,
"answer": 46149,
"timestamp": "2026-02-08T17:02:05.572131Z"
} | 5499b5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1246
},
"timestamp": "2026-02-17T18:02:14.423Z",
"answer": 46149
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9796a4 | nt_max_prime_below_v1_717093673_1403 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be a prime number satisfying $n \geq |S|$ and $n \leq 55440$. Determine the value of the largest such prime $n$. | 55,439 | graphs = [
Graph(
let={
"upper": Const(55440),
"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 | 2.823 | 2026-02-08T16:03:03.674524Z | {
"verified": true,
"answer": 55439,
"timestamp": "2026-02-08T16:03:06.497282Z"
} | b05352 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1823
},
"timestamp": "2026-02-16T20:37:09.489Z",
"answer": 55439
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
33e1b1 | algebra_quadratic_discriminant_v1_1439011603_277 | Let $a = -2$, $b = 0$, and $c = 72$. Let $n = 2$. Compute the value of $$b^n - a \cdot c \cdot N,$$ where $N$ is the number of positive integers $p$ for which there exists an integer $q$ such that $p \cdot q = 750$, $\gcd(p, q) = 1$, and $p < q$. Find the value of this expression. | 576 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": Const(0),
"c": Const(72),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), co... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T15:23:24.790812Z | {
"verified": true,
"answer": 576,
"timestamp": "2026-02-08T15:23:24.792569Z"
} | 147fc2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 1550
},
"timestamp": "2026-02-16T05:17:55.747Z",
"answer": 576
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
43089d | lte_diff_endings_v1_1918700295_122 | Let $a = 25$, $b = 10$, $p = 3$, and $n = 2430$. Define $d$ to be the largest integer $k$ such that $3^k$ divides $25^{2430} - 10^{2430}$. Compute the remainder when $5499 \cdot d$ is divided by $100000$. | 32,994 | graphs = [
Graph(
let={
"a_val": Const(25),
"b_val": Const(10),
"p_val": Const(3),
"n_val": Const(2430),
"a_pow": Pow(Ref("a_val"), Ref("n_val")),
"b_pow": Pow(Ref("b_val"), Ref("n_val")),
"pow_diff": Sub(Ref("a_pow"), Ref("... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:00:42.045558Z | {
"verified": true,
"answer": 32994,
"timestamp": "2026-02-08T03:00:42.046225Z"
} | ad2680 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 766
},
"timestamp": "2026-02-08T22:58:08.058Z",
"answer": 32994
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"sta... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
2ac35f | comb_count_derangements_v1_2051736721_4680 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 40$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{5}$. Let $r$ be the number of derangements of $n$ elements. Compute the remainder when $44121 \cdot r$ is divided by $82199$. | 60,554 | graphs = [
Graph(
let={
"_n": Const(40),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=5))))),
... | NT | COMB | COUNT | sympy | LTE_SUM | [
"L3C"
] | 73f8b0 | comb_count_derangements_v1 | null | 5 | 0 | [
"L3C",
"LTE_SUM"
] | 2 | 0.004 | 2026-02-08T18:06:16.904965Z | {
"verified": true,
"answer": 60554,
"timestamp": "2026-02-08T18:06:16.909454Z"
} | 8ffff5 | 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": 2665
},
"timestamp": "2026-02-18T13:26:09.342Z",
"answer": 60554
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a07911 | antilemma_k3_v1_238844314_1047 | Let $n = 23885$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $Q = 50400 - x$. Compute $Q$. | 26,515 | graphs = [
Graph(
let={
"_n": Const(23885),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(50400),
"Q": Sub(Ref("_c"), Ref("x")),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:51:59.154107Z | {
"verified": true,
"answer": 26515,
"timestamp": "2026-02-08T13:51:59.155215Z"
} | f6f838 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 401
},
"timestamp": "2026-02-15T21:23:24.212Z",
"answer": 26515
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
2a2dfa | nt_count_gcd_equals_v1_1742523217_4563 | Let $N$ be the number of integers $t$ for which there exist integers $u$ and $v$ with $1 \le u \le 828$, $1 \le v \le 218$, $15 \le t \le 6930$, and
$$t = 6u + 9v.$$
Let $M$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = N$.
Let $P$ be the maximum value of $xy$ over a... | 1,455 | 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=828)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3/B1"
] | 8c8f5e | nt_count_gcd_equals_v1 | negation_mod | 8 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 2.335 | 2026-02-08T08:58:13.098897Z | {
"verified": true,
"answer": 1455,
"timestamp": "2026-02-08T08:58:15.433720Z"
} | 3cf369 | 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": 4830
},
"timestamp": "2026-02-13T22:39:55.337Z",
"answer": 1455
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"le... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
dced45_n | alg_telescope_v1_1218484723_2215 | A hiker walks along a rectangular trail whose area is exactly 881721 square meters, with side lengths being positive integers. She chooses the rectangle with the smallest possible perimeter. Let $s$ be the semi-perimeter $x + y$ of this rectangle. She then computes the sum of the first $s + 1$ odd numbers (since $(k+1)... | 4,209 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_telescope_v1 | null | 4 | null | [
"B3"
] | 1 | 0.127 | 2026-02-25T03:59:20.071745Z | null | 657041 | dced45 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 2557
},
"timestamp": "2026-03-30T18:07:12.473Z",
"answer": 4209
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
04983a | comb_count_partitions_v1_458359167_177 | Let $n$ be the largest positive integer $k$ such that $2^k \leq 1224714534020$. Compute the number of integer partitions of $n$. | 37,338 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(1224714534020)))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | comb_count_partitions_v1 | null | 6 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T03:03:09.654724Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T03:03:09.656077Z"
} | 62745e | 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": 735
},
"timestamp": "2026-02-10T12:32:09.649Z",
"answer": 37338
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
70c2ac | comb_binomial_compute_v1_677425708_3679 | Let $n_2 = 10$. Define $s = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = 0$ and define $c = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 15c$ and $k = 6 + s$. Let $\text{result} = \binom{n}{k}$ and $Q = 68454 \cdot \text{result} \mod 70045$. Compute $Q$. | 22,175 | graphs = [
Graph(
let={
"n2": Const(10),
"s": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), ... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T05:53:35.835726Z | {
"verified": true,
"answer": 22175,
"timestamp": "2026-02-08T05:53:35.837081Z"
} | 8af7c2 | 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": 1193
},
"timestamp": "2026-02-24T04:46:03.333Z",
"answer": 22175
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
6e3714 | nt_count_divisors_in_range_v1_124444284_2056 | Let $n = 83160$. Define $a$ to be the number of integers $t$ with $9 \leq t \leq 59$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 12$, $1 \leq b \leq 5$, and $t = 2a + 7b$. Let $b = 1083$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 63 | graphs = [
Graph(
let={
"n": Const(83160),
"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=12)), Geq(left=Va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.026 | 2026-02-08T04:17:00.401266Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T04:17:00.427182Z"
} | 401b3c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 4221
},
"timestamp": "2026-02-10T16:31:07.843Z",
"answer": 63
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
758dae_l | comb_count_permutations_fixed_v1_1125832087_2368 | Let $k$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 136$ and $\binom{136}{j}$ is odd.
Compute $\binom{7}{k} \cdot !(7 - k)$, where $!n$ denotes the number of derangements of $n$ elements. | 0 | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T04:34:30.408131Z | {
"verified": false,
"answer": 70,
"timestamp": "2026-02-08T04:34:30.410036Z"
} | e99de1 | 758dae | legacy_text | 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": 553
},
"timestamp": "2026-02-24T01:00:56.241Z",
"answer": 70
},
{
"id":... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | |
bbdf06 | nt_max_prime_below_v1_1125832087_1313 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $P$. Let $T$ be the set of all prime numbers $n$ such that $m \leq n \leq 59340$. Let $r$ be the largest element of $T$. Compute the re... | 18,854 | graphs = [
Graph(
let={
"upper": Const(59340),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.359 | 2026-02-08T03:41:02.044930Z | {
"verified": true,
"answer": 18854,
"timestamp": "2026-02-08T03:41:03.404070Z"
} | cdd8f5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 7320
},
"timestamp": "2026-02-10T14:07:38.008Z",
"answer": 18854
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6d6f8b | antilemma_v1_legendre_260342960_151 | Let $m = 13013$ and $n = 41076$. Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 24$, and $\gcd(p, q) = 1$. Let $t$ be the number of elements in $S$. Let $D$ be the set of all positive divisors $d$ of $m$ such that $d \geq t$. Let $b$ be the smallest ele... | 6,844 | graphs = [
Graph(
let={
"_m": Const(13013),
"_n": Const(41076),
"x": MaxKDivides(target=Factorial(Ref("_n")), base=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p'))... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR/V1",
"V1"
] | 08fea4 | antilemma_v1_legendre | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR",
"V1"
] | 3 | 0.002 | 2026-02-08T11:16:41.517405Z | {
"verified": true,
"answer": 6844,
"timestamp": "2026-02-08T11:16:41.519810Z"
} | 268d62 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 1912
},
"timestamp": "2026-02-08T20:32:29.786Z",
"answer": 6840
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
... | {
"lo": -2.08,
"mid": 1.77,
"hi": 4.93
} | ||
40ed89 | nt_min_phi_inverse_v1_971394319_1151 | Let $U = 50$ and $k = 12$. Define $m$ as the smallest positive integer $n \leq U$ such that $\phi(n) = k$, where $\phi$ is Euler's totient function. Let $S$ be the set of all real solutions to the equation $x^2 - 639x + 11780 = 0$, and let $V$ be the sum of all elements of $S$. Define $c$ as the number of positive inte... | 243 | graphs = [
Graph(
let={
"upper": Const(50),
"k": Const(12),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"_c": CountOverSet(set=SolutionsSet(var=V... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM/C4"
] | 9b53b9 | nt_min_phi_inverse_v1 | negation_mod | 6 | 0 | [
"C4",
"VIETA_SUM"
] | 2 | 0.011 | 2026-02-08T13:31:01.378655Z | {
"verified": true,
"answer": 243,
"timestamp": "2026-02-08T13:31:01.389414Z"
} | 3affd6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1403
},
"timestamp": "2026-02-15T16:35:07.236Z",
"answer": 243
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e574f2 | comb_count_surjections_v1_1918700295_4092 | Let $m = 8$. Let $n$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i, j \leq 8$ such that $i + j = m$. Let $k$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i, j \leq 5$ such that $i + j = 5$. Compute $k!$ multiplied by the Stirling number of the second kind $S(5, k)$. | 240 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Cons... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS"
] | 756129 | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.021 | 2026-02-08T09:08:52.261979Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T09:08:52.283435Z"
} | b78e2b | 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": 1005
},
"timestamp": "2026-02-24T10:34:43.223Z",
"answer": 240
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
99ea9d | nt_count_primes_v1_153355830_66 | Let $U = 23409$, and let $P$ be the number of primes $n$ with $2 \le n \le U$.
Let $p_{\max}$ be the largest prime $n$ with $2 \le n \le 12$. Let
$$h = \gcd(p_{\max}, 13).$$
Define
$$m = \sum_{d \mid h} \mu(d),$$
where $\mu$ is the Möbius function, and let
$$L = \varphi(m),$$
where $\varphi$ is Euler's totient functio... | 20,915 | graphs = [
Graph(
let={
"upper": Const(23409),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Summation(var="n", start=EulerPhi(n=SumOverDivisors(n=GCD(a=MaxOverSet(set=S... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MOBIUS_COPRIME/ONE_PHI_1"
] | 15d58c | nt_count_primes_v1 | sum_divisor_count | 7 | 0 | [
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | 3 | 0.541 | 2026-02-08T02:52:58.050437Z | {
"verified": true,
"answer": 20915,
"timestamp": "2026-02-08T02:52:58.591825Z"
} | 141b87 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 6065
},
"timestamp": "2026-02-08T22:39:33.432Z",
"answer": 21117
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status... | {
"lo": 3.31,
"mid": 6.77,
"hi": 10
} | ||
813052 | nt_count_intersection_v1_168721529_1893 | Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 25000000$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 49$. Define $a = 3$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq N$, $n$ is di... | 1,429 | graphs = [
Graph(
let={
"_n": Const(49),
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25000000)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.486 | 2026-02-08T13:58:40.649928Z | {
"verified": true,
"answer": 1429,
"timestamp": "2026-02-08T13:58:41.135739Z"
} | 69c184 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 3999
},
"timestamp": "2026-02-09T23:07:57.062Z",
"answer": 1429
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
ae8eb0 | nt_gcd_compute_v1_865884756_3156 | Let $a = 239928$ and $b = 449865$. Define $\text{result} = \gcd(a, b)$. Let $Q$ be the remainder when $44121 \times \text{result}$ is divided by $69602$. Find the value of $Q$. | 29,289 | graphs = [
Graph(
let={
"a": Const(239928),
"b": Const(449865),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(69602)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | DIVISOR_PARITY | [
"DIVISOR_PARITY",
"OMEGA_ZERO"
] | d7c8f3 | nt_gcd_compute_v1 | null | 2 | 0 | [
"DIVISOR_PARITY",
"OMEGA_ZERO"
] | 2 | 0.008 | 2026-02-08T17:12:19.194831Z | {
"verified": true,
"answer": 29289,
"timestamp": "2026-02-08T17:12:19.202338Z"
} | 9366c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 1538
},
"timestamp": "2026-02-17T20:58:51.630Z",
"answer": 29289
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "V1",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
35bd5e | algebra_poly_eval_v1_1918700295_3633 | Let $ s $ be the largest prime number between $ 2 $ and $ 5 $, inclusive. Compute $ 2 \cdot 7^4 - 5 \cdot 7^3 - 5 \cdot 7^2 + 3 \cdot 7 + s $. | 2,868 | graphs = [
Graph(
let={
"_n": Const(2),
"y": Const(7),
"result": Sum(Mul(Ref("_n"), Pow(Ref("y"), Const(4))), Mul(Const(-5), Pow(Ref("y"), Const(3))), Mul(Const(-5), Pow(Ref("y"), Const(2))), Mul(Const(3), Ref("y")), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T08:47:05.636227Z | {
"verified": true,
"answer": 2868,
"timestamp": "2026-02-08T08:47:05.638960Z"
} | f17db7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 576
},
"timestamp": "2026-02-13T21:40:03.765Z",
"answer": 2868
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
c40347 | antilemma_cartesian_v1_458359167_1253 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 8, inclusive, and $b$ is an integer from 1 to 9, inclusive. Compute $$
x + \phi\left(|x| + \binom{16}{0}\right) + \tau\left(|x| + \binom{3}{3}\right),
$$
where $\phi(n)$ denotes Euler's totient function and $\tau(n)$ denotes the number ... | 146 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(9)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Binom(n=Const(16), k=Const(0)))), NumDivisors(n=Sum(Abs(arg=Re... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_BINOM_N",
"ONE_BINOM_0"
] | 1c4c00 | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_0",
"ONE_BINOM_N"
] | 3 | 0.002 | 2026-02-08T04:30:48.894659Z | {
"verified": true,
"answer": 146,
"timestamp": "2026-02-08T04:30:48.896418Z"
} | fc00ff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 469
},
"timestamp": "2026-02-24T00:51:00.652Z",
"answer": 146
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
3ebb4a | modular_modexp_compute_v1_1742523217_2482 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 9437184$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $e$ be the number of positive integers $n$ such that $1 \leq n \leq s_{\text{min}}$ and the $n$-th Fibonacci number is even. Compute the... | 972 | graphs = [
Graph(
let={
"a": Const(2),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(ar... | NT | null | COMPUTE | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.003 | 2026-02-08T04:47:54.456814Z | {
"verified": true,
"answer": 972,
"timestamp": "2026-02-08T04:47:54.459748Z"
} | 46e018 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 6989
},
"timestamp": "2026-02-11T22:04:49.035Z",
"answer": 972
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
983ebc | comb_sum_binomial_row_v1_717093673_2395 | Let $n$ be the largest prime number less than or equal to $13$. Compute $2^n$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(13)), IsPrime(Var("n1"))))),
"result": Pow(Ref("_n"), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:47:38.807019Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T16:47:38.808580Z"
} | 3e8e01 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 79,
"completion_tokens": 160
},
"timestamp": "2026-02-16T07:53:17.546Z",
"answer": 2048
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
63d052 | antilemma_k3_v1_1918700295_4635 | Let $S$ be the set of all positive integers $x$ such that $x^2 - 8405x + 542100 = 0 \pmod{11}$. Let $n$ be the sum of all elements in $S$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 8,405 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverDivisors(n=SumOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Ref(name='_n')), Mul(Const(value=-8405), Var(name='x')), Const(value=542100)), right=Mod(value=Const(value=11), modulus=Cons... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K3",
"IDENTITY_MOD_SELF",
"K3"
] | c8105d | antilemma_k3_v1 | null | 7 | 0 | [
"IDENTITY_MOD_SELF",
"K13",
"K3",
"VIETA_SUM"
] | 4 | 0.002 | 2026-02-08T09:29:31.891208Z | {
"verified": true,
"answer": 8405,
"timestamp": "2026-02-08T09:29:31.893159Z"
} | bc8832 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 2420
},
"timestamp": "2026-02-14T04:31:59.876Z",
"answer": 8405
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "IDENTITY_MOD_SELF",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
aed2b6 | comb_binomial_compute_v1_1978505735_4228 | Let $n = 13$. Let $k$ be the largest prime number such that $2 \leq k \leq 8$. Compute $\binom{n}{k}$. | 1,716 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(13),
"k": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(8)), IsPrime(Var("n1"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=R... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T18:05:05.464253Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T18:05:05.466996Z"
} | 409207 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 934
},
"timestamp": "2026-02-16T12:07:50.912Z",
"answer": 1716
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
85f18c | diophantine_fbi2_count_v1_2051736721_1596 | Let $k = 360$. Determine the number of positive integers $d$ such that $5 \leq d \leq 148$, $d$ divides $k$, and the quotient $\frac{k}{d}$ satisfies $3 \leq \frac{k}{d} \leq 146$. | 18 | graphs = [
Graph(
let={
"k": Const(360),
"a": Const(4),
"b": Const(2),
"upper": Const(144),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(148)), Divides(divisor=Var("d"), dividend=R... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"MIN_PRIME_FACTOR/K14",
"SUM_ARITHMETIC"
] | 3b224d | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"K14",
"MIN_PRIME_FACTOR",
"ONE_PHI_2",
"SUM_ARITHMETIC"
] | 4 | 2.173 | 2026-02-08T16:07:09.004584Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T16:07:11.178029Z"
} | a3c0f8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 1266
},
"timestamp": "2026-02-16T21:15:10.989Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f49a4b | nt_count_divisible_and_v1_655260480_2936 | Let $d_1 = 8$. Let $d_2$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 36$. Determine the number of positive integers $n$ such that $1 \leq n \leq 38088$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 1,587 | graphs = [
Graph(
let={
"upper": Const(38088),
"d1": Const(8),
"d2": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(36)))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 9.714 | 2026-02-08T17:04:25.772586Z | {
"verified": true,
"answer": 1587,
"timestamp": "2026-02-08T17:04:35.487014Z"
} | 62de75 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 282
},
"timestamp": "2026-02-16T08:58:39.659Z",
"answer": 365
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
108bd3 | nt_count_divisible_and_v1_784195855_8291 | Let $d_1 = 8$. Let $d_2$ be the number of prime numbers $n$ such that $2 \leq n \leq 37$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 74256$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute the number of elements in $S$. | 3,094 | graphs = [
Graph(
let={
"upper": Const(74256),
"d1": Const(8),
"d2": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(37)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condit... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 3.063 | 2026-02-08T15:59:51.675424Z | {
"verified": true,
"answer": 3094,
"timestamp": "2026-02-08T15:59:54.738579Z"
} | de1ff8 | 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": 779
},
"timestamp": "2026-02-16T18:59:42.555Z",
"answer": 3094
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
37a4ae | algebra_vieta_sum_v1_1915831931_915 | Let $s$ be the sum of all real numbers $x$ such that $x^3 - 2x^2 - 85x + m = 0$, where $m$ is the minimum value of $x_1 + y$ over all pairs of positive integers $(x_1, y)$ satisfying $x_1 y = 30625$. Let $t$ be the minimum value of $x_2 + y_1$ over all pairs of positive integers $(x_2, y_1)$ satisfying $x_2 y_1 = 32400... | 3,598 | graphs = [
Graph(
let={
"_n": Const(3),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-2), Pow(Var("x"), Const(2))), Mul(Const(-85), Var("x")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("y"... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | algebra_vieta_sum_v1 | negation_mod | 7 | 0 | [
"B3"
] | 1 | 0.023 | 2026-02-08T15:45:44.856412Z | {
"verified": true,
"answer": 3598,
"timestamp": "2026-02-08T15:45:44.879886Z"
} | 6c9ab0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1687
},
"timestamp": "2026-02-16T12:20:31.148Z",
"answer": 3598
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
77c570 | nt_count_divisible_and_v1_1978505735_7846 | Let $d_1 = 6$ and $d_2 = \sum_{k=1}^{4} k$. Let $Q$ be the number of positive integers $n$ such that $1 \le n \le 26910$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Find the value of $Q$. | 897 | graphs = [
Graph(
let={
"upper": Const(26910),
"d1": Const(6),
"d2": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(M... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.854 | 2026-02-08T20:31:11.532661Z | {
"verified": true,
"answer": 897,
"timestamp": "2026-02-08T20:31:12.386727Z"
} | 1cea7d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 886
},
"timestamp": "2026-02-19T00:38:51.219Z",
"answer": 897
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6c0163 | lin_form_endings_v1_1520064083_1993 | Let $a = 42$, $b = 98$, $A = 39$, and $B = 31$. Let $g$ be the greatest common divisor of $a$ and $b$. Define $$ n = \left\lfloor \frac{aA + bB - (a + b)}{g} \right\rfloor + 1. $$ Let $k = 5686$ and $M = 55569$. Compute the remainder when $k \cdot n$ is divided by $M$. | 14,173 | graphs = [
Graph(
let={
"a_coeff": Const(42),
"b_coeff": Const(98),
"A_val": Const(39),
"B_val": Const(31),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:27:03.933753Z | {
"verified": true,
"answer": 14173,
"timestamp": "2026-02-08T04:27:03.935510Z"
} | d67eb2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 763
},
"timestamp": "2026-02-10T16:36:56.373Z",
"answer": 14173
},
{
"... | 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": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6d916e | alg_qf_psd_orbit_v1_601307018_8100 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $10a^2 - 18ab + 25b^2 \le 6757$. Let $S$ denote the number of ordered pairs $(a_2, b_2)$ with $1 \le a_2, b_2 \le 35$ satisfying $41a_2^2 - 12a_2b_2 + 20b_2^2 \le 15217$. Find the number of ordered triples $(a_1, b_1... | 5 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": 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)), Leq(Sum(Mul(Const(10), Pow(Var("a"), Ref("_m"))), ... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_COUNT_LEQ"
] | cbd80a | alg_qf_psd_orbit_v1 | null | 8 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 2.543 | 2026-03-10T08:35:25.233653Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-03-10T08:35:27.776966Z"
} | 818058 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 15712
},
"timestamp": "2026-04-19T08:18:41.560Z",
"answer": 5
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
3616de | comb_sum_binomial_row_v1_1218484723_3907 | Let $S = \sum_{k=1}^{21} \varphi(k) \cdot \left\lfloor \frac{21}{k} \right\rfloor$. Find the number of positive integers $n$ with $1 \le n \le S$ such that $\gcd(n, 10) = 1$ and $7 \mid n$. Let $R = 2^n$. Compute $57841 - R$. | 41,457 | graphs = [
Graph(
let={
"_m": Const(21),
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(21), Var("k")... | COMB | NT | SUM | sympy | K2 | [
"K2/C5"
] | 26a204 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"C5",
"K2"
] | 2 | 0.002 | 2026-02-25T05:30:57.566795Z | {
"verified": true,
"answer": 41457,
"timestamp": "2026-02-25T05:30:57.568819Z"
} | 45cb46 | 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": 1470
},
"timestamp": "2026-03-29T12:49:32.462Z",
"answer": 41457
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
80c71a | nt_max_prime_below_v1_124444284_5927 | Let $p$ be the largest prime number less than or equal to 19044. Determine the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 19454$. Compute the remainder when the product of this count and $p$ is divided by 84993. | 58,145 | graphs = [
Graph(
let={
"_n": Const(84993),
"upper": Const(19044),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Mul(CountOverSet(set=SolutionsSet(va... | NT | null | EXTREMUM | sympy | COMB1 | [
"COMB1"
] | 54ff32 | nt_max_prime_below_v1 | affine_mod | 4 | 0 | [
"COMB1"
] | 1 | 0.77 | 2026-02-08T06:57:15.493293Z | {
"verified": true,
"answer": 58145,
"timestamp": "2026-02-08T06:57:16.263177Z"
} | 5eba9e | 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": 3221
},
"timestamp": "2026-02-13T06:15:50.956Z",
"answer": 58145
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7bd80d | comb_sum_binomial_row_v1_865884756_4456 | Let $n$ be the largest prime number less than or equal to $14$. Let $r = 2^n$. Compute the remainder when $70661 \cdot r$ is divided by $74620$. | 27,572 | graphs = [
Graph(
let={
"_n": Const(14),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Pow(Const(2), Ref("n")),
"_c": Const(70661),
"Q": Mod(value... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T17:56:04.777000Z | {
"verified": true,
"answer": 27572,
"timestamp": "2026-02-08T17:56:04.778703Z"
} | b2b03e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 3116
},
"timestamp": "2026-02-18T10:29:43.976Z",
"answer": 27572
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
17701e | alg_poly3_min_v1_1419126231_130 | Let $A$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1, b_1 \leq 40$ such that $25b_1^2 + 10a_1^2 - 18a_1b_1 \leq 2825$. Find the minimum value of $6435a^3 + 8580a^2b + 34320ab^2 + 45760b^3$ over all positive integers $a, b$ with $1 \leq a \leq A$ and $1 \leq b \leq 222$. | 95,095 | graphs = [
Graph(
let={
"_n": Const(40),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_min_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.096 | 2026-02-25T09:40:33.416294Z | {
"verified": true,
"answer": 95095,
"timestamp": "2026-02-25T09:40:33.512041Z"
} | b22352 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 6348
},
"timestamp": "2026-03-30T07:10:19.996Z",
"answer": 95095
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
366d33 | nt_sum_totient_over_divisors_v1_1742523217_774 | Let $c = 14351$, and let $m$ be the smallest divisor of $c$ that is at least $2$.
Let $n_0$ be the number of positive integers $n$ such that $1 \leq n \leq m$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$.
Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 231361$ and $k$ is divi... | 6,253 | graphs = [
Graph(
let={
"_c": Const(14351),
"_m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_c"))))),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Le... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/L3C/C2"
] | 2d2a69 | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"C2",
"L3C",
"MIN_PRIME_FACTOR"
] | 3 | 0.005 | 2026-02-08T03:14:15.287815Z | {
"verified": true,
"answer": 6253,
"timestamp": "2026-02-08T03:14:15.292682Z"
} | b421ee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 4546
},
"timestamp": "2026-02-09T22:35:52.029Z",
"answer": 6253
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"s... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
e8b05e | nt_count_coprime_v1_153355830_1274 | Let $A$ be the set of positive integers $n$ such that $1 \le n \le 32768$ and $\gcd(n, 14) = 1$. Let $r$ be the number of elements in $A$.
Let $B$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14992384$. Let $c$ be the minimum value of $x + y$ over all such pairs.
Let $C$ be the set of... | 36,367 | graphs = [
Graph(
let={
"upper": Const(32768),
"k": Const(14),
"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")), Const(1))))),
"_c": MinOverSet(set=MapOverS... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 9cd48e | nt_count_coprime_v1 | quadratic_mod | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 3.859 | 2026-02-08T06:16:37.640400Z | {
"verified": true,
"answer": 36367,
"timestamp": "2026-02-08T06:16:41.499487Z"
} | 3bc01c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 2863
},
"timestamp": "2026-02-12T21:51:12.631Z",
"answer": 36367
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
02922f | nt_count_divisible_and_v1_397696148_2293 | Compute the number of positive integers $n$ such that $n \leq 11832$, $n \equiv \sum_{k=0}^{1} (-1)^k \binom{1}{k} \pmod{8}$, and $n \equiv 0 \pmod{12}$. | 493 | graphs = [
Graph(
let={
"upper": Const(11832),
"d1": Const(8),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Summation(var="... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 2.964 | 2026-02-08T13:05:33.941005Z | {
"verified": true,
"answer": 493,
"timestamp": "2026-02-08T13:05:36.904704Z"
} | 7dec43 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 731
},
"timestamp": "2026-02-24T17:08:20.210Z",
"answer": 493
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
d92403 | nt_sum_divisors_compute_v1_809748730_1668 | Let $n = 31684$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Let $s = \sigma(n)$. Compute the value of
$$
s + 2^{s \bmod 15} \bmod 74000.
$$ | 56,205 | graphs = [
Graph(
let={
"_n": Const(74000),
"n": Const(31684),
"result": SumDivisors(n=Ref("n")),
"Q": Sum(Ref("result"), Mod(value=Pow(Const(2), Mod(value=Ref("result"), modulus=Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")))), modulus=Ref("_... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 129eee | nt_sum_divisors_compute_v1 | mod_exp | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T12:36:54.787725Z | {
"verified": true,
"answer": 56205,
"timestamp": "2026-02-08T12:36:54.789602Z"
} | 723d1f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 902
},
"timestamp": "2026-02-15T02:54:48.565Z",
"answer": 56205
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
377173 | sequence_count_fib_divisible_v1_168721529_524 | Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 48841$. Let $r$ be the number of positive integers $n \leq s$ such that the $n$-th Fibonacci number is divisible by 19. Find the remainder when $44121 \cdot r$ is divided by 89377. | 75,757 | 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(48841)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(19... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.047 | 2026-02-08T13:05:25.479368Z | {
"verified": true,
"answer": 75757,
"timestamp": "2026-02-08T13:05:25.526718Z"
} | 8f5c60 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 1681
},
"timestamp": "2026-02-09T05:56:50.886Z",
"answer": 75757
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -2,
"mid": 1.85,
"hi": 5.2
} | ||
c57858 | comb_count_derangements_v1_601307018_4764 | Let $D_n$ denote the number of derangements of $n$ elements. For each integer $a$ with $0 \leq a \leq 4912$, define $R = a^3 \bmod 4913$, $S = R^3 \bmod 4913$, $T = S^3 \bmod 4913$, and $K = T^3 \bmod 4913$. Let $n$ be the number of such $a$ for which $K = a$, but $R \ne a$, $S \ne a$, and $T \ne a$. Let $L = D_n$. Fin... | 13,357 | graphs = [
Graph(
let={
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(4912)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a"))))),
... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_derangements_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.003 | 2026-03-10T05:26:42.222323Z | {
"verified": true,
"answer": 13357,
"timestamp": "2026-03-10T05:26:42.224887Z"
} | 2b5cb8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 5010
},
"timestamp": "2026-03-29T13:21:58.784Z",
"answer": 13357
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
2e7139 | antilemma_sum_factor_cartesian_v1_677425708_3655 | Compute the sum of $i \cdot j$ over all ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 12$ and $1 \leq j \leq 7$. | 2,184 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(7)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 2 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T05:52:45.933645Z | {
"verified": true,
"answer": 2184,
"timestamp": "2026-02-08T05:52:45.934364Z"
} | c978ef | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 440
},
"timestamp": "2026-02-18T20:52:38.813Z",
"answer": 2184
}
] | 2 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
06eaa2 | comb_binomial_compute_v1_601307018_7624 | Let $n$ be the minimum value of $34b^2 - 50ab + \left| \left\{ (a_1, b_1) \mid 1 \leq a_1, b_1 \leq 35,\ 10a_1b_1 + 5a_1^2 + 5b_1^2 = 4500 \right\} \right| \cdot a^2$ over all positive integers $a$, $b$ with $1 \leq a, b \leq 23$. Let $Q = \binom{n}{7}$. Compute $Q$. | 1,716 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(23),
"n": 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)), Leq(Var("b"), Const(23)))), expr=Su... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/QF_PSD_MIN"
] | 2a0653 | comb_binomial_compute_v1 | null | 6 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_MIN"
] | 2 | 0.005 | 2026-03-10T08:09:47.680306Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-03-10T08:09:47.685249Z"
} | c1683f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1997
},
"timestamp": "2026-04-19T07:08:00.905Z",
"answer": 1716
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_MIN"... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
41e675 | algebra_quadratic_discriminant_v1_124444284_1563 | Let $a = 3$, $b = -1$, and $c$ be the sum of the integers from $1$ to $3$. Let $D = b^2 - 4ac$. Define
\[
\alpha = \begin{cases}
2 & \text{if } D > 0, \\
0 & \text{otherwise},
\end{cases}
\quad
\beta = \begin{cases}
1 & \text{if } D = 0, \\
0 & \text{otherwise}.
\end{cases}
\]
Compute $\alpha + \beta$. | 0 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(3),
"b": Const(-1),
"c": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Ref("_n... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.011 | 2026-02-08T03:59:12.331716Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T03:59:12.342543Z"
} | 050abd | 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": 198
},
"timestamp": "2026-02-11T15:47:16.216Z",
"answer": 0
},
{
"id": ... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
8853ae | comb_binomial_compute_v1_1125832087_1192 | Let $n_1 = 0$ and $n_2 = 7$. Define
$$
h = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}
\quad\text{and}\quad
u = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 16$, $1 \le j \le 16$, and $i + j = 16$. Define $k = 8\nu$ and let $r = \binom{n}{k}$. ... | 45,214 | graphs = [
Graph(
let={
"_n": Const(84461),
"n2": Const(7),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"u": Summation(var="k", start=Const(0), end=Ref(... | COMB | null | COMPUTE | sympy | K2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | b9499e | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"K2"
] | 3 | 0.025 | 2026-02-08T03:36:42.362497Z | {
"verified": true,
"answer": 45214,
"timestamp": "2026-02-08T03:36:42.387834Z"
} | 604176 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 2059
},
"timestamp": "2026-02-10T15:09:04.200Z",
"answer": 45214
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "C... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
15f1c5 | nt_count_divisible_and_v1_349078426_545 | Let $n = 3$ and $u = 56268$. Let $d_1 = 4$ and
$$
d_2 = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{\sum_{k=1}^{2} k}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $r$ be the number of positive integers $m$ such that $1 \leq m \leq u$, $m$ is divisible by $d_1$, and $m$ is divisible by $d_2$. Co... | 12,659 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(56268),
"d1": Const(4),
"d2": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")), Var("k"))))),
... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2"
] | 06cc86 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 3.502 | 2026-02-08T13:07:28.892039Z | {
"verified": true,
"answer": 12659,
"timestamp": "2026-02-08T13:07:32.393618Z"
} | 3fd595 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2146
},
"timestamp": "2026-02-15T10:18:31.396Z",
"answer": 12659
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5ffe43 | nt_gcd_compute_v1_798873815_53 | Let $u$ be the number of prime factors of $1$ counted with multiplicity. Let $p = 13$, and define $n = p^2$. Let $h$ be the number of distinct prime factors of $n$. Let $a = 164104 + u$ and $b = 369234 \cdot h$. Compute $\gcd(a, b)$. | 41,026 | graphs = [
Graph(
let={
"n1": Const(1),
"u": BigOmega(n=Ref(name='n1')),
"p": Const(13),
"n": Pow(Ref("p"), Const(2)),
"h": SmallOmega(n=Ref(name='n')),
"a": Sum(Const(164104), Ref("u")),
"b": Mul(Const(369234), Ref("h")),
... | NT | null | COMPUTE | sympy | BIG_OMEGA_ZERO | [
"BIG_OMEGA_ZERO",
"OMEGA_ONE"
] | ab331a | nt_gcd_compute_v1 | null | 2 | 2 | [
"BIG_OMEGA_ZERO",
"OMEGA_ONE"
] | 2 | 0.002 | 2026-02-08T02:25:33.638172Z | {
"verified": true,
"answer": 41026,
"timestamp": "2026-02-08T02:25:33.640451Z"
} | 081fd4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 453
},
"timestamp": "2026-02-08T18:32:06.603Z",
"answer": 41026
},
{
"i... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -4.84,
"mid": -1.65,
"hi": 1.89
} | ||
cc7e77 | geo_count_lattice_rect_v1_1742523217_1252 | Let $a = 34$ and $b = 51$. Define the quantity $R$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $c = 49100$ and define $Q$ to be the remainder when $c \cdot R$ is divided by $93751$. Compute $Q$. | 17,297 | graphs = [
Graph(
let={
"a": Const(34),
"b": Const(51),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(49100),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(93751)),
},
goal=Ref("Q"),
)
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T03:35:05.827922Z | {
"verified": true,
"answer": 17297,
"timestamp": "2026-02-08T03:35:05.828785Z"
} | 794bc3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1302
},
"timestamp": "2026-02-10T05:43:36.516Z",
"answer": 17297
},
{
"... | 1 | [] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||||
81ce5c | modular_mod_compute_v1_865884756_3497 | Let $n = 50176$ and $a = 8192$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 16000000$. Let $m$ be the minimum value of $x + y$ over all such pairs. Compute the value of $n - (a \bmod m)$. | 49,984 | graphs = [
Graph(
let={
"_n": Const(50176),
"a": Const(8192),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16000000))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T17:29:06.407480Z | {
"verified": true,
"answer": 49984,
"timestamp": "2026-02-08T17:29:06.410213Z"
} | 18b072 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 417
},
"timestamp": "2026-02-16T09:44:08.941Z",
"answer": 49184
},
{
"id": 11... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"sta... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
0f3ca7 | geo_count_lattice_triangle_v1_784195855_8761 | Let $A = (0,0)$, $B = (120,8)$, and $C = (222,121)$. The area of triangle $ABC$ is $\frac{1}{2} \cdot \text{area}_\text{2x}$, where $\text{area}_\text{2x}$ is the absolute value of $120 \cdot 121 + 222 \cdot (-8)$. Let $b$ be the number of lattice points on the boundary of triangle $ABC$, which is given by the sum
\[
\... | 6,368 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=121)), Mul(Const(value=222), Sub(left=Const(value=0), right=Const(value=8))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=8))), GCD(a=Abs(arg=Sub(left=Const(value=222), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.003 | 2026-02-08T16:18:08.032520Z | {
"verified": true,
"answer": 6368,
"timestamp": "2026-02-08T16:18:08.035231Z"
} | dc839b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 762
},
"timestamp": "2026-02-17T01:08:03.214Z",
"answer": 6368
},
{
... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
e39e4f | algebra_quadratic_discriminant_v1_1218484723_7773 | Compute $32^2 - 4(-2)(-128)$. | 0 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(32),
"c": Const(-128),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
},
goal=Ref("result"),
)
] | ALG | null | COMPUTE | sympy | LIN_FORM | [
"BINOMIAL_ALTERNATING",
"POLY_ORBIT_LEGENDRE"
] | d6c628 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM",
"POLY_ORBIT_LEGENDRE"
] | 3 | 0.747 | 2026-02-25T09:20:05.696725Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-25T09:20:06.443519Z"
} | 32b11a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 154
},
"timestamp": "2026-03-30T06:20:53.525Z",
"answer": 0
},
{
"id": ... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
9c81d5 | sequence_count_fib_divisible_v1_153355830_297 | Let $u$ be the number of positive integers $k$ such that $1 \leq k \leq 54189$ and $81$ divides $k$. Let $d = 12$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $d$ divides the $n$th Fibonacci number. | 55 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(54189)), Divides(divisor=Const(81), dividend=Var("k"))), domain='positive_integers')),
"d": Const(12),
"result": CountOverSet(set=Soluti... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C2"
] | 1 | 0.029 | 2026-02-08T03:00:36.250239Z | {
"verified": true,
"answer": 55,
"timestamp": "2026-02-08T03:00:36.279014Z"
} | a2fdaa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 2468
},
"timestamp": "2026-02-10T12:26:33.345Z",
"answer": 55
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
b46486 | comb_sum_binomial_row_v1_1125832087_1443 | Let $m = n = 16402$. Let $A$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq m$ and $\binom{n}{j}$ is odd. Let $B$ be the set of integers $k$ in the range $1 \leq k \leq 2$ such that $\phi(k) \cdot \left\lfloor \frac{2}{k} \right\rfloor$ contributes to a sum. Define $n$ to be the sum of the number o... | 2,048 | graphs = [
Graph(
let={
"_m": Const(16402),
"_n": Const(16402),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonneg... | NT | null | SUM | sympy | K2 | [
"K2/V8"
] | c69745 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"K2",
"V8"
] | 2 | 0.002 | 2026-02-08T03:44:47.286206Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T03:44:47.288371Z"
} | 2d6bbf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 1293
},
"timestamp": "2026-02-10T15:28:58.256Z",
"answer": 2048
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
a39203 | geo_count_lattice_rect_v1_349078426_18 | Let $a = 200$ and $b = 63$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$.
Find the value of this quantity. | 12,864 | graphs = [
Graph(
let={
"a": Const(200),
"b": Const(63),
"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 | 0.004 | 2026-02-08T12:46:53.316422Z | {
"verified": true,
"answer": 12864,
"timestamp": "2026-02-08T12:46:53.320366Z"
} | 3c64b4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 332
},
"timestamp": "2026-02-24T16:20:24.807Z",
"answer": 12864
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
d1f1a0 | lin_form_endings_v1_677425708_2907 | Let $a = 24$ and $b = 18$. Let $A = 45$ and $B = 30$. Define $g = \gcd(a, b)$. Let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Define
$$
T = a'A + b'B - a'b'.
$$
Let
$$
S = aA + bB - a - b + 1.
$$
Compute $S - T$. | 1,321 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(18),
"A_val": Const(45),
"B_val": Const(30),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:22:22.008167Z | {
"verified": true,
"answer": 1321,
"timestamp": "2026-02-08T05:22:22.009262Z"
} | b6f216 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 530
},
"timestamp": "2026-02-11T22:31:16.480Z",
"answer": 1347
},
{
"id": 11,... | 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": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a78899 | comb_bell_compute_v1_1820931509_658 | Let $A$ be the set of all nonnegative integers $j$ such that $j \leq 36928$ and $\binom{36928}{j}$ is odd. Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers satisfying $x_1 + x_2 = 14$. Define
$$
s = \sum_{k=0}^{m} (-1)^k \binom{7}{k}.
$$
Let $n$ be the number of elements in $A$ that are at l... | 4,140 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(36928),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositi... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING/V8"
] | 6d6eee | comb_bell_compute_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"V8"
] | 3 | 0.004 | 2026-02-08T11:49:15.642919Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T11:49:15.647416Z"
} | 7f2c0f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 1330
},
"timestamp": "2026-02-24T14:48:33.516Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
59dd3e | comb_count_permutations_fixed_v1_1520064083_3785 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = 11$, $1 \leq i \leq 10$, and $1 \leq j \leq 11$. Let $n$ be the number of elements in $S$ multiplied by the value of $\sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Let $w = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and let $k = 5w$. Compute the va... | 11,088 | graphs = [
Graph(
let={
"_n": Const(5),
"n2": Const(0),
"w": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sub(Binom(n=Const(18), k=Const(18)), Binom(n=Const(18), k=Const(18))),
... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING",
"ZERO_BINOM_N",
"ONE_BINOM_N"
] | f69814 | comb_count_permutations_fixed_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ONE_BINOM_N",
"ZERO_BINOM_N"
] | 4 | 0.015 | 2026-02-08T05:52:15.438644Z | {
"verified": true,
"answer": 11088,
"timestamp": "2026-02-08T05:52:15.453334Z"
} | aa6133 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 884
},
"timestamp": "2026-02-24T04:50:04.946Z",
"answer": 11088
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lem... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
7a5cfd | nt_sum_totient_over_divisors_v1_1520064083_624 | Let $m = 150$ and let $n$ be the largest integer such that $7^n$ divides $\binom{150}{60}$. Define $N = 329840537342525960761212613426147510168936200102419780766262451751763999903931843012248970567087665858619183685374251530979699437296135511460025670307310544656766341224079729842951046962237968404767732062727231685331... | 3,954 | graphs = [
Graph(
let={
"_m": Const(150),
"_n": MaxKDivides(target=Binom(n=Ref("_m"), k=Const(60)), base=Const(7)),
"n": MaxKDivides(target=Mul(Const(32984053734252596076121261342614751016893620010241978076626245175176399990393184301224897056708766585861918368537425153097... | NT | null | COMPUTE | sympy | V7 | [
"V7/K13"
] | a3c267 | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"K13",
"V7"
] | 2 | 0.001 | 2026-02-08T03:30:05.594899Z | {
"verified": true,
"answer": 3954,
"timestamp": "2026-02-08T03:30:05.596320Z"
} | ddbbcb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 1365,
"completion_tokens": 428
},
"timestamp": "2026-02-18T01:23:25.903Z",
"answer": 1
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
47d0a7 | diophantine_product_count_v1_1520064083_9291 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Let $\mathcal{S}$ be the set of all positive integers $x$ such that $1 \leq x \leq 249$, $x$ divides $k$, and $\frac{k}{x} \leq 249$. Compute the remainder when $53399 \cdot |\mathcal{S}|$ is divided by... | 50,947 | graphs = [
Graph(
let={
"_n": Const(58149),
"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")), Const(396900)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.03 | 2026-02-08T10:40:15.836015Z | {
"verified": true,
"answer": 50947,
"timestamp": "2026-02-08T10:40:15.865588Z"
} | cbe0ba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 2600
},
"timestamp": "2026-02-14T08:03:17.089Z",
"answer": 50947
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
57b375 | nt_min_phi_inverse_v1_349078426_1380 | Let $$k = \sum_{j=1}^{3} \phi(j) \left\lfloor \frac{3}{j} \right\rfloor,$$ where $\phi$ denotes Euler's totient function. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 20$ and $\phi(n) = k$. Determine the smallest element of $S$. Let $m$ be this value. Compute the remainder when $28723 \cdot ... | 20,943 | graphs = [
Graph(
let={
"_m": Const(90059),
"_n": Const(28723),
"upper": Const(20),
"k": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2"
] | 06cc86 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.017 | 2026-02-08T13:35:35.553413Z | {
"verified": true,
"answer": 20943,
"timestamp": "2026-02-08T13:35:35.570800Z"
} | e5ba3e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 861
},
"timestamp": "2026-02-15T17:58:07.555Z",
"answer": 20943
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"statu... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
886067 | nt_count_intersection_v1_48377204_793 | Let $N = 100000$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $5$ divides $n$, and $\gcd(n, 12) = 1$. | 6,667 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(5),
"b": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"K2/B3"
] | 07a241 | nt_count_intersection_v1 | null | 4 | 0 | [
"B3",
"K2",
"MAX_PRIME_BELOW"
] | 3 | 8.668 | 2026-02-08T15:42:33.247069Z | {
"verified": true,
"answer": 6667,
"timestamp": "2026-02-08T15:42:41.914916Z"
} | 4c0ae1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 1110
},
"timestamp": "2026-02-16T11:18:51.313Z",
"answer": 6667
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
02410a | sequence_count_fib_divisible_v1_898971024_3077 | Let $S$ be the set of all integers $t$ such that $11 \leq t \leq 340$ and there exist positive integers $a \leq 4$ and $b \leq 78$ for which $t = 7a + 4b$. Let $d_1$ be a positive divisor of 97656 that does not exceed the number of elements in $S$. Let $U$ be the maximum possible value of such $d_1$. Determine the numb... | 1,269 | graphs = [
Graph(
let={
"_m": Const(99923),
"_n": Const(44121),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_DIVISOR"
] | 8c55ae | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 0.031 | 2026-02-08T17:08:44.869850Z | {
"verified": true,
"answer": 1269,
"timestamp": "2026-02-08T17:08:44.901194Z"
} | 7d75f9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 4157
},
"timestamp": "2026-02-17T19:29:32.108Z",
"answer": 1269
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7e66d0 | nt_count_coprime_and_v1_1116507919_301 | Let $n$ be a positive integer such that $1 \leq n \leq 37063$. Define $k_1 = 7$ and $k_2 = 9$. Consider the condition that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = \sum_{d \mid \gcd(13,17)} \mu(d)$, where $\mu$ denotes the M\"obius function. Compute the number of such integers $n$ satisfying these conditions. | 21,179 | graphs = [
Graph(
let={
"upper": Const(37063),
"k1": Const(7),
"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("k1")), Const(1)), Eq(GCD(a=Var("n... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 3.738 | 2026-02-08T02:30:40.071588Z | {
"verified": true,
"answer": 21179,
"timestamp": "2026-02-08T02:30:43.809886Z"
} | 86a7a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1393
},
"timestamp": "2026-02-08T19:21:31.570Z",
"answer": 21179
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
85ef2b | algebra_quadratic_discriminant_v1_717093673_2720 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$. Let $P$ be the maximum value of $xy$ over all pairs $(x, y) \in S$. Compute $(-40)^2 - P \cdot (-2) \cdot (-200)$. | 0 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": Const(-40),
"c": Const(-200),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg... | NT | null | COMPUTE | sympy | B3 | [
"B1"
] | 5b950e | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B1",
"B3"
] | 2 | 0.013 | 2026-02-08T17:08:06.492196Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T17:08:06.504975Z"
} | 782080 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 346
},
"timestamp": "2026-02-16T09:03:51.419Z",
"answer": 800
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
255601 | modular_sum_quadratic_residues_v1_1248542787_546 | Let $p$ be the smallest prime divisor of $31056173$, and let $n = 4$. Compute $\frac{p(p-1)}{n}$. | 24,414 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(31056173))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
},
goal=... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T03:12:27.077270Z | {
"verified": true,
"answer": 24414,
"timestamp": "2026-02-08T03:12:27.078474Z"
} | 2795a3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 4414
},
"timestamp": "2026-02-23T17:36:04.010Z",
"answer": 24414
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status":... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
e1cd47 | modular_mod_compute_v1_601307018_1161 | Find the number of positive integers $t$ with $9 \le t \le 3095$ such that $t = 4c + 5b$ for some integers $c, b$ satisfying $1 \le c \le 230$ and $1 \le b \le 435$. Let $S = 82944 \bmod 46225$. Compute the remainder when $N \cdot S$ is divided by $59236$. | 7,109 | graphs = [
Graph(
let={
"_n": Const(59236),
"a": Const(82944),
"m": Const(46225),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | modular_mod_compute_v1 | affine_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-03-10T01:46:43.109166Z | {
"verified": true,
"answer": 7109,
"timestamp": "2026-03-10T01:46:43.111711Z"
} | 0b8ce4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T01:25:16.844Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "... | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
cbc8f4 | antilemma_k2_v1_898971024_793 | Compute the value of $$
\sum_{k=1}^{113} \phi(k) \left\lfloor \frac{113}{k} \right\rfloor.
$$ | 6,441 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(113), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(113), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T15:38:50.662422Z | {
"verified": true,
"answer": 6441,
"timestamp": "2026-02-08T15:38:50.662908Z"
} | 55b60b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 450
},
"timestamp": "2026-02-16T11:51:16.310Z",
"answer": 6441
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
497786 | alg_qf_psd_orbit_v1_1218484723_111 | Let $S$ be the number of integer pairs $(a_1, b_1)$ with $1 \leq a_1, b_1 \leq 30$ satisfying $20b_1^2 - 12a_1b_1 + 41a_1^2 \leq 16336$. Let $T$ be the number of integer pairs $(a_2, b_2)$ with $1 \leq a_2, b_2 \leq 30$ satisfying $384a_2^2b_2 + 128a_2^3 + 128b_2^3 + 384a_2b_2^2 = 628864$. Find the number of ordered pa... | 5 | graphs = [
Graph(
let={
"_m": Const(30),
"_n": Const(128),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(497)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=Solutions... | ALG | null | COUNT | sympy | POLY4_COUNT | [
"QF_PSD_COUNT_LEQ",
"POLY3_COUNT"
] | 6b3631 | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"POLY4_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 3.137 | 2026-02-25T01:49:45.694641Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-25T01:49:48.831665Z"
} | e51060 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T08:21:31.669Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 5.81,
"mid": 8.21,
"hi": 10
} | ||
c0c59e | modular_mod_compute_v1_601307018_7782 | Let $m$ be the largest positive integer divisor of $1505525$ such that $m^2 \leq 1505525$. Let $M = -44444 \bmod m$. Find the remainder when $\left(5^{|M|} \bmod 99991\right) + 36864$ is divided by $53756$. | 27,728 | graphs = [
Graph(
let={
"_n": Const(36864),
"a": Const(-44444),
"m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(1505525)), Leq(Mul(Var("d"), Var("d")), Const(1505525))))),
"result":... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | modular_mod_compute_v1 | null | 5 | 0 | [
"B3_CLOSEST"
] | 1 | 0.003 | 2026-03-10T08:21:23.438202Z | {
"verified": true,
"answer": 27728,
"timestamp": "2026-03-10T08:21:23.440996Z"
} | 2c1aff | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 8903
},
"timestamp": "2026-04-19T07:30:08.026Z",
"answer": 27728
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
ae913f | comb_binomial_compute_v1_151522320_1117 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 28$. Compute $\binom{n}{7}$. | 3,432 | graphs = [
Graph(
let={
"_n": Const(28),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"COMB1"
] | 567f58 | comb_binomial_compute_v1 | null | 4 | 0 | [
"COMB1",
"SUM_ARITHMETIC"
] | 2 | 0.011 | 2026-02-08T03:48:48.152318Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-08T03:48:48.163810Z"
} | cae883 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 998
},
"timestamp": "2026-02-10T15:49:17.239Z",
"answer": 3432
},
{
"id... | 2 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
60bbbe | modular_sum_quadratic_residues_v1_1520064083_10092 | Let $p$ be the largest prime number satisfying $2 \leq p \leq 460$. Let $r = \frac{p(p-1)}{4}$. Find the remainder when $44121 \cdot r$ is divided by $81142$. | 25,282 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(460)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=Mul(... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T11:12:04.478145Z | {
"verified": true,
"answer": 25282,
"timestamp": "2026-02-08T11:12:04.479534Z"
} | e30ae9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 2498
},
"timestamp": "2026-02-14T10:48:10.554Z",
"answer": 25282
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ca8a40 | antilemma_k3_v1_865884756_3 | Let $n = 92888$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the remainder when $44121 \cdot x$ is divided by $88469$. | 73,492 | graphs = [
Graph(
let={
"_n": Const(92888),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(88469)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:06:37.429368Z | {
"verified": true,
"answer": 73492,
"timestamp": "2026-02-08T15:06:37.430312Z"
} | df9361 | 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": 1741
},
"timestamp": "2026-02-10T02:24:59.700Z",
"answer": 73492
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
681ebe | comb_count_derangements_v1_2051736721_1348 | Let $n$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $p \cdot q = 9261000$ and $\gcd(p, q) = 1$. Let $r = !n$, the subfactorial of $n$. Compute the remainder when $18227 \cdot r$ is divided by $75552$. | 36,035 | graphs = [
Graph(
let={
"_n": Const(75552),
"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=9261000)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T15:59:14.101330Z | {
"verified": true,
"answer": 36035,
"timestamp": "2026-02-08T15:59:14.104388Z"
} | 7c7d33 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 3161
},
"timestamp": "2026-02-16T18:22:06.103Z",
"answer": 36035
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c7eea | nt_sum_over_divisible_v1_168721529_1090 | Let $n = 146$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. For each such pair, compute the product $xy$. Let $M$ be the maximum value of $xy$ over all such pairs.
Now, let $S$ be the set of all positive integers $k$ such that $k \leq M$ and $k$ is divisible by 150. Comput... | 94,500 | graphs = [
Graph(
let={
"_n": Const(146),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y"))))... | NT | null | SUM | sympy | ONE_PHI_1 | [
"B1"
] | 5b950e | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"B1",
"ONE_PHI_1"
] | 2 | 8.996 | 2026-02-08T13:27:46.010183Z | {
"verified": true,
"answer": 94500,
"timestamp": "2026-02-08T13:27:55.006608Z"
} | 359910 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 820
},
"timestamp": "2026-02-09T13:40:11.339Z",
"answer": 94500
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.65,
"mid": -2.15,
"hi": 1.88
} | ||
d3945b | sequence_count_fib_divisible_v1_1742523217_298 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 142884$. Let $\sigma$ be the minimum value of $x + y$ over all such pairs. Determine the number of positive integers $n$ such that $1 \leq n \leq \sigma$ and $9$ divides $F_n$, where $F_n$ is the $n$th Fibonacci number. | 63 | 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(142884)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(9... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 0.058 | 2026-02-08T02:57:52.992312Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T02:57:53.050404Z"
} | 95c97e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1979
},
"timestamp": "2026-02-09T16:03:58.840Z",
"answer": 63
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -0.21,
"mid": 2.08,
"hi": 3.97
} | ||
758146 | sequence_fibonacci_compute_v1_1520064083_7565 | Let $n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $F_n$ be the $n$-th Fibonacci number. Compute the remainder when $44121 \cdot F_n$ is divided by $77948$. | 60,606 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), modulus=Con... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T09:08:57.298071Z | {
"verified": true,
"answer": 60606,
"timestamp": "2026-02-08T09:08:57.298822Z"
} | 4b44e9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 4173
},
"timestamp": "2026-02-14T01:07:07.241Z",
"answer": 60606
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3b0d9c | nt_min_coprime_above_v1_458359167_4769 | Let $ a $ be the smallest integer $ n $ such that $ 23436 < n \leq 23579 $ and $ \gcd(n, 133) = 1 $. Let $ b $ be the maximum value of $ xy $ over all pairs of positive integers $ (x, y) $ such that $ x + y = 66 $. Compute the remainder when $ a^2 + 48a + b $ is divided by $ 65290 $. | 24,334 | graphs = [
Graph(
let={
"_n": Const(65290),
"start": Const(23436),
"upper": Const(23579),
"modulus": Const(133),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | bf138c | nt_min_coprime_above_v1 | quadratic_mod | 4 | 0 | [
"B1"
] | 1 | 0.015 | 2026-02-08T12:02:23.791777Z | {
"verified": true,
"answer": 24334,
"timestamp": "2026-02-08T12:02:23.807199Z"
} | 0a3105 | 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": 1951
},
"timestamp": "2026-02-14T21:51:59.840Z",
"answer": 24334
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d1b38f | comb_count_derangements_v1_1218484723_5325 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 9$. Compute the number of derangements of $n$ elements, denoted $D_n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(9),
"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(9)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_derangements_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.006 | 2026-02-25T06:56:19.087606Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-25T06:56:19.093874Z"
} | 76793f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 878
},
"timestamp": "2026-03-29T20:31:53.436Z",
"answer": 14833
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
2845f4 | nt_count_divisors_in_range_v1_48377204_3109 | Let $n$ be the number of positive integers at most $9449$ that are relatively prime to $30$. Let $r$ be the number of positive divisors of $n$ that are between $1$ and $364$, inclusive. Compute the value of $$ r + 2^r \bmod 54327, $$ where the exponent $r$ is reduced modulo $$ \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{... | 4,138 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(9449)), Eq(GCD(a=Var("n1"), b=Const(30)), Const(1))))),
"a": Const(1),
"b": Const(364),
"result": CountOverSet(set=SolutionsS... | NT | null | COUNT | sympy | K2 | [
"K2",
"C4"
] | 895faa | nt_count_divisors_in_range_v1 | mod_exp | 6 | 0 | [
"C4",
"K2"
] | 2 | 0.014 | 2026-02-08T17:11:37.028708Z | {
"verified": true,
"answer": 4138,
"timestamp": "2026-02-08T17:11:37.042832Z"
} | 3de5e6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 2973
},
"timestamp": "2026-02-17T21:39:08.442Z",
"answer": 4138
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_S... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
081593 | nt_count_coprime_v1_1520064083_2731 | Let $k = 17$ and $N = 48205$. Let $r$ be the number of positive integers $n \leq 48205$ such that $\gcd(n, 17) = 1$. Let $c$ be the largest prime number in the range $2 \leq n \leq 5008$. Compute the value of
$$
Q = \left( (r \bmod 293) + c \cdot (r \bmod 337) \right) \bmod 72290.
$$ | 48,824 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(48205),
"k": Const(17),
"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")), Const(1))))),
"... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_coprime_v1 | two_moduli | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 4.187 | 2026-02-08T04:57:56.173969Z | {
"verified": true,
"answer": 48824,
"timestamp": "2026-02-08T04:58:00.361448Z"
} | f07b4b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1727
},
"timestamp": "2026-02-11T22:38:46.808Z",
"answer": 48824
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6578b0 | diophantine_sum_product_min_v1_655260480_687 | Let $S$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 25$.
Let $P = 9$. Find the smallest positive integer $x_1 \leq 9$ such that $x_1(S - x_1) = P$.
Compute $65239$ times this value of $x_1$. | 65,239 | graphs = [
Graph(
let={
"S": 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(25)))), expr=Sum(Var("x"), Var("y")))),
"P": Const(9),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.012 | 2026-02-08T15:31:59.993002Z | {
"verified": true,
"answer": 65239,
"timestamp": "2026-02-08T15:32:00.004693Z"
} | 0a4e2e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 323
},
"timestamp": "2026-02-16T06:08:29.315Z",
"answer": 65239
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
63da00 | algebra_poly_eval_v1_655260480_824 | Let $k$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 10$. Define $\text{result} = 6k^2 + 2k + 1$. Compute $\text{result}$. | 3,801 | graphs = [
Graph(
let={
"_n": Const(6),
"k": 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(10)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T15:38:42.990166Z | {
"verified": true,
"answer": 3801,
"timestamp": "2026-02-08T15:38:42.993515Z"
} | e44aed | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 251
},
"timestamp": "2026-02-16T06:12:50.290Z",
"answer": 3801
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
55c118 | sequence_count_fib_divisible_v1_784195855_8812 | Let $d$ be the largest prime number between 2 and 22, inclusive. Let $N$ be the number of positive integers $n$ less than or equal to 958 such that $d$ divides the $n$th Fibonacci number. Compute the remainder when $|N|$ is divided by 84270. | 53 | graphs = [
Graph(
let={
"upper": Const(958),
"d": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(22)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), ... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.07 | 2026-02-08T16:22:20.162565Z | {
"verified": true,
"answer": 53,
"timestamp": "2026-02-08T16:22:20.232779Z"
} | 41e0be | 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": 1572
},
"timestamp": "2026-02-17T02:08:13.542Z",
"answer": 53
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
87606a | nt_num_divisors_compute_v1_1978505735_1273 | Compute the number of positive divisors of 66666. | 16 | graphs = [
Graph(
let={
"n": Const(66666),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"B1/BIG_OMEGA_ZERO/MOBIUS_COPRIME"
] | 90f8ed | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B1",
"BIG_OMEGA_ZERO",
"MOBIUS_COPRIME"
] | 3 | 0.037 | 2026-02-08T16:00:13.325749Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T16:00:13.362671Z"
} | eb75fd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 70,
"completion_tokens": 348
},
"timestamp": "2026-02-16T06:49:40.743Z",
"answer": 48
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_l... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
3e63ca | sequence_lucas_compute_v1_153355830_592 | Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 96$ and there exist positive integers $a \leq 2$ and $b \leq 11$ satisfying $t = 15a + 6b$. Let $n$ be the number of elements in $T$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. ... | 27,096 | graphs = [
Graph(
let={
"_n": Const(51389),
"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=2)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:10:38.864018Z | {
"verified": true,
"answer": 27096,
"timestamp": "2026-02-08T03:10:38.865158Z"
} | c5ab32 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 3013
},
"timestamp": "2026-02-10T15:15:18.948Z",
"answer": 27096
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3938f7 | nt_count_digit_sum_v1_784195855_8339 | Let $S$ be the set of all positive integers $n$ such that $n \leq 99999$ and the sum of the digits of $n$ is 21. Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 392$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 28$, $1 \leq b \leq 84$, and $t = 5a + 3b$. Compute the remainder when $... | 60,699 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": Const(21),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
"Q": Mod(value=Sub(C... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | nt_count_digit_sum_v1 | negation_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 14.052 | 2026-02-08T16:00:52.741064Z | {
"verified": true,
"answer": 60699,
"timestamp": "2026-02-08T16:01:06.793017Z"
} | 849564 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 4797
},
"timestamp": "2026-02-16T19:08:46.021Z",
"answer": 60699
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
58e50e | nt_count_coprime_and_v1_1520064083_850 | Let $k_1 = 11$. Let $k_2$ be the largest prime number $n$ with $1 \le n \le 16$ such that $n$ is at least the number of positive integers $p$ for which there exists an integer $q > p$ with $pq = 36$ and $\gcd(p, q) = 1$.
Find the number of positive integers $n$ with $1 \le n \le 16175$ such that $\gcd(n, k_1) = 1$ and... | 13,574 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": Const(16175),
"k1": Const(11),
"k2": 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... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | nt_count_coprime_and_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 2.117 | 2026-02-08T03:37:47.292301Z | {
"verified": true,
"answer": 13574,
"timestamp": "2026-02-08T03:37:49.409713Z"
} | 3e3f63 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1374
},
"timestamp": "2026-02-10T15:07:39.303Z",
"answer": 13575
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
69e6d1 | nt_count_divisible_and_v1_1248542787_950 | Let $n$ be a positive integer such that $1 \leq n \leq 206880$, $n$ is divisible by 10, and the remainder when $n$ is divided by 12 equals $\sum_{d\mid 11} \mu(d)$, where $\mu$ denotes the M\"obius function. Determine the number of such integers $n$, and let this number be $R$. Compute the remainder when $82121 \cdot R... | 16,568 | graphs = [
Graph(
let={
"upper": Const(206880),
"d1": Const(10),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq... | NT | null | COUNT | sympy | MOBIUS_SUM | [
"MOBIUS_SUM"
] | 518e32 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"MOBIUS_SUM"
] | 1 | 9.74 | 2026-02-08T03:30:10.645501Z | {
"verified": true,
"answer": 16568,
"timestamp": "2026-02-08T03:30:20.385508Z"
} | 8a94d7 | 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": 1815
},
"timestamp": "2026-02-09T10:26:01.476Z",
"answer": 16568
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
7394ae_l | comb_factorial_compute_v1_1978505735_4144 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 1282$ for which $\binom{1282}{j}$ is odd. Let $r = n!$. Compute the remainder when $12151 \cdot r$ is divided by $86385$. | 0 | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.004 | 2026-02-08T18:02:21.338626Z | {
"verified": false,
"answer": 38985,
"timestamp": "2026-02-08T18:02:21.342485Z"
} | 617a18 | 7394ae | legacy_text | 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": 6168
},
"timestamp": "2026-02-18T12:40:44.404Z",
"answer": 38985
},
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | |
c87dd6 | geo_count_lattice_rect_v1_1526740231_366 | Let $a = 353$ and $b = 192$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Find the value of this number. | 68,322 | graphs = [
Graph(
let={
"a": Const(353),
"b": Const(192),
"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 | 2026-02-08T11:29:29.264891Z | {
"verified": true,
"answer": 68322,
"timestamp": "2026-02-08T11:29:29.265832Z"
} | 374594 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 385
},
"timestamp": "2026-02-24T14:01:27.599Z",
"answer": 68322
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||||
c5bcd8 | geo_count_lattice_rect_v1_1526740231_384 | Compute the number of lattice points in the rectangle defined by $0 \leq x \leq 111$ and $0 \leq y \leq 49$, including the boundary. Determine the value of this count. | 5,600 | graphs = [
Graph(
let={
"a": Const(111),
"b": Const(49),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T11:30:25.434049Z | {
"verified": true,
"answer": 5600,
"timestamp": "2026-02-08T11:30:25.434797Z"
} | e6f6bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 209
},
"timestamp": "2026-02-24T14:02:12.674Z",
"answer": 5600
},
{
"id... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
d39048 | alg_sum_ap_v1_601307018_3126 | Let $M = \sum_{k=0}^{\left|\{ (a, b) \in \mathbb{Z}^+ \times \mathbb{Z}^+ : a \leq 35, b \leq 35,\ 10a^2 - 18ab + 25b^2 \leq 12913 \}\right|} (5k + 16) \bmod 6887$. Find the remainder when $44121M$ is divided by $60217$. | 38,054 | graphs = [
Graph(
let={
"_n": Const(6887),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_sum_ap_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.027 | 2026-03-10T03:42:19.346097Z | {
"verified": true,
"answer": 38054,
"timestamp": "2026-03-10T03:42:19.373266Z"
} | fa36de | 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": 9404
},
"timestamp": "2026-03-29T07:34:55.041Z",
"answer": 38054
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
7d7c50 | comb_bell_compute_v1_784195855_3360 | Let $n = 9$ and let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of size $n$. Let $C$ be the number of positive integers $k \leq 240$ for which the $k$th Fibonacci number is even. Compute the remainder when $C - B_n$ is divided by 73647. | 52,580 | graphs = [
Graph(
let={
"_n": Const(240),
"n": Const(9),
"result": Bell(Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(2), dividend=Fibonacci(arg=Var(name='n')... | COMB | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 222f73 | comb_bell_compute_v1 | negation_mod | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.003 | 2026-02-08T06:22:28.572173Z | {
"verified": true,
"answer": 52580,
"timestamp": "2026-02-08T06:22:28.575420Z"
} | 15f7f1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 863
},
"timestamp": "2026-02-12T23:25:07.859Z",
"answer": 52580
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
43f40f | comb_count_permutations_fixed_v1_601307018_4999 | Let $D_n$ denote the number of derangements of $n$ elements. For each non-negative integer $a$ with $0 \le a \le 9408$, define the sequence
$$
M = a^3 + 3a \bmod 9409,\quad R = M^3 + 3M \bmod 9409,\quad S = R^3 + 3R \bmod 9409,\quad T = S^3 + 3S \bmod 9409.
$$
Let $k$ be the number of values of $a$ such that $T = a$, $... | 5,544 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(9),
"k": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(9408)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.004 | 2026-03-10T05:40:43.854069Z | {
"verified": true,
"answer": 5544,
"timestamp": "2026-03-10T05:40:43.858507Z"
} | ec6f63 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 6038
},
"timestamp": "2026-04-19T00:39:18.634Z",
"answer": 5544
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V8"... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} |
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