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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
b1c538 | comb_count_surjections_v1_2051736721_1523 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 4$, $1 \leq j \leq 5$, and $i + j = 6$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Compute the value of $k! \cdot S(4, k)$, where $S(n, k)$ denotes the Stirling number of the... | 14 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(5))))),
"n": Co... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1"
] | 5b2e59 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.018 | 2026-02-08T16:05:07.491852Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T16:05:07.509841Z"
} | 5ab874 | 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": 622
},
"timestamp": "2026-02-24T19:47:54.894Z",
"answer": 14
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
179aad | geo_count_lattice_rect_v1_677425708_1524 | Let $a = 90$ and $b = 34$. Consider the rectangle in the coordinate plane with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Compute the number of lattice points (points with integer coordinates) that lie inside or on the boundary of this rectangle. | 3,185 | graphs = [
Graph(
let={
"a": Const(90),
"b": Const(34),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T04:14:29.992514Z | {
"verified": true,
"answer": 3185,
"timestamp": "2026-02-08T04:14:29.993081Z"
} | e5a645 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 324
},
"timestamp": "2026-02-09T21:03:21.964Z",
"answer": 3185
},
{
"id... | 1 | [] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||||
0f3498 | nt_sum_gcd_range_mod_v1_1248542787_654 | Let $N$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 44467$ and $\binom{44467}{j}$ is odd. Let $k = 336$ and $M = 10337$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $M$. | 9,444 | graphs = [
Graph(
let={
"_n": Const(44467),
"N": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(44467), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"k... | NT | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.091 | 2026-02-08T03:17:06.356377Z | {
"verified": true,
"answer": 9444,
"timestamp": "2026-02-08T03:17:06.447617Z"
} | 707e90 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 5750
},
"timestamp": "2026-02-09T06:41:15.923Z",
"answer": 8940
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
8919a1 | algebra_poly_eval_v1_124444284_5523 | Let $z = 19$. Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \le a \le 3$, $1 \le b \le 3$, $5 \le t \le 15$, and $t = 2a + 3b$. Let $n = 4$. Compute $5z^3 - 9z^2 + |S| \cdot z + n$. | 31,221 | graphs = [
Graph(
let={
"_n": Const(4),
"z": Const(19),
"result": Sum(Mul(Const(5), Pow(Ref("z"), Const(3))), Mul(Const(-9), Pow(Ref("z"), Const(2))), Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), c... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:40:07.466979Z | {
"verified": true,
"answer": 31221,
"timestamp": "2026-02-08T06:40:07.468951Z"
} | 7501bf | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1088
},
"timestamp": "2026-02-15T17:42:41.617Z",
"answer": 31039
},
{
"id": 1... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
bdd18e | comb_bell_compute_v1_1470522791_1107 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 36750$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$. Compute the $n$-th Bell number, which is the number of ways to partition a set of $n$ elements. | 4,140 | 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=36750)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T13:26:14.151290Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T13:26:14.153277Z"
} | 081ff7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 2522
},
"timestamp": "2026-02-15T15:38:57.439Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e3f1aa | antilemma_k3_v1_784195855_9548 | Compute the sum $\sum_{d \mid 18385} \phi(d)$, where $\phi$ denotes Euler's totient function. | 18,385 | graphs = [
Graph(
let={
"_n": Const(18385),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:53:13.543720Z | {
"verified": true,
"answer": 18385,
"timestamp": "2026-02-08T16:53:13.544293Z"
} | 4d00fc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 936
},
"timestamp": "2026-02-16T08:37:42.532Z",
"answer": 7200
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
a91bc8 | modular_mod_compute_v1_1080341949_393 | Let $a$ be the number of positive integers $k$ such that $1 \leq k \leq 3038049$ and $441$ divides $k$. Let $m = 2048$, and let $r$ be the remainder when $a$ is divided by $m$. Compute $16384 - r$. | 15,639 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(3038049)), Divides(divisor=Const(441), dividend=Var("k"))), domain='positive_integers')),
"m": Const(2048),
"result": Mod(value=Ref("a"), mo... | ALG | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | modular_mod_compute_v1 | null | 3 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T13:28:29.332382Z | {
"verified": true,
"answer": 15639,
"timestamp": "2026-02-08T13:28:29.333496Z"
} | 8bb8c9 | 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": 900
},
"timestamp": "2026-02-15T16:09:58.446Z",
"answer": 15639
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ae31bc | comb_factorial_compute_v1_458359167_3864 | Let $n$ be the smallest integer $d \geq 2$ that divides the number of positive integers $n$ such that $n \leq \sum x$, where the sum is taken over all real numbers $x$ satisfying $x^2 - 2117x - 171210 = 0$, and $\gcd(n, 20) = 1$. Compute the remainder when $99360 \cdot n!$ is divided by 78173. | 76,335 | graphs = [
Graph(
let={
"_m": Const(20),
"_n": Const(78173),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/C4/MIN_PRIME_FACTOR"
] | 81e893 | comb_factorial_compute_v1 | null | 6 | 0 | [
"C4",
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 3 | 0.005 | 2026-02-08T11:23:56.317272Z | {
"verified": true,
"answer": 76335,
"timestamp": "2026-02-08T11:23:56.322267Z"
} | 4bebde | 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": 2140
},
"timestamp": "2026-02-14T13:48:03.484Z",
"answer": 76335
},
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"sta... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
504414 | nt_min_crt_v1_2051736721_2381 | Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 4$. Let $n$ be the smallest positive integer at most 20 such that $n \equiv 0 \pmod{m}$ and $n \equiv 3 \pmod{5}$. Compute the remainder when $44121n$ is divided by $72848$. | 61,576 | graphs = [
Graph(
let={
"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(4)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(5),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_crt_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T16:38:46.753989Z | {
"verified": true,
"answer": 61576,
"timestamp": "2026-02-08T16:38:46.762570Z"
} | 9e87ac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 596
},
"timestamp": "2026-02-17T08:43:42.284Z",
"answer": 61576
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f6fed4 | comb_count_partitions_v1_898971024_57 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 16211$ and $377$ divides $k$. Define $P(n)$ to be the number of integer partitions of $n$. Compute $P(n)$. | 63,261 | graphs = [
Graph(
let={
"_n": Const(16211),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Const(377), dividend=Var("k"))), domain='positive_integers')),
"result": Partition(arg=Ref(name='n... | COMB | NT | COUNT | sympy | C2 | [
"C2"
] | 9685eb | comb_count_partitions_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.002 | 2026-02-08T15:10:27.456443Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T15:10:27.458120Z"
} | fd6f23 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 934
},
"timestamp": "2026-02-16T01:00:13.813Z",
"answer": 63261
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
33c7fd | algebra_poly_eval_v1_238844314_0 | Compute the value of $9^4 - 3 \cdot 9^3 + 5 \cdot 9^2 + 9 \cdot 9 + N$, where $N$ is the number of ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 9$, $1 \le j \le 10$, and $i + j = 11$. Find the remainder when $78393$ times this value is divided by $71296$. | 48,029 | graphs = [
Graph(
let={
"_n": Const(9),
"x": Const(9),
"result": Sum(Pow(Ref("x"), Const(4)), Mul(Const(-3), Pow(Ref("x"), Const(3))), Mul(Const(5), Pow(Ref("x"), Const(2))), Mul(Ref("_n"), Ref("x")), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]),... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | algebra_poly_eval_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.075 | 2026-02-08T13:04:35.160612Z | {
"verified": true,
"answer": 48029,
"timestamp": "2026-02-08T13:04:35.235706Z"
} | 42a8c6 | 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": 2568
},
"timestamp": "2026-02-15T09:29:41.623Z",
"answer": 48029
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6324f3 | comb_factorial_compute_v1_349078426_1011 | Let $m = 2$. Let $p$ be the largest prime number $n$ such that $m \leq n \leq 7$. Let $q$ be the largest prime number $n$ such that $2 \leq n \leq p$. Compute $q!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(7)), IsPrime(Var("n"))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T13:22:08.436270Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T13:22:08.439579Z"
} | a70c42 | 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": 428
},
"timestamp": "2026-02-15T14:29:02.485Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
e94891 | antilemma_k3_v1_1439011603_818 | Compute the sum $$\sum_{d \mid 93134} \phi(d),$$ where $\phi(d)$ denotes Euler's totient function. | 93,134 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=93134), 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 | 2026-02-08T15:45:34.799038Z | {
"verified": true,
"answer": 93134,
"timestamp": "2026-02-08T15:45:34.799536Z"
} | 8cd1ca | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 944
},
"timestamp": "2026-02-16T06:18:36.944Z",
"answer": 54003
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
464a85 | comb_count_permutations_fixed_v1_2080023795_39 | Let $n = 10$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9$. Define $k$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute $\binom{10}{k} \cdot ! (10 - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 1,890 | graphs = [
Graph(
let={
"n": Const(10),
"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(9)))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T11:30:16.392275Z | {
"verified": true,
"answer": 1890,
"timestamp": "2026-02-08T11:30:16.394357Z"
} | 28cbc4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 594
},
"timestamp": "2026-02-08T20:37:27.899Z",
"answer": 1890
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
10d1a9 | modular_count_residue_v1_784195855_2680 | Let $n = 79781$ and let $m$ be the smallest divisor of $n$ that is at least $2$. Let $r = 12$ and let $U = 88209$. Consider the set of all positive integers $k$ such that $1 \leq k \leq U$ and $k \equiv r \pmod{m}$. Compute the number of elements in this set. Multiply this number by $44121$, and find the remainder when... | 59,215 | graphs = [
Graph(
let={
"_n": Const(79781),
"upper": Const(88209),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"r": Const(12),
"result": CountOverSet(set=So... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 7.707 | 2026-02-08T05:55:50.281581Z | {
"verified": true,
"answer": 59215,
"timestamp": "2026-02-08T05:55:57.988704Z"
} | 816582 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1998
},
"timestamp": "2026-02-12T16:59:14.490Z",
"answer": 59215
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"stat... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
094721 | geo_count_lattice_rect_v1_124444284_5557 | Compute the number of lattice points $(x, y)$ such that $0 \le x \le 361$ and $0 \le y \le 212$. | 77,106 | graphs = [
Graph(
let={
"a": Const(361),
"b": Const(212),
"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 | 2026-02-08T06:42:39.748974Z | {
"verified": true,
"answer": 77106,
"timestamp": "2026-02-08T06:42:39.749427Z"
} | 4011c0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 231
},
"timestamp": "2026-02-24T06:52:05.964Z",
"answer": 77106
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||||
2bf0d3 | antilemma_v8_lucas_548369836_218 | Let $s$ be the sum of $\mu(d)$ over all positive divisors $d$ of $\gcd(110, 110)$, where $\mu$ is the M\"obius function. Determine the number of integers $j$ such that $s \leq j \leq 61631$ and $\binom{61631}{j}$ is odd. | 2,048 | graphs = [
Graph(
let={
"_n": Const(61631),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), SumOverDivisors(n=GCD(a=Const(value=110), b=Const(value=110)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(616... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"V8"
] | 0d4771 | antilemma_v8_lucas | null | 6 | 0 | [
"MOBIUS_COPRIME",
"V8"
] | 2 | 0.001 | 2026-02-08T02:49:19.858462Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T02:49:19.859937Z"
} | 537ca8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1115
},
"timestamp": "2026-02-08T20:15:17.583Z",
"answer": 2048
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"... | {
"lo": -1.89,
"mid": 1.79,
"hi": 4.93
} | ||
a564ac | sequence_fibonacci_compute_v1_349078426_2000 | Let $m = 72350$. Define $p$ to be a positive integer such that there exists a positive integer $q$ satisfying $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all such integers $p$. Let $n$ be the largest integer $k$ such that $|S|^k \leq 31547857$. Compute the remainder when $24003 \cdot F_n$ is... | 11,054 | graphs = [
Graph(
let={
"_m": Const(72350),
"_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=216)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_VAL"
] | aa93c6 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_VAL"
] | 2 | 0.005 | 2026-02-08T14:03:40.196005Z | {
"verified": true,
"answer": 11054,
"timestamp": "2026-02-08T14:03:40.201073Z"
} | fd2217 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 2576
},
"timestamp": "2026-02-15T23:15:18.693Z",
"answer": 11054
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
{
"lem... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
86ac10 | diophantine_sum_product_min_v1_1520064083_490 | Let $S = 89$ and $P = 790$. Consider the set of all positive integers $x$ such that $1 \leq x \leq 88$ and $x(S - x) = P$. Let $r$ be the smallest such $x$. Compute the remainder when the Bell number $B_{|r| \bmod 11}$ is divided by $79712$. | 36,263 | graphs = [
Graph(
let={
"S": Const(89),
"P": Const(790),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(88)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
"Q": Mod(value=Bell(Mod(value... | COMB | null | EXTREMUM | sympy | B1 | [
"B1/B3/LIN_FORM"
] | 565f4a | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 0.112 | 2026-02-08T03:26:39.838142Z | {
"verified": true,
"answer": 36263,
"timestamp": "2026-02-08T03:26:39.949780Z"
} | 6c0037 | 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": 896
},
"timestamp": "2026-02-10T14:25:08.035Z",
"answer": 36263
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
516f7f | nt_euler_phi_compute_v1_865884756_204 | Let $n = 34969$ and define $r = \phi(n)$, where $\phi$ is Euler's totient function. Consider the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 182895773590530$, $\gcd(p, q) = 1$, and $p < q$. Let $C$ be the number of such integers $p$. Determine the set of all ordered pa... | 22,426 | graphs = [
Graph(
let={
"_n": Const(52314),
"n": Const(34969),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=V... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 7948cf | nt_euler_phi_compute_v1 | negation_mod | 5 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.005 | 2026-02-08T15:15:52.010622Z | {
"verified": true,
"answer": 22426,
"timestamp": "2026-02-08T15:15:52.016082Z"
} | 21e979 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 7171
},
"timestamp": "2026-02-11T11:05:42.592Z",
"answer": 22426
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": 0.22,
"hi": 7.52
} | ||
b56fbb_n | geo_count_lattice_rect_v1_1218484723_3845 | An artist paints on a canvas divided into unit squares. The width of the canvas is determined by the sum $\sum_{k=1}^{10} \varphi(k) \cdot \lfloor 10/k \rfloor$, which counts reduced fractions with denominator up to 10. The height is fixed at 30 units (from $y=0$ to $y=29$). How many grid points lie within or on the bo... | 1,680 | GEOM | GEOM | COUNT | sympy | K2 | [
"K2"
] | 6897ab | geo_count_lattice_rect_v1 | null | 3 | null | [
"K2"
] | 1 | 0.003 | 2026-02-25T05:30:01.931335Z | null | 928284 | b56fbb | narrative | 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": 9001
},
"timestamp": "2026-03-30T20:42:59.514Z",
"answer": 1680
},
{
"i... | 1 | [
{
"lemma": "K2",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
b7f93f | comb_sum_binomial_row_v1_1218484723_3123 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 20$ such that $$17a^4 + 68ab^3 + 17b^4 + 68a^3b + 102a^2b^2 = 352512.$$ Compute $2^n$. | 2,048 | graphs = [
Graph(
let={
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Eq(Sum(Mul(Const(17), Pow(Var("a"), Ref("_n"))), Mu... | COMB | null | SUM | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"POLY4_COUNT"
] | 1 | 0.003 | 2026-02-25T04:51:10.548497Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-25T04:51:10.551268Z"
} | 53872b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1426
},
"timestamp": "2026-03-29T08:29:45.415Z",
"answer": 2048
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
a2169b_l | comb_count_surjections_v1_1520064083_6163 | Let $n$ be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 5$, $1 \leq j \leq 6$, and $i + j = 7$. Compute the value of $5! \cdot S(n, 5)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $m$ be the number of integers $t$ with $5 \leq t \leq 17$ for which there exist positive integers $a \le... | 1 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | ca8181 | comb_count_surjections_v1 | bell_mod | 7 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.013 | 2026-02-08T07:54:34.596382Z | {
"verified": false,
"answer": 40728,
"timestamp": "2026-02-08T07:54:34.609097Z"
} | a288ea | a2169b | 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": 287,
"completion_tokens": 1498
},
"timestamp": "2026-02-24T08:35:35.966Z",
"answer": 40728
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | |
f1aba9 | algebra_quadratic_discriminant_v1_784195855_6367 | Let $a = 1$, $b$ be the number of positive integers $j$ such that $1 \leq j \leq 5$ and $j^4 \leq 625$, and $c = 12$. Define $D = b^2 - 4ac$.
Let $r = 2$ if $D > 0$, and $r = 1$ if $D = 0$. (If $D < 0$, let $r = 0$.)
Compute the Bell number $B_k$, where $k$ is the remainder when $|r|$ is divided by 11. | 1 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(1),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(5)), Leq(Pow(Var("j"), Const(4)), Const(625))), domain='positive_integers')),
"c": Const(12),
... | COMB | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"C3"
] | 1 | 0.004 | 2026-02-08T08:36:41.200121Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T08:36:41.204243Z"
} | f03235 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 256
},
"timestamp": "2026-02-24T09:43:57.895Z",
"answer": 1
},
{
"id": ... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
ed3c85 | lin_form_endings_v1_784195855_7339 | Let $a = 70$ and $b = 28$. Compute the least positive integer $x$ such that
$$
x \equiv 14625 \cdot \text{lcm}(a, b) \pmod{64638}.
$$ | 43,722 | graphs = [
Graph(
let={
"a_coeff": Const(70),
"b_coeff": Const(28),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(14625),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(64638),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:13:17.042500Z | {
"verified": true,
"answer": 43722,
"timestamp": "2026-02-08T09:13:17.043012Z"
} | e24ba7 | 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": 1453
},
"timestamp": "2026-02-14T01:28:51.417Z",
"answer": 43722
},
{... | 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",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
49d2e3 | nt_sum_gcd_range_mod_v1_1520064083_41 | Let $N$ be the number of positive integers $t$ such that $14 \leq t \leq 6074$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 967$, $1 \leq b \leq 34$, and $t = 6a + 8b$. Let $k = 288$ and $M = 10597$. Compute the remainder when
$$
\sum_{n=1}^{N} \gcd(n, k)
$$
is divided by $M$. | 3,431 | 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=967)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.167 | 2026-02-08T02:58:12.003423Z | {
"verified": true,
"answer": 3431,
"timestamp": "2026-02-08T02:58:12.170915Z"
} | 8b59d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T21:08:05.117Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
d2b272 | nt_count_gcd_equals_v1_809748730_223 | Let $d$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 771750$, $\gcd(p,q) = 1$, and $p < q$. Compute the number of positive integers $n \leq 13924$ such that $\gcd(n, 176) = d$. Multiply this count by $44121$ and find the remainder when the result is divided by $54... | 5,215 | graphs = [
Graph(
let={
"upper": Const(13924),
"k": Const(176),
"d": 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=771750)), Eq(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.136 | 2026-02-08T11:23:31.707323Z | {
"verified": true,
"answer": 5215,
"timestamp": "2026-02-08T11:23:32.842970Z"
} | b68115 | 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": 2162
},
"timestamp": "2026-02-14T13:56:18.791Z",
"answer": 5215
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8ebcc4 | comb_count_partitions_v1_1978505735_8024 | Let $m = 10$ and $n_2 = 12$. Define
$$
t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $a$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $b = 5$ and define $n_1 = a + b$. Now define
$$
e = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}.
$$
Let $n$ be the sum of t... | 66,243 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": Const(44121),
"n2": Const(12),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": CountOverSet(set=SolutionsSet(var=Tuple(e... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/BINOMIAL_ALTERNATING",
"COMB1/BINOMIAL_ALTERNATING"
] | ea9a24 | comb_count_partitions_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"COUNT_CARTESIAN"
] | 3 | 0.003 | 2026-02-08T20:37:28.622641Z | {
"verified": true,
"answer": 66243,
"timestamp": "2026-02-08T20:37:28.625273Z"
} | a4c587 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 2651
},
"timestamp": "2026-02-19T00:47:57.590Z",
"answer": 66243
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INT... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
ba75b3 | antilemma_k2_v1_168721529_1918 | Let $x$ be a real number satisfying $x^2 - 169x + 5734 = 0$. Compute the sum of all such real numbers $x$. Let $n$ be this sum. Determine the value of $$\sum_{k=1}^{169} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. | 14,365 | graphs = [
Graph(
let={
"_m": Const(169),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-169), Var("x")), Const(5734)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")),... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"VIETA_SUM"
] | 3 | 0.006 | 2026-02-08T13:59:07.734313Z | {
"verified": true,
"answer": 14365,
"timestamp": "2026-02-08T13:59:07.739851Z"
} | 673f3e | 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": 1662
},
"timestamp": "2026-02-09T23:29:25.092Z",
"answer": 14365
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VI... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
e4d21f | nt_sum_divisors_compute_v1_865884756_149 | Let $n = 41616$ and let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the remainder when $$\sigma(n) + \varphi\left(|\sigma(n)| + \varphi\left(\sum_{d\mid\gcd(4,9)} \mu(d)\right)\right) + \tau(|\sigma(n)| + \varphi(1))$$ is divided by $75210$, where $\varphi$ is Euler's totient function, $\mu$ is ... | 35,165 | graphs = [
Graph(
let={
"n": Const(41616),
"result": SumDivisors(n=Ref("n")),
"Q": Mod(value=Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), EulerPhi(n=SumOverDivisors(n=GCD(a=Const(value=4), b=Const(value=9)), var='d', expr=MoebiusMu(n=Var(name='d')))))), ... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | 8084fa | nt_sum_divisors_compute_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | 2 | 0.003 | 2026-02-08T15:12:36.586975Z | {
"verified": true,
"answer": 35165,
"timestamp": "2026-02-08T15:12:36.590202Z"
} | 28ff69 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 7895
},
"timestamp": "2026-02-10T04:53:12.875Z",
"answer": 35165
}
] | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"st... | {
"lo": -10,
"mid": -1.96,
"hi": 6.09
} | ||
60f311 | antilemma_sum_equals_v1_898971024_2360 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 47$, $1 \leq i \leq 45$, and $1 \leq j \leq 46$. Let $x$ be the number of ordered pairs $(i_1, j_1)$ of positive integers such that $i_1 + j_1 = n$, $1 \leq i_1 \leq 44$, and $1 \leq j_1 \leq 44$. Find the value of $15876 - x$. | 15,832 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(47)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(45)), right=IntegerRange(start=Const(1), end=Const(46))))),
"x":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.018 | 2026-02-08T16:42:38.000501Z | {
"verified": true,
"answer": 15832,
"timestamp": "2026-02-08T16:42:38.018219Z"
} | 75adae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 2011
},
"timestamp": "2026-02-24T21:47:53.762Z",
"answer": 15832
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
1b42f0 | comb_count_surjections_v1_784195855_7668 | Let $n_2 = 0$. Define $t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $a = 3$ and $b = 3$, and define $n_1 = a + b$. Define $m = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 8$ and $k = 3t + m$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the value of this exp... | 5,796 | graphs = [
Graph(
let={
"n2": Const(0),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": Const(3),
"b": Const(3),
"n1": Sum(Ref("a"), Ref("b")),
"m": Summat... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_surjections_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.003 | 2026-02-08T09:26:32.524799Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-02-08T09:26:32.527525Z"
} | fcba90 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 1119
},
"timestamp": "2026-02-24T11:19:07.921Z",
"answer": 5796
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
26ebdd | alg_poly_preperiod_count_v1_1218484723_3593 | For a non-negative integer $a$, define $N = a^3 + 4a \bmod 31$, $M = N^3 + 4N \bmod 31$, $R = M^3 + 4M \bmod 31$, $S = R^3 + 4R \bmod 31$, and $T = S^3 + 4S \bmod 31$. Find the number of integers $a$ with $0 \le a \le 46840$ such that $T = N$, but $M \neq N$, $R \neq N$, and $S \neq N$. | 18,132 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(4), Var("a"))), modulus=Const(31)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(4), Ref("p1"))), modulus=Const(31)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(4), Ref(... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.024 | 2026-02-25T05:13:27.576236Z | {
"verified": true,
"answer": 18132,
"timestamp": "2026-02-25T05:13:27.600169Z"
} | 7f1f04 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 10965
},
"timestamp": "2026-03-29T11:08:32.655Z",
"answer": 18132
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
83f9d1 | comb_factorial_compute_v1_865884756_3134 | Let $m = 7$. Let $p$ be the largest prime number less than or equal to $m$. Let $n$ be the largest prime number less than or equal to $p$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_m")), IsPrime(Var("n1"))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(2)), Leq(V... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | comb_factorial_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T17:11:31.443659Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T17:11:31.445498Z"
} | d8a2e6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 489
},
"timestamp": "2026-02-16T09:08:01.285Z",
"answer": 5040
},
{
"id": 11,
... | 2 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
74ab5f | comb_count_partitions_v1_1080341949_457 | Let $S$ be the set of all positive integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 7$, $7 \leq t \leq 49$, and $t = 2a + 5b$. Let $n$ be the number of elements in $S$. Compute the number of integer partitions of $n$. | 31,185 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:31:01.861532Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T13:31:01.862735Z"
} | c52973 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2485
},
"timestamp": "2026-02-24T18:34:10.985Z",
"answer": 31185
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
5c5b3c | antilemma_sum_equals_v1_1520064083_9591 | Determine the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 36$, $1 \leq j \leq 36$, and $i + j = 37$. | 36 | graphs = [
Graph(
let={
"_n": Const(37),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(36)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.05 | 2026-02-08T10:53:11.347696Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T10:53:11.397312Z"
} | 9f9a8b | 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": 175
},
"timestamp": "2026-02-24T12:30:02.836Z",
"answer": 36
},
{
"id":... | 2 | [
{
"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": -10,
"mid": -7.79,
"hi": -5.57
} | ||
b484cf | diophantine_fbi2_count_v1_809748730_1826 | Let $k = 360$. Consider the set of all integers $d$ such that $5 \leq d \leq 68$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 65$. Compute the number of elements in this set. | 14 | graphs = [
Graph(
let={
"k": Const(360),
"a": Const(4),
"b": Const(1),
"upper": Const(64),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(68)), Divides(divisor=Var("d"), dividend=Ref... | NT | null | COUNT | sympy | K14 | [
"K14"
] | a49bcb | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"K14"
] | 1 | 0.045 | 2026-02-08T12:42:19.590954Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T12:42:19.636451Z"
} | d2cb2e | 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": 1295
},
"timestamp": "2026-02-15T04:18:17.266Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1ff459 | nt_sum_divisors_mod_v1_1978505735_3626 | Let $\_n = 48$. Let $A$ be the set of all positive integers $n_1 \leq 240$ such that $n_1$ is divisible by $\_n$. Define $n$ to be the sum of $\phi(d)$ over all positive divisors $d$ of the sum of the elements of $A$, where $\phi$ denotes Euler's totient function. Let $M = 11119$ and let $\sigma$ be the sum of the posi... | 2,418 | graphs = [
Graph(
let={
"_n": Const(48),
"n": SumOverDivisors(n=SumOverSet(set=SolutionsSet(var=Var(name='n1'), condition=And(Geq(left=Var(name='n1'), right=Const(value=1)), Leq(left=Var(name='n1'), right=Const(value=240)), Eq(left=Mod(value=Var(name='n1'), modulus=Ref(name='_n')), r... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/K3"
] | f11ce5 | nt_sum_divisors_mod_v1 | null | 3 | 0 | [
"K3",
"SUM_DIVISIBLE"
] | 2 | 0.005 | 2026-02-08T17:45:24.353702Z | {
"verified": true,
"answer": 2418,
"timestamp": "2026-02-08T17:45:24.358218Z"
} | 51cd23 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 748
},
"timestamp": "2026-02-18T07:34:45.281Z",
"answer": 2418
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ca62a0 | antilemma_k3_v1_1125832087_1834 | Let $n = 81089$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ of $n$ and $\phi$ is Euler's totient function. Let $c$ be the sum of all real solutions $x$ to the equation $x^2 - 8836x + 674443 = 0$. Compute the remainder when $x^2 + 7x + c$ is divided by $95697$. | 87,328 | graphs = [
Graph(
let={
"_n": Const(81089),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-8836), Var("x")), Const(674443)), Const(0)))),... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"K3"
] | 74525f | antilemma_k3_v1 | quadratic_mod | 5 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T03:58:11.522936Z | {
"verified": true,
"answer": 87328,
"timestamp": "2026-02-08T03:58:11.524523Z"
} | 2dbdb4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 2757
},
"timestamp": "2026-02-10T16:24:13.601Z",
"answer": 86928
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
a778bc | alg_qf_psd_orbit_v1_1218484723_7463 | Let
$$M = \min\{x + y : (x,y) \text{ are positive integers with } xy = 2825761\}.$$
Let
$$B = \left|\{(a_1,b_1) : 1 \le a_1 \le 20,\ 1 \le b_1 \le 20,\ 13a_1^{2} - 2a_1b_1 + 2b_1^{2} \le M\}\right|.$$
Let $Q$ be the number of ordered pairs $(a,b)$ of positive integers with $1 \le a \le b$ and $1 \le b \le B$ such that
... | 118 | graphs = [
Graph(
let={
"_m": Const(20),
"_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(2825761)))), expr=Sum(Var("x"), Var("y")))... | ALG | null | COUNT | sympy | B3 | [
"B3/QF_PSD_COUNT_LEQ"
] | 0168fb | alg_qf_psd_orbit_v1 | null | 8 | 0 | [
"B3",
"QF_PSD_COUNT_LEQ"
] | 2 | 1.01 | 2026-02-25T08:53:24.235102Z | {
"verified": true,
"answer": 118,
"timestamp": "2026-02-25T08:53:25.244986Z"
} | b064e3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 291,
"completion_tokens": 3771
},
"timestamp": "2026-03-30T04:39:34.851Z",
"answer": 118
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
27960a | nt_sum_gcd_range_mod_v1_1918700295_4390 | Let $N$ be the number of integers $t$ such that $7 \leq t \leq 5941$ and there exist positive integers $a \leq 844$ and $b \leq 855$ satisfying $t = 4a + 3b$. Let $k$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 144$, $j \leq 145$, and $i + j = 146$. Let $s = \sum_{n=1}^{N} \gcd(n, k)$... | 10,670 | graphs = [
Graph(
let={
"_m": Const(146),
"_n": Const(60848),
"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'), righ... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 7b3310 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.401 | 2026-02-08T09:19:47.742442Z | {
"verified": true,
"answer": 10670,
"timestamp": "2026-02-08T09:19:48.143210Z"
} | 780811 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 7396
},
"timestamp": "2026-02-14T03:20:41.845Z",
"answer": 10670
},
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8c267d | nt_gcd_compute_v1_168721529_203 | Let $c=82687$ and $m=82687$.
Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that
$$pq=216,\quad \gcd(p,q)=1,\quad p<q.$$
Let $n$ be the number of elements of $P$.
Let $a=698864$ and $b=1310370$, and let $g=\gcd(a,b)$.
Let $R$ be the set of all integers $t$ for whic... | 21,055 | graphs = [
Graph(
let={
"_c": Const(82687),
"_m": Const(82687),
"_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=216)), Eq(le... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B1",
"LIN_FORM/B1"
] | b755c4 | nt_gcd_compute_v1 | mod_exp | 7 | 0 | [
"B1",
"COPRIME_PAIRS",
"LIN_FORM"
] | 3 | 0.008 | 2026-02-08T12:54:12.896563Z | {
"verified": true,
"answer": 21055,
"timestamp": "2026-02-08T12:54:12.904122Z"
} | 71167a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 501,
"completion_tokens": 2671
},
"timestamp": "2026-02-09T02:27:54.274Z",
"answer": 6
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"... | {
"lo": 1.49,
"mid": 4.54,
"hi": 7.77
} | ||
e91218 | algebra_quadratic_discriminant_v1_865884756_3466 | Let $n = 4$, $a = 2$, and $c = 1$. Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $b = |P|$. Compute $b^2 - 4ac$. Let $Q$ be the remainder when $59446$ times this value is divided by $71811$. Determine the value of $Q$... | 49,460 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(2),
"b": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=6)), Eq(left=GCD(a=Var... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.006 | 2026-02-08T17:28:01.455162Z | {
"verified": true,
"answer": 49460,
"timestamp": "2026-02-08T17:28:01.460965Z"
} | 89fbe7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 938
},
"timestamp": "2026-02-18T02:24:28.624Z",
"answer": 49460
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
63feab | geo_count_lattice_triangle_v1_784195855_2428 | Let the area of a triangle with vertices at $(233, 256)$, $(300, 377)$, and $(0, 0)$ be denoted by $A$. Define $\text{area}_{2x} = \left| 2 \cdot A \right|$. Let $b$ be the number of lattice points on the boundary of this triangle, computed as the sum of the greatest common divisors of the differences in coordinates al... | 48,436 | graphs = [
Graph(
let={
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=233), Const(value=377)), Mul(Const(value=300), Sub(left=Const(value=0), right=Const(value=256))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=233)), b=Abs(arg=Const(value=256))), GCD(a=Abs(arg=... | NT | null | COUNT | sympy | C3 | [
"MIN_PRIME_FACTOR"
] | bc3776 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"C3",
"MIN_PRIME_FACTOR"
] | 2 | 0.135 | 2026-02-08T05:44:37.376958Z | {
"verified": true,
"answer": 48436,
"timestamp": "2026-02-08T05:44:37.512348Z"
} | d4ec96 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 4603
},
"timestamp": "2026-02-12T13:17:51.253Z",
"answer": 48436
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"sta... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bff00f | antilemma_k3_v1_1520064083_9341 | Let $ n = 10764 $. Define $$
S = \sum_{d \mid n} \phi(d),
$$ where the sum is taken over all positive divisors $ d $ of $ n $, and $ \phi $ denotes Euler's totient function.
Compute $ S $. | 10,764 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=10764), 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 | 2026-02-08T10:41:32.396654Z | {
"verified": true,
"answer": 10764,
"timestamp": "2026-02-08T10:41:32.397077Z"
} | db4911 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 266
},
"timestamp": "2026-02-14T08:06:17.291Z",
"answer": 10764
},
{... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1a03f6 | antilemma_sum_equals_v1_1520064083_7396 | Let $m = 84921$. Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 8$ and $1 \leq j \leq 9$. Let $x$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 70$ and $1 \leq j \leq 70$ such that $i + j = n$. Compute the remainder when $84921 \cdot x$ is divided by $90691$. | 55,325 | graphs = [
Graph(
let={
"_m": Const(84921),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(9)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.024 | 2026-02-08T09:00:35.587786Z | {
"verified": true,
"answer": 55325,
"timestamp": "2026-02-08T09:00:35.611644Z"
} | d614fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 1142
},
"timestamp": "2026-02-24T10:21:14.496Z",
"answer": 55325
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
c7f42a | sequence_count_fib_divisible_v1_1915831931_1290 | Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 151321$. Let $s$ be the minimum value of $x + y$ over all such pairs. Compute the number of positive integers $n$ such that $1 \leq n \leq s$ and $13$ divides the $n$-th Fibonacci number. Let this number be $r$. Compute $$\sum_{n=1}^{... | 3,788 | 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(151321)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(1... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.083 | 2026-02-08T15:58:54.824486Z | {
"verified": true,
"answer": 3788,
"timestamp": "2026-02-08T15:58:54.907674Z"
} | 8332cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 2953
},
"timestamp": "2026-02-16T19:27:51.698Z",
"answer": 3788
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2f7fd0 | comb_bell_compute_v1_153355830_1789 | Let $p$ and $q$ be positive integers such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Compute the number of such integers $p$, and let this count be $m$. Let $n = 8$. Compute the Bell number $B_n$, the number of partitions of an $n$-element set, and let this value be $b$. Let $d$ be the smallest integer such that $d... | 52,678 | graphs = [
Graph(
let={
"_m": Const(56585),
"_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=54)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 902529 | comb_bell_compute_v1 | negation_mod | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T06:36:59.230948Z | {
"verified": true,
"answer": 52678,
"timestamp": "2026-02-08T06:36:59.232609Z"
} | 9a22a5 | 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": 2256
},
"timestamp": "2026-02-13T02:38:23.583Z",
"answer": 52678
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
85b032 | sequence_lucas_compute_v1_865884756_1519 | Let $n$ be the number of integers $t$ with $45 \leq t \leq 120$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 10$, $1 \leq b \leq 2$, and $t = 6a + 21b + 18$. Let $L_n$ denote the $n$th Lucas number. Compute the remainder when $44121 \cdot L_n$ is divided by $57506$. | 3,731 | graphs = [
Graph(
let={
"_n": Const(57506),
"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=10)), Geq(left=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:06:36.804593Z | {
"verified": true,
"answer": 3731,
"timestamp": "2026-02-08T16:06:36.806922Z"
} | 6491d5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 1994
},
"timestamp": "2026-02-16T21:38:52.070Z",
"answer": 3731
},
{... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a0eda0 | comb_factorial_compute_v1_601307018_7094 | Let $M$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers with $1 \le x \le y$ and $xy = 1936$. Let $n$ be the largest positive integer $d$ such that $d^2 \le M$ and $d \mid 88$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_m": Const(88),
"_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(1936)), Leq(Var("x"), Var("y")))), expr=Su... | COMB | NT | COMPUTE | sympy | B3 | [
"B3/B3_CLOSEST"
] | c16e36 | comb_factorial_compute_v1 | null | 4 | 0 | [
"B3",
"B3_CLOSEST"
] | 2 | 0.003 | 2026-03-10T07:44:25.589009Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-03-10T07:44:25.591851Z"
} | 54fd8d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 671
},
"timestamp": "2026-04-19T05:57:44.649Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
c8508e | nt_sum_over_divisible_v1_809748730_583 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1444$. Let $s_{\text{min}}$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $T$ be the set of all positive integers $n$ such that $1 \le n \le 27889$ and $n$ is divisible by $s_{\text{min}}$. Let $\text{result}$ be th... | 2,872 | graphs = [
Graph(
let={
"_n": Const(80876),
"upper": Const(27889),
"divisor": 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... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"B3"
] | 1 | 1.848 | 2026-02-08T11:36:14.211773Z | {
"verified": true,
"answer": 2872,
"timestamp": "2026-02-08T11:36:16.060035Z"
} | 05f08b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1487
},
"timestamp": "2026-02-14T17:02:56.973Z",
"answer": 2872
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
691958 | diophantine_fbi2_count_v1_784195855_8378 | Let $k = 240$. Define $A$ to be the set of all integers $d$ such that $4 \leq d \leq 81$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 79$. Let $\text{result} = |A|$, the number of elements in $A$.
Let $N = 35574$. Define $B$ to be the set of all positive integers $n$ such that $1 \leq n \leq N$ and $8$ divides the $... | 6,349 | graphs = [
Graph(
let={
"_n": Const(35574),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(81)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Di... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | a43f88 | diophantine_fbi2_count_v1 | quadratic_mod | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.019 | 2026-02-08T16:02:22.225959Z | {
"verified": true,
"answer": 6349,
"timestamp": "2026-02-08T16:02:22.244998Z"
} | 50249e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1915
},
"timestamp": "2026-02-16T19:08:13.417Z",
"answer": 6349
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
511aab | nt_euler_phi_compute_v1_124444284_974 | Let $n = 91483$. Let $n_1$ be the number of integers $t$ such that $18 \leq t \leq 110$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 19$, and $t = 5a + 4b + 9$. Let $f$ be the number of distinct prime factors of $n_1$. Let $p = 19$ and let $c$ be the remainder when $ (p - f)! + 1 $ is div... | 49,450 | graphs = [
Graph(
let={
"_n": Const(91483),
"n1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/OMEGA_ONE",
"WILSON"
] | 119196 | nt_euler_phi_compute_v1 | null | 6 | 2 | [
"LIN_FORM",
"OMEGA_ONE",
"WILSON"
] | 3 | 0.004 | 2026-02-08T03:37:30.853042Z | {
"verified": true,
"answer": 49450,
"timestamp": "2026-02-08T03:37:30.856587Z"
} | 21c562 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 310,
"completion_tokens": 5299
},
"timestamp": "2026-02-09T08:11:05.381Z",
"answer": 49450
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "OMEGA_ONE",
"status": "ok_later... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
dd0f6b | comb_count_surjections_v1_1218484723_1770 | Let $k$ be the number of non-negative integers $a$ with $0 \le a \le 7920$ such that
$$\left(\left(a^{2} -1437 \bmod 7921\right)^{2} -1437 \bmod 7921\right)^{2} -1437 \bmod 7921 = a,$$
and $a^{2} -1437 \bmod 7921 \ne a$, and $\left(a^{2} -1437 \bmod 7921\right)^{2} -1437 \bmod 7921 \ne a$. Compute $k! \cdot S(5, k)$, w... | 150 | graphs = [
Graph(
let={
"n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(7920)), Eq(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-1437)), modulus=Const(7921)), Const(2)), Con... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_surjections_v1 | null | 5 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.002 | 2026-02-25T03:26:11.047163Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-25T03:26:11.048721Z"
} | 068084 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T01:19:40.937Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
e56eef | nt_max_prime_below_v1_865884756_1518 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Determine the largest prime number $n$ such that $n \geq k$ and $n \leq 66049$. | 66,047 | graphs = [
Graph(
let={
"upper": Const(66049),
"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 | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.712 | 2026-02-08T16:06:35.086046Z | {
"verified": true,
"answer": 66047,
"timestamp": "2026-02-08T16:06:36.797772Z"
} | c4bbdb | 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": 2241
},
"timestamp": "2026-02-16T21:38:00.548Z",
"answer": 66047
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e39974 | nt_count_coprime_and_v1_1978505735_2373 | Let $k_1 = 4$ and let $k_2$ be one more than the number of nonnegative integers $j$ such that $0 \leq j \leq 448$ and $\binom{448}{j}$ is odd. Let $C$ be the number of positive integers $n$ such that $1 \leq n \leq 80085$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Compute the remainder when $24242 \cdot C$ is divided... | 41,066 | graphs = [
Graph(
let={
"_n": Const(50729),
"upper": Const(80085),
"k1": Const(4),
"k2": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(448)), Eq(Mod(value=Binom(n=Const(448), k=Var("j")), modulus=Con... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_coprime_and_v1 | null | 6 | 0 | [
"V8"
] | 1 | 20.126 | 2026-02-08T16:51:16.758600Z | {
"verified": true,
"answer": 41066,
"timestamp": "2026-02-08T16:51:36.884517Z"
} | 3dffcf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2261
},
"timestamp": "2026-02-17T13:57:04.947Z",
"answer": 41066
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8734a1 | antilemma_k3_v1_168721529_412 | Let $n = 8418$. Define $S = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute $\sum_{d \mid S} \phi(d)$. | 8,418 | graphs = [
Graph(
let={
"_n": Const(8418),
"x": SumOverDivisors(n=SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3",
"K3"
] | 79f53d | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:02:39.021591Z | {
"verified": true,
"answer": 8418,
"timestamp": "2026-02-08T13:02:39.022581Z"
} | 12e934 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 675
},
"timestamp": "2026-02-09T04:44:21.739Z",
"answer": 8418
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.66,
"mid": -2.15,
"hi": 1.82
} | ||
698da0 | nt_sum_totient_over_divisors_v1_151522320_809 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2149156$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute $\sum_{d\mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. | 2,932 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2149156)))), expr=Sum(Var("x"), Var("y")))),
"result": SumOv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T03:32:57.390751Z | {
"verified": true,
"answer": 2932,
"timestamp": "2026-02-08T03:32:57.400461Z"
} | c3cf01 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1370
},
"timestamp": "2026-02-10T13:52:55.578Z",
"answer": 2932
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ae5340 | nt_count_coprime_and_v1_1742523217_5361 | Let $U = 31418$. Let $k_1 = 5$ and let $k_2$ be the largest prime number not exceeding $12$. Determine the number of positive integers $n$ with $1 \leq n \leq U$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. | 22,850 | graphs = [
Graph(
let={
"upper": Const(31418),
"k1": Const(5),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 4.113 | 2026-02-08T10:56:23.399836Z | {
"verified": true,
"answer": 22850,
"timestamp": "2026-02-08T10:56:27.513260Z"
} | a9e7e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 908
},
"timestamp": "2026-02-14T09:40:39.579Z",
"answer": 22850
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
63d296 | sequence_fibonacci_compute_v1_1431428450_693 | Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 3$. Let $f = F_{23}$.
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 8242641$. Let $c$ be the minimum value of $x + y$ as $(x, y)$ ranges over $T$.
Compute the rema... | 6,385 | graphs = [
Graph(
let={
"_n": Const(68077),
"n": Const(23),
"result": Fibonacci(arg=Ref(name='n')),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name=... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | e0298c | sequence_fibonacci_compute_v1 | affine_mod | 3 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T13:38:13.282527Z | {
"verified": true,
"answer": 6385,
"timestamp": "2026-02-08T13:38:13.285898Z"
} | 49cef5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1352
},
"timestamp": "2026-02-15T18:59:58.160Z",
"answer": 6385
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
95156c | modular_mod_compute_v1_1520064083_5267 | Let $n = 11$ and let $a = -11025$. Let $m$ be the smallest divisor of $6602797855853$ that is at least $2$. Define $r$ to be the remainder when $a$ is divided by $m$, and let $b = |r|$. Compute the Bell number $B_k$, where $k$ is the remainder when $b$ is divided by $n$. Find the value of this Bell number. | 1 | graphs = [
Graph(
let={
"_n": Const(11),
"a": Const(-11025),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(6602797855853))))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.012 | 2026-02-08T06:42:34.164540Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T06:42:34.176418Z"
} | 1169a9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2176
},
"timestamp": "2026-02-13T03:28:34.861Z",
"answer": 21147
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
47dcd8 | nt_sum_gcd_range_mod_v1_2051736721_4112 | Let $N = 5476$ and $k = 108$. Define $S = \sum_{n=1}^{N} \gcd(n, k)$. Let $R$ be the remainder when $S$ is divided by $11087$. Compute the sum of the squares of the positions (starting from position 1 for the units digit) of each digit in the decimal representation of $R$, multiplied by the digit itself. That is, if $R... | 3,093 | graphs = [
Graph(
let={
"_n": Const(10),
"N": Const(5476),
"k": Const(108),
"M": Const(11087),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod(value=Ref("sum"), modulus=Ref("M")),... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 23544e | nt_sum_gcd_range_mod_v1 | digits_weighted_mod | 6 | 0 | [
"C4"
] | 1 | 0.394 | 2026-02-08T17:44:39.190755Z | {
"verified": true,
"answer": 3093,
"timestamp": "2026-02-08T17:44:39.584322Z"
} | 7f8574 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 4694
},
"timestamp": "2026-02-18T07:58:46.889Z",
"answer": 3093
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
273710_n | alg_telescope_v1_1218484723_5577 | A digital counter cycles through levels, and at each level $k$ from $0$ to $29^0 + 29^1 + 29^2$, it emits $3k^2 + 3k + 1$ energy units. The total energy emitted, reduced modulo $3784$, is $M$. Compute the remainder when $42809M$ is divided by $69690$. | 2,012 | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | alg_telescope_v1 | null | 3 | null | [
"SUM_GEOM"
] | 1 | 0.056 | 2026-02-25T07:04:39.374542Z | null | e3b46e | 273710 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 3272
},
"timestamp": "2026-03-30T23:43:31.945Z",
"answer": 2012
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
9d1978 | comb_count_derangements_v1_601307018_3504 | Let $D_n$ denote the number of derangements of $n$ elements. For each integer $a$ with $0 \le a \le 72$, define:
\[
\begin{aligned}
M &= a^{36} \bmod 73, \\
R &= (a^2 - 31) \bmod 73, \\
S &= R^{36} \bmod 73, \\
T &= (R^2 - 31) \bmod 73, \\
K &= T^{36} \bmod 73, \\
L &= (T^2 - 31) \bmod 73, \\
P &= L^{36} \bmod 73, \\
Q... | 14,833 | graphs = [
Graph(
let={
"_n": Const(72),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Ref("_n")), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a")), Congruent(... | COMB | NT | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE"
] | 7c2be8 | comb_count_derangements_v1 | null | 6 | 0 | [
"POLY_ORBIT_LEGENDRE"
] | 1 | 0.002 | 2026-03-10T04:06:45.952358Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-03-10T04:06:45.954825Z"
} | edd59a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 348,
"completion_tokens": 15069
},
"timestamp": "2026-03-29T08:55:00.901Z",
"answer": 14833
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "V7",... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
c229d7 | comb_catalan_compute_v1_1742523217_178 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 20$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 5b$. Let $n$ be the number of elements in $T$. Define $C_n$ to be the $n$-th Catalan number. Let $Q$ be the smallest positive integer $k$ such that the $k$-th... | 228 | 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=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T02:54:54.522857Z | {
"verified": true,
"answer": 228,
"timestamp": "2026-02-08T02:54:54.526158Z"
} | 153a34 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 7577
},
"timestamp": "2026-02-09T14:32:02.960Z",
"answer": 228
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 0.61,
"mid": 2.4,
"hi": 3.92
} | ||
1ec359 | alg_poly_orbit_count_v1_1218484723_2979 | For a non-negative integer $a$ with $0 \le a \le 57027$, define the sequence $N = (a^3 - 3a) \bmod 53$, $M = (N^3 - 3N) \bmod 53$, and $R = (M^3 - 3M) \bmod 53$. Find the number of such $a$ for which $R = a$, $N \neq a$, and $M \neq a$. | 12,912 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-3), Var("a"))), modulus=Const(53)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-3), Ref("p1"))), modulus=Const(53)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(-3), R... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.013 | 2026-02-25T04:42:30.958211Z | {
"verified": true,
"answer": 12912,
"timestamp": "2026-02-25T04:42:30.970914Z"
} | 941c1b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 16172
},
"timestamp": "2026-03-29T07:43:17.474Z",
"answer": 9
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
36604c | algebra_quadratic_discriminant_v1_153355830_2951 | Let $S$ be the set of all pairs of positive integers $(p, q)$ such that $p < q$, $pq = 18$, and $\gcd(p, q) = 1$. Let $T$ be the set of all pairs of positive integers $(p, q)$ such that $p < q$, $pq = 6750$, and $\gcd(p, q) = 1$. Let $m = |S|$ and $n = |T|$. Compute the value of $$
75365 \cdot \left((-16)^m - (-1) \cdo... | 0 | graphs = [
Graph(
let={
"a": Const(-1),
"b": Const(-16),
"c": Const(-64),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Va... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T07:29:12.496378Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T07:29:12.499387Z"
} | 0fce40 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 2298
},
"timestamp": "2026-02-13T10:33:08.373Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
a92552 | comb_catalan_compute_v1_1520064083_1876 | Let $m = 24$. Let $s$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $n$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 11$ and $1 \leq j \leq 12$ such that $i + j = s$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"_m": Const(24),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS"
] | 4d9cac | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T04:21:15.984286Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T04:21:15.995920Z"
} | 40d7f8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2617
},
"timestamp": "2026-02-24T00:24:04.217Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
b9c0f5 | nt_sum_divisors_compute_v1_1248542787_254 | Let $n = 20323$. Compute $\sigma(n)$, the sum of the positive divisors of $n$. Let $c$ be the number of integers $k$ such that $\mu(\gcd(5,7)) \le k \le 20665$ and $\gcd(k, 12) = 1$, where $\mu$ is the M\"obius function. Compute the remainder when $c - \sigma(n)$ is divided by $73316$. | 59,881 | graphs = [
Graph(
let={
"_n": Const(12),
"n": Const(20323),
"result": SumDivisors(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=5), b=Const(value=7)), var='d', expr=MoebiusMu(n=Va... | NT | null | COMPUTE | sympy | C4 | [
"C4",
"MOBIUS_COPRIME"
] | 33f0a2 | nt_sum_divisors_compute_v1 | negation_mod | 5 | 0 | [
"C4",
"MOBIUS_COPRIME"
] | 2 | 0.002 | 2026-02-08T03:02:02.271010Z | {
"verified": true,
"answer": 59881,
"timestamp": "2026-02-08T03:02:02.273482Z"
} | e50c1d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 2287
},
"timestamp": "2026-02-09T14:23:41.262Z",
"answer": 59881
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": ... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
629d99 | comb_count_derangements_v1_1874849503_857 | Let $m = 13013$. Let $d_{\min}$ be the smallest divisor of $m$ that is at least $2$. Define $n$ to be the largest prime number $p$ such that $2 \leq p \leq d_{\min}$. Let $!n$ denote the number of derangements of $n$ elements. Compute the remainder when $38363 \cdot (!n)$ is divided by $62039$. | 28,308 | graphs = [
Graph(
let={
"_m": Const(13013),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), divi... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | comb_count_derangements_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T13:21:32.482643Z | {
"verified": true,
"answer": 28308,
"timestamp": "2026-02-08T13:21:32.485798Z"
} | 6a21a6 | 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": 1760
},
"timestamp": "2026-02-09T21:51:41.254Z",
"answer": 28308
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"s... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
af9dcc | modular_modexp_compute_v1_865884756_3796 | Let $s = 136$. Consider all ordered pairs $(x, y)$ of positive integers such that $x + y = s$. Let $e$ be the maximum value of $xy$ over all such pairs.
Let $a = 17$ and $m = 16384$. Compute the remainder when $a^e$ is divided by $m$. | 6,401 | graphs = [
Graph(
let={
"_n": Const(136),
"a": Const(17),
"e": 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=M... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T17:34:47.307272Z | {
"verified": true,
"answer": 6401,
"timestamp": "2026-02-08T17:34:47.310415Z"
} | f829a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 2598
},
"timestamp": "2026-02-18T04:09:01.110Z",
"answer": 6401
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cc6ae4 | geo_count_lattice_rect_v1_1915831931_336 | Let $a = 66$ and $b = 15$. Compute the number of lattice points in the rectangle defined by $0 \leq x \leq a$ and $0 \leq y \leq b$, including the boundary. | 1,072 | graphs = [
Graph(
let={
"a": Const(66),
"b": Const(15),
"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 | 2026-02-08T15:22:02.707637Z | {
"verified": true,
"answer": 1072,
"timestamp": "2026-02-08T15:22:02.708448Z"
} | 048c49 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 112
},
"timestamp": "2026-02-24T20:41:58.179Z",
"answer": 1072
},
{
"id... | 2 | [] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||||
dabce5 | modular_mod_compute_v1_809748730_533 | Let $a$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 3739$ and $\binom{3739}{j}$ is odd. Compute the remainder when $a$ is divided by 70756. | 256 | graphs = [
Graph(
let={
"_n": Const(2),
"a": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(3739)), Eq(Mod(value=Binom(n=Const(3739), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"m":... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_mod_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T11:33:54.955995Z | {
"verified": true,
"answer": 256,
"timestamp": "2026-02-08T11:33:54.959016Z"
} | eec4bc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1862
},
"timestamp": "2026-02-24T14:26:20.408Z",
"answer": 256
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
c161c3 | geo_count_lattice_rect_v1_1915831931_4148 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 196$ and $0 \leq y \leq 56$. | 11,229 | graphs = [
Graph(
let={
"a": Const(196),
"b": Const(56),
"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 | 2026-02-08T18:07:46.843307Z | {
"verified": true,
"answer": 11229,
"timestamp": "2026-02-08T18:07:46.843873Z"
} | f17b66 | 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": 474
},
"timestamp": "2026-02-18T14:32:39.514Z",
"answer": 11229
},
{
... | 1 | [] | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||||
db8707 | diophantine_fbi2_min_v1_1520064083_1503 | Let $k$ be the number of positive integers $n$ with $1 \leq n \leq 1800$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $S$ be the set of all integers $d$ such that $4 \leq d \leq 370$, $d$ divides $k$, and $\frac{k}{d} \geq 7$. Determine the value of the smallest element in $S$. | 4 | graphs = [
Graph(
let={
"_n": Const(1800),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=5))))),
... | NT | null | EXTREMUM | sympy | SUM_INDEPENDENT | [
"L3C"
] | 73f8b0 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"L3C",
"SUM_INDEPENDENT"
] | 2 | 0.172 | 2026-02-08T04:02:54.266063Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T04:02:54.437940Z"
} | 4a6e64 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 1456
},
"timestamp": "2026-02-10T15:23:49.005Z",
"answer": 4
},
{
"id"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
fc287e | comb_count_surjections_v1_124444284_3594 | Let $n = 6$ and $k = 3$. Define $S(n,k)$ to be the Stirling number of the second kind, which counts the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. Let $r = k! \cdot S(n,k)$. Compute the remainder when $44121 \cdot r$ is divided by $57086$. | 20,478 | graphs = [
Graph(
let={
"n": Const(6),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(57086)),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.038 | 2026-02-08T05:28:16.499348Z | {
"verified": true,
"answer": 20478,
"timestamp": "2026-02-08T05:28:16.537580Z"
} | aeb829 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1368
},
"timestamp": "2026-02-24T03:48:12.051Z",
"answer": 20478
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"le... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
ec52c4 | modular_sum_quadratic_residues_v1_1248542787_232 | Let $n_0 = 2$ and $p = 613$. Define $r = \frac{p(p-1)}{4}$. Let $m$ be the largest prime number satisfying $n_0 \leq m \leq 41$. Compute the remainder when $m - r$ is divided by $97361$. | 3,613 | graphs = [
Graph(
let={
"_n": Const(2),
"p": Const(613),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=Sub(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(41)), IsPrime(Var... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | modular_sum_quadratic_residues_v1 | negation_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T03:01:34.470912Z | {
"verified": true,
"answer": 3613,
"timestamp": "2026-02-08T03:01:34.472529Z"
} | 8bea2f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 646
},
"timestamp": "2026-02-09T01:42:01.223Z",
"answer": 3613
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"sta... | {
"lo": -2.26,
"mid": 0.01,
"hi": 1.87
} | ||
5a7b82 | modular_count_residue_v1_1978505735_1046 | Let $m$ be the average of the first components of all ordered pairs $(k, j)$ where $k$ ranges from 1 to 5 and $j$ ranges from 1 to 3, multiplied by 5. Let $r = 3$ and let $N$ be the number of positive integers $n \leq 83160$ such that $n \equiv r \pmod{m}$. Compute the remainder when $57521 \cdot N$ is divided by 83532... | 54,780 | graphs = [
Graph(
let={
"_n": Const(83532),
"upper": Const(83160),
"m": Div(Mul(Const(5), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), rig... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | modular_count_residue_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 2.756 | 2026-02-08T15:45:18.386456Z | {
"verified": true,
"answer": 54780,
"timestamp": "2026-02-08T15:45:21.142351Z"
} | c06607 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 3087
},
"timestamp": "2026-02-16T13:07:29.695Z",
"answer": 54780
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "SUM_INDEPENDENT",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ea3929 | geo_count_lattice_rect_v1_153355830_2331 | Compute the number of lattice points in the rectangle $[0, 81] \times [0, 125]$, including the boundary. | 10,332 | graphs = [
Graph(
let={
"a": Const(81),
"b": Const(125),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0 | 2026-02-08T07:04:01.168060Z | {
"verified": true,
"answer": 10332,
"timestamp": "2026-02-08T07:04:01.168521Z"
} | 7c7182 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 208
},
"timestamp": "2026-02-24T07:31:30.124Z",
"answer": 10332
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
d8a8c3 | nt_count_with_divisor_count_v1_2051736721_519 | Let $n_0 = 4$ and $U = 25200$. Let $d$ be the largest prime number $n$ such that $2 \leq n \leq n_0$. Determine the number of positive integers $n_1$ with $1 \leq n_1 \leq U$ such that the number of positive divisors of $n_1$ is equal to $d$. | 37 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(25200),
"div_count": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), ... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_with_divisor_count_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 7.988 | 2026-02-08T15:29:12.863966Z | {
"verified": true,
"answer": 37,
"timestamp": "2026-02-08T15:29:20.851533Z"
} | 7581f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1057
},
"timestamp": "2026-02-16T06:43:45.510Z",
"answer": 37
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
267438 | nt_gcd_compute_v1_548369836_415 | Consider all ordered pairs of positive integers $(x, y)$ such that $xy = 7022500$. Let $a$ be the minimum value of $x + y$ over all such pairs. Let $b = 11925$. Compute $\gcd(a, b)$. Let $k$ be the smallest positive integer such that the $k$-th Fibonacci number is divisible by $|\gcd(a, b)| + 2$. Find the value of $k$. | 1,328 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(7022500)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(1192... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_gcd_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T02:54:15.275567Z | {
"verified": true,
"answer": 1328,
"timestamp": "2026-02-08T02:54:15.277320Z"
} | 9e3bcf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 24086
},
"timestamp": "2026-02-23T18:12:11.211Z",
"answer": 1328
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": 3.22,
"mid": 4.85,
"hi": 6.59
} | ||
94e93a | geo_visible_lattice_v1_1248542787_750 | Let $n = 88$. Define a visible lattice point as an ordered pair $(x, y)$ of positive integers with $1 \leq x, y \leq n$ such that $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points for this $n$. Compute $51529 - R$. | 46,794 | graphs = [
Graph(
let={
"n": Const(88),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(51529), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.258 | 2026-02-08T03:23:09.686760Z | {
"verified": true,
"answer": 46794,
"timestamp": "2026-02-08T03:23:09.945067Z"
} | d2558b | 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": 4465
},
"timestamp": "2026-02-09T07:50:33.951Z",
"answer": 46794
},
{
"... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
0daade | antilemma_k2_v1_784195855_5833 | Compute $\sum_{k=1}^{230} \phi(k) \left\lfloor \frac{230}{k} \right\rfloor$. | 26,565 | graphs = [
Graph(
let={
"_n": Const(230),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(230), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T08:08:43.781683Z | {
"verified": true,
"answer": 26565,
"timestamp": "2026-02-08T08:08:43.782099Z"
} | 40dc36 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 775
},
"timestamp": "2026-02-13T15:15:48.819Z",
"answer": 26565
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d498ed | comb_count_surjections_v1_865884756_6611 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 6$, $1 \leq j \leq 6$, and $i + j = 6$. Let $k = 3$. Define $S(n, k)$ to be the Stirling number of the second kind, which counts the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. Compute the remainder whe... | 19,860 | graphs = [
Graph(
let={
"_n": Const(97655),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T19:19:43.770419Z | {
"verified": true,
"answer": 19860,
"timestamp": "2026-02-08T19:19:43.782940Z"
} | 8813c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1663
},
"timestamp": "2026-02-18T21:51:48.485Z",
"answer": 19860
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
65938e | comb_sum_binomial_row_v1_458359167_4483 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 9258489240$, and $\gcd(p, q) = 1$. Let $t$ be the number of elements in $A$. Let $P$ be the set of all prime numbers $n$ such that $2 \leq n \leq t$. Let $p_{\max}$ be the largest element of $P$. Let $... | 206 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(13),
"result": Pow(Const(2), Ref("n")),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='result')), k=Var(n... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | c12eb2 | comb_sum_binomial_row_v1 | digits_weighted_mod | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T11:48:54.316264Z | {
"verified": true,
"answer": 206,
"timestamp": "2026-02-08T11:48:54.320406Z"
} | 2d6795 | 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": 2677
},
"timestamp": "2026-02-14T20:01:11.642Z",
"answer": 206
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0b597d | nt_count_divisible_and_v1_124444284_3740 | Let $d_1$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 9000$, $\gcd(p, q) = 1$, and $p < q$. Let $d_2 = 6$. Determine the value of the number of positive integers $n \leq 53292$ such that $n$ is divisible by both $d_1$ and $d_2$. | 4,441 | graphs = [
Graph(
let={
"upper": Const(53292),
"d1": 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=9000)), Eq(left=GCD(a=Var(name='p'), b=Va... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisible_and_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.514 | 2026-02-08T05:34:28.727172Z | {
"verified": true,
"answer": 4441,
"timestamp": "2026-02-08T05:34:31.241364Z"
} | bd6a2d | 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": 1746
},
"timestamp": "2026-02-12T11:06:18.834Z",
"answer": 4441
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c67a46 | nt_count_divisible_and_v1_784195855_8608 | Let $n = 16512$ and $u = 22356$. Let $d_1$ be the number of nonnegative integers $j$ such that $0 \leq j \leq n$ and $\binom{n}{j}$ is odd. Let $d_2 = 6$. Define $r$ to be the number of positive integers $k$ such that $1 \leq k \leq u$, $k$ is divisible by $d_1$, and $k$ is divisible by $d_2$. Compute $r$. | 1,863 | graphs = [
Graph(
let={
"_n": Const(16512),
"upper": Const(22356),
"d1": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16512)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='non... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_divisible_and_v1 | null | 6 | 0 | [
"V8"
] | 1 | 3.58 | 2026-02-08T16:12:54.001729Z | {
"verified": true,
"answer": 1863,
"timestamp": "2026-02-08T16:12:57.581569Z"
} | 7e3f1b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 756
},
"timestamp": "2026-02-24T20:19:55.332Z",
"answer": 1863
},
{
"i... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
25f2f6 | nt_sum_gcd_range_mod_v1_124444284_4951 | Let $N$ be the number of positive integers $n \leq 17776$ such that the sum of the decimal digits of $n$ is even. Let $k = 120$ and $M = 10477$. Define $s = \sum_{n=1}^{N} \gcd(n, k)$. Find the value of $s \bmod M$. | 3,768 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(17776)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"k": Const(120),
"M": Const(10477),
"sum": Summation(... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"L3B"
] | 1 | 1.216 | 2026-02-08T06:19:08.363833Z | {
"verified": true,
"answer": 3768,
"timestamp": "2026-02-08T06:19:09.579461Z"
} | 29faf0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 4084
},
"timestamp": "2026-02-12T22:39:59.825Z",
"answer": 3768
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
467a7d | comb_bell_compute_v1_1116507919_438 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 6$. Let $T$ be the set of all values of $xy$ as $(x,y)$ ranges over $S$. Let $n$ be the maximum value in $T$. Compute the Bell number $B_n$, which counts the number of partitions of a set of size $n$. | 21,147 | graphs = [
Graph(
let={
"_n": Const(6),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_bell_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T02:34:12.093209Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T02:34:12.094630Z"
} | 557a25 | 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": 641
},
"timestamp": "2026-02-08T19:32:59.326Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -4.79,
"mid": -2.86,
"hi": -0.85
} | ||
0662cc | comb_binomial_compute_v1_717093673_2500 | Let $n = 12$. Define $k$ to be
$$
\frac{2}{8} \sum_{\substack{k_1 = 1}^{3} \sum_{j = 1}^{4} \varphi(k_1) \left\lfloor \frac{3}{k_1} \right\rfloor.
$$
Compute the value of $\binom{n}{k}$, and let $Q$ be the remainder when $80089$ times this value is divided by $76780$. Find the value of $Q$. | 63,096 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(76780),
"n": Const(12),
"k": Div(Mul(Const(2), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k1"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(... | NT | null | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/K2"
] | 8580e7 | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.003 | 2026-02-08T16:53:35.991121Z | {
"verified": true,
"answer": 63096,
"timestamp": "2026-02-08T16:53:35.993728Z"
} | e84ccb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1692
},
"timestamp": "2026-02-17T15:00:39.904Z",
"answer": 63096
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
73b9e8 | comb_factorial_compute_v1_1520064083_6682 | Let $c = 46525$ and $m$ be the sum of all positive integers $n$ such that $1 \leq n \leq 16$ and $n \equiv 0 \pmod{16}$. Let $n$ be the largest prime number not exceeding the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = m$. Let $r = n!$. Compute the remainder when $c \cd... | 48,826 | graphs = [
Graph(
let={
"_c": Const(46525),
"_m": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(16)), Eq(Mod(value=Var("n"), modulus=Const(16)), Const(0))))),
"_n": Const(54293),
"n": MaxOverSet(set=Soluti... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/B3/MAX_PRIME_BELOW"
] | f1cc84 | comb_factorial_compute_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"SUM_DIVISIBLE"
] | 3 | 0.004 | 2026-02-08T08:15:55.847286Z | {
"verified": true,
"answer": 48826,
"timestamp": "2026-02-08T08:15:55.851533Z"
} | eab094 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 768
},
"timestamp": "2026-02-13T16:51:41.645Z",
"answer": 48826
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
8e2c51 | modular_sum_quadratic_residues_v1_601307018_9618 | Let $p$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $10a^2 - 18ab + 25b^2 \le 5578$. Compute $\frac{p(p-1)}{4}$. | 50,288 | graphs = [
Graph(
let={
"_n": Const(10),
"p": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Leq(Sum(Mul(Ref("_n"), Pow(Var("a"), Const(2))), M... | NT | null | SUM | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.004 | 2026-03-10T10:03:21.074391Z | {
"verified": true,
"answer": 50288,
"timestamp": "2026-03-10T10:03:21.077952Z"
} | 53bbbf | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 4702
},
"timestamp": "2026-04-19T11:39:19.047Z",
"answer": 50288
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SU... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
ba99ef | comb_count_surjections_v1_971394319_1938 | Let $n = 7$ and $k = 4$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $T$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ satisfying $1 \le a \le 210$, $1 \le b \le 26$, $10 \le t \le 1548$, and $t = 7a + 3b$. Compute t... | 62,328 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(n... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | comb_count_surjections_v1 | affine_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T14:00:49.523972Z | {
"verified": true,
"answer": 62328,
"timestamp": "2026-02-08T14:00:49.527620Z"
} | 3748a9 | 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": 32768
},
"timestamp": "2026-02-24T19:43:15.178Z",
"answer": 62328
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
17f68b | nt_sum_divisors_range_v1_1080341949_109 | Let $N$ be the largest prime number less than or equal to $6717$. Compute the sum of the number of positive divisors of each integer from $1$ to $N$. | 60,151 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(6717)), IsPrime(Var("n"))))),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_divisors_range_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.343 | 2026-02-08T13:13:24.866980Z | {
"verified": true,
"answer": 60151,
"timestamp": "2026-02-08T13:13:25.210140Z"
} | 7082c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 85,
"completion_tokens": 6444
},
"timestamp": "2026-02-15T10:49:17.222Z",
"answer": 60151
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ed59cb | diophantine_fbi2_min_v1_677425708_3109 | Let $d$ be an integer satisfying $d \geq 3$, $d \leq 190$, $d$ divides $180$, and $\frac{180}{d} \geq 5$. Determine the value of the smallest such $d$. | 3 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(180),
"upper": Const(190),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.009 | 2026-02-08T05:29:45.106340Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T05:29:45.115358Z"
} | 3d1be7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 536
},
"timestamp": "2026-02-11T22:51:30.715Z",
"answer": 3
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"... | {
"lo": -10,
"mid": -7.3,
"hi": -4.61
} | ||
83b1fb | lin_form_endings_v1_717093673_2870 | Let $a = 10$ and $b = 8$. Define $d = \gcd(a, b)$. Let $k = 14832$ and $M = 54813$. Compute the remainder when $k \cdot d$ is divided by $M$. | 29,664 | graphs = [
Graph(
let={
"a_coeff": Const(10),
"b_coeff": Const(8),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(14832),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(54813),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:14:33.924334Z | {
"verified": true,
"answer": 29664,
"timestamp": "2026-02-08T17:14:33.924886Z"
} | dedea5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 210
},
"timestamp": "2026-02-16T09:12:50.392Z",
"answer": 29664
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
c33477 | antilemma_sum_equals_v1_349078426_249 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 81$, $1 \leq j \leq 82$, and $i + j = 82$. Compute the value of
$$
x + \phi(x + 1) + \tau\left(x + \binom{10}{0}\right),
$$
where $\phi(n)$ denotes Euler's totient function and $\tau(n)$ denotes the number of positive divisors... | 125 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(82)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(81)), right=IntegerRange(start=Const(1), end=Const(82))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | ec98de | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 3 | 0.091 | 2026-02-08T12:54:03.426168Z | {
"verified": true,
"answer": 125,
"timestamp": "2026-02-08T12:54:03.517348Z"
} | 61d176 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 814
},
"timestamp": "2026-02-24T16:36:45.818Z",
"answer": 125
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
5780c6 | nt_count_divisible_and_v1_1874849503_1285 | Let $d_1$ be the number of integers $t$ such that $7 \leq t \leq 20$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 5a + 2b$. Let $d_2 = 15$ and let $N = 44760$. Compute the number of positive integers $n \leq N$ such that $n$ is divisible by both $d_1$ and $d_2$. Multiply this... | 46,373 | graphs = [
Graph(
let={
"upper": Const(44760),
"d1": 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(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 3.025 | 2026-02-08T13:45:11.574950Z | {
"verified": true,
"answer": 46373,
"timestamp": "2026-02-08T13:45:14.600419Z"
} | 8f8033 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 1667
},
"timestamp": "2026-02-10T03:09:34.657Z",
"answer": 46373
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
a57958 | comb_count_derangements_v1_1742523217_914 | Let $m = 25$ and $n_0 = 2$. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $n_{\text{max}}$ be the minimum value in $T$. Determine the value of $n$, defined as the largest prime number $n$ satisfying $n_0 \l... | 1,854 | graphs = [
Graph(
let={
"_m": Const(25),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=... | NT | COMB | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | comb_count_derangements_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T03:21:18.860080Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T03:21:18.861645Z"
} | 05eb8c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1215
},
"timestamp": "2026-02-10T00:33:27.718Z",
"answer": 1854
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"le... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
6c095c | antilemma_k2_v1_1520064083_4702 | Let $n = 254$. Define $x = \sum_{k=1}^{254} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $c = 13$. Compute the value of $(c - x) \mod 81422$. | 49,050 | graphs = [
Graph(
let={
"_n": Const(254),
"x": Summation(var="k", start=Const(1), end=Const(254), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(13),
"Q": Mod(value=Sub(Ref("_c"), Ref("x")), modulus=Const(81422)),
},
... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T06:23:19.632959Z | {
"verified": true,
"answer": 49050,
"timestamp": "2026-02-08T06:23:19.633820Z"
} | 76869b | 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": 809
},
"timestamp": "2026-02-12T23:30:18.408Z",
"answer": 49050
},
{... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} |
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