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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
19c3ed | nt_sum_divisors_mod_v1_798873815_105 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 396900$. For each pair $(x,y)$ in $S$, compute the sum $x + y$. Let $n$ be the smallest such sum. Define $\sigma$ to be the sum of all positive divisors of $n$. Let $M = 10739$. Compute the remainder when $44121 \cdot (\sigma \bmod M)$... | 32,889 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10739... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T02:26:11.372256Z | {
"verified": true,
"answer": 32889,
"timestamp": "2026-02-08T02:26:11.373672Z"
} | b97365 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 4340
},
"timestamp": "2026-02-23T15:26:44.807Z",
"answer": 33889
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.12,
"mid": 2.54,
"hi": 3.89
} | ||
bacb34 | nt_sum_totient_over_divisors_v1_1431428450_192 | Let $n = 94461$. Define $\varphi(d)$ as Euler's totient function. Compute the sum
$$
\sum_{d \mid n} \varphi(d),
$$
where the sum is taken over all positive divisors $d$ of $n$.
Let $c$ be the number of ordered pairs $(x, y)$ such that $1 \leq x \leq 37$ and $1 \leq y \leq 37$. Let $Q$ be the remainder when $c - 94461... | 33,408 | graphs = [
Graph(
let={
"_n": Const(63250),
"n": Const(94461),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(37)), right=IntegerRange(sta... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 009729 | nt_sum_totient_over_divisors_v1 | negation_mod | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T13:17:40.051980Z | {
"verified": true,
"answer": 33408,
"timestamp": "2026-02-08T13:17:40.054961Z"
} | 2fccc2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 567
},
"timestamp": "2026-02-15T12:02:32.004Z",
"answer": 33408
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8baa89 | comb_count_permutations_fixed_v1_971394319_1848 | 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 $i + j = 8$. Compute $\binom{n}{2} \cdot !(n - 2)$, where $!k$ denotes the number of derangements of $k$ elements. | 20 | graphs = [
Graph(
let={
"_n": Const(8),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.023 | 2026-02-08T13:57:51.131607Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T13:57:51.154601Z"
} | a52c37 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 865
},
"timestamp": "2026-02-24T19:29:36.528Z",
"answer": 20
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
7d9c7e | comb_count_partitions_v1_458359167_1931 | Let $n$ be the number of integers $t$ such that $8 \leq t \leq 54$ and there exist positive integers $a \leq 6$ and $b \leq 8$ satisfying $t = 5a + 3b$. 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=6)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.018 | 2026-02-08T04:56:19.193415Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T04:56:19.211887Z"
} | 6d04b7 | 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": 4707
},
"timestamp": "2026-02-11T22:31:25.459Z",
"answer": 31185
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
d00b8e | nt_min_coprime_above_v1_1874849503_689 | Let $n$ be a positive integer such that $x \cdot y = 4900$ for some positive integers $x$ and $y$. Define $s = x + y$. Let $m$ be the minimum possible value of $s$ over all such pairs $(x, y)$. Find the smallest integer $n$ satisfying $62500 < n \leq 62650$ such that $\gcd(n, m) = \phi(1)$, where $\phi$ is the Euler to... | 62,501 | graphs = [
Graph(
let={
"_n": Const(4900),
"start": Const(62500),
"upper": Const(62650),
"modulus": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')),... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"B3"
] | d3bb9b | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3",
"ONE_PHI_1"
] | 2 | 0.087 | 2026-02-08T13:15:12.545616Z | {
"verified": true,
"answer": 62501,
"timestamp": "2026-02-08T13:15:12.632554Z"
} | 7998cf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 2146
},
"timestamp": "2026-02-09T19:52:29.578Z",
"answer": 62501
},
{
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
4ebf71 | nt_count_intersection_v1_2051736721_1918 | Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 200$. Let $b$ be the number of integers $t$ with $25 \le t \le 94$ for which there exist positive integers $a \le 11$ and $b \le 2$ such that $t = 6a + 9b + 10$. Compute the number of positive integers $n \le N$ such th... | 909 | graphs = [
Graph(
let={
"_n": Const(200),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B1"
] | 2f9b70 | nt_count_intersection_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.389 | 2026-02-08T16:19:10.925572Z | {
"verified": true,
"answer": 909,
"timestamp": "2026-02-08T16:19:11.314801Z"
} | 37d22f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1595
},
"timestamp": "2026-02-17T02:34:39.099Z",
"answer": 909
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f2ad0b | comb_count_derangements_v1_1125832087_1424 | Let $N$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 11319000$, and $\gcd(p, q) = 1$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = N$. Define $n$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Let $R$ b... | 82,563 | graphs = [
Graph(
let={
"_m": Const(99832),
"_n": Const(91963),
"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")), CountOverSet(s... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 3f0fb0 | comb_count_derangements_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.003 | 2026-02-08T03:43:48.527741Z | {
"verified": true,
"answer": 82563,
"timestamp": "2026-02-08T03:43:48.530902Z"
} | a73952 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 6618
},
"timestamp": "2026-02-10T15:28:33.564Z",
"answer": 82563
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
96bea6 | nt_count_gcd_equals_v1_865884756_3593 | Let $k$ be the minimum value of $x + y$ over all positive integers $x, y$ such that $xy = m$, where $m$ is the number of positive integers at most $201204$ that are divisible by $276$. Let $r$ be the number of positive integers $n$ with $1 \leq n \leq 10946$ such that $\gcd(n, k) = 2$. Compute the remainder when $44121... | 17,978 | graphs = [
Graph(
let={
"upper": Const(10946),
"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")), CountOverSet(set=SolutionsSet(var=Var("k1")... | NT | null | COUNT | sympy | C2 | [
"C2/B3"
] | 7c8509 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"B3",
"C2"
] | 2 | 2.408 | 2026-02-08T17:30:46.366018Z | {
"verified": true,
"answer": 17978,
"timestamp": "2026-02-08T17:30:48.774087Z"
} | 1057e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1513
},
"timestamp": "2026-02-18T02:48:49.887Z",
"answer": 17978
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f8a55 | diophantine_product_count_v1_655260480_2915 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 57600$. For each such pair, compute $x + y$. Let $T$ be the set of all such sums. Let $m$ be the minimum element of $T$. Define $k = \sum_{d \mid m} \phi(d)$, where $\phi$ is Euler's totient function. Let $\mathrm{result}$ be the numb... | 17,458 | graphs = [
Graph(
let={
"_n": Const(93907),
"k": SumOverDivisors(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(left=Mul(Var(name='x'), Var(name='y')), rig... | NT | null | COUNT | sympy | B3 | [
"B3/K3"
] | 4a4ef2 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"K3"
] | 2 | 0.012 | 2026-02-08T17:03:48.486742Z | {
"verified": true,
"answer": 17458,
"timestamp": "2026-02-08T17:03:48.499129Z"
} | b82149 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 906
},
"timestamp": "2026-02-17T18:18:05.934Z",
"answer": 17458
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0ce662 | nt_max_prime_below_v1_124444284_9613 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 2$ and $n$ is even. Let $m$ be the sum of all elements in $S$. Determine the largest prime number $n$ such that $m \leq n \leq 51529$. | 51,521 | graphs = [
Graph(
let={
"upper": Const(51529),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2)), Eq(Mod(value=Var("n"), modulus=Const(2)), Const(0))... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_max_prime_below_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 1.276 | 2026-02-08T12:35:10.500589Z | {
"verified": true,
"answer": 51521,
"timestamp": "2026-02-08T12:35:11.776604Z"
} | e6acfd | 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": 1933
},
"timestamp": "2026-02-15T02:40:19.734Z",
"answer": 51521
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f4b073 | geo_visible_lattice_v1_1915831931_1191 | Let $n = 60$. Define $L$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $c = 23893$. Compute the remainder when $c \cdot L$ is divided by $79800$. | 48,079 | graphs = [
Graph(
let={
"n": Const(60),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(23893),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(79800)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.303 | 2026-02-08T15:56:23.819169Z | {
"verified": true,
"answer": 48079,
"timestamp": "2026-02-08T15:56:24.122134Z"
} | 1568b6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 3379
},
"timestamp": "2026-02-24T19:08:20.839Z",
"answer": 71972
},
{
... | 1 | [] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||||
2022f9 | geo_count_lattice_rect_v1_548369836_59 | Let $a = 24$ and $b = 91$. Define $R$ as the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Compute $25600 - R$. | 23,300 | graphs = [
Graph(
let={
"a": Const(24),
"b": Const(91),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Sub(Const(25600), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T02:44:46.118757Z | {
"verified": true,
"answer": 23300,
"timestamp": "2026-02-08T02:44:46.119437Z"
} | f15480 | 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": 660
},
"timestamp": "2026-02-08T19:46:18.013Z",
"answer": 23300
},
{
"i... | 1 | [] | {
"lo": -7.73,
"mid": -5.63,
"hi": -3.79
} | ||||
d434b7 | sequence_fibonacci_compute_v1_1431428450_536 | Let $n$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 10$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Define $m = |F_n| + 2$. The Fibonacci entry point modulo $m$ is the smallest positive integer ... | 308 | graphs = [
Graph(
let={
"_n": Const(10),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T13:31:02.127679Z | {
"verified": true,
"answer": 308,
"timestamp": "2026-02-08T13:31:02.128971Z"
} | 759d28 | 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": 3478
},
"timestamp": "2026-02-15T16:30:44.734Z",
"answer": 308
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
265798 | modular_count_residue_v1_655260480_3086 | Let $m$ be the number of nonnegative integers $j \leq 37184$ such that $\binom{37184}{j}$ is odd. Let $r$ be the number of integers $t$ with $7 \leq t \leq 24$ that can be expressed in the form $3a + 4b$ for positive integers $a \leq 4$ and $b \leq 3$. Determine the number of positive integers $n \leq 84100$ such that ... | 5,256 | graphs = [
Graph(
let={
"_n": Const(37184),
"upper": Const(84100),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(37184), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonn... | ALG | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"V8"
] | a2d4b4 | modular_count_residue_v1 | null | 6 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 5.924 | 2026-02-08T17:10:38.821678Z | {
"verified": true,
"answer": 5256,
"timestamp": "2026-02-08T17:10:44.745550Z"
} | e26808 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1961
},
"timestamp": "2026-02-17T21:04:32.830Z",
"answer": 5256
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "ok... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
eb4508 | nt_count_divisible_and_v1_1742523217_2282 | Let $T$ be the set of all integers $t$ such that $10 \le t \le 28$ and there exist positive integers $a$ and $b$ with $1 \le a \le 4$, $1 \le b \le 2$, and $t = 4a + 6b$. Let $d_2$ be the number of elements in $T$. Let $d_1 = 6$. Compute the number of positive integers $n$ such that $1 \le n \le 106968$, $n \equiv \sum... | 4,457 | graphs = [
Graph(
let={
"upper": Const(106968),
"d1": Const(6),
"d2": 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'), r... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 3.598 | 2026-02-08T04:40:19.775449Z | {
"verified": true,
"answer": 4457,
"timestamp": "2026-02-08T04:40:23.373516Z"
} | d5617e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 1577
},
"timestamp": "2026-02-24T01:29:42.664Z",
"answer": 4457
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma"... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
1261e9 | comb_sum_binomial_row_v1_865884756_6914 | Let $n$ be the number of integers $t$ with $9 \le t \le 28$ that can be expressed in the form $2a + 7b$ for positive integers $a \le 7$ and $b \le 2$. Compute $2^n$. | 16,384 | graphs = [
Graph(
let={
"_n": Const(2),
"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(na... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T19:27:24.840069Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-08T19:27:24.841545Z"
} | 00986b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 1304
},
"timestamp": "2026-02-18T22:24:23.322Z",
"answer": 16384
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a436cb | nt_num_divisors_compute_v1_1918700295_859 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 146$. Let $n$ be the maximum value of $xy$ over all such pairs. Let $d(n)$ denote the number of positive divisors of $n$. Compute the remainder when $75606 \cdot d(n)$ is divided by $99121$. | 28,576 | graphs = [
Graph(
let={
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(146)))), expr=Mul(Var("x"), Var("y")))),
"result": NumDiviso... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T03:32:46.449193Z | {
"verified": true,
"answer": 28576,
"timestamp": "2026-02-08T03:32:46.452424Z"
} | 829d5d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 437
},
"timestamp": "2026-02-11T22:33:11.788Z",
"answer": 24576
},
{
"id": 11... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
c52d36 | geo_count_lattice_rect_v1_1978505735_1362 | Let $a = 50$ and $b = 20$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $Q = 44121 \cdot \text{result} \mod 86257$, where the result is the unique integer $r$ with $0 \le r < 86257$ such that $r \equiv 44121 \cdot \text{result} \pmod{8625... | 71,012 | graphs = [
Graph(
let={
"a": Const(50),
"b": Const(20),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(86257)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T16:06:15.873082Z | {
"verified": true,
"answer": 71012,
"timestamp": "2026-02-08T16:06:15.874448Z"
} | b2d946 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 963
},
"timestamp": "2026-02-24T19:49:28.174Z",
"answer": 71012
},
{
"... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
e91378 | comb_count_surjections_v1_1218484723_5181 | Let $k = 4$ and $n = \sum_{d=1}^{3} \varphi(d) \left\lfloor \frac{3}{d} \right\rfloor$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 1,560 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(3), Var("k1"))))),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
... | COMB | NT | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_surjections_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-25T06:49:11.057949Z | {
"verified": true,
"answer": 1560,
"timestamp": "2026-02-25T06:49:11.061347Z"
} | a67b23 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 720
},
"timestamp": "2026-03-29T19:49:25.022Z",
"answer": 1560
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
33bfdc | nt_euler_phi_compute_v1_1470522791_1293 | Let $n = 36100$. Define $r = \phi(n)$, where $\phi$ is Euler's totient function. Let $s$ be the sum
$$
\sum_{i = k_{\text{start}}}^{d-1} \left( \text{digit}_i(r) \cdot (i+1)^2 \right),
$$
where $d$ is the number of decimal digits of $|r|$, $\text{digit}_i(r)$ denotes the $i$-th decimal digit of $|r|$ (with $i=0$ being ... | 7,936 | graphs = [
Graph(
let={
"n": Const(36100),
"result": EulerPhi(n=Ref("n")),
"Q": Sum(Summation(var="i", start=Summation(var="k", start=Sub(Binom(n=Const(4), k=Const(4)), Const(1)), end=Const(8), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(8), k=Var("k")))), end=Sub(Nu... | COMB | NT | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 81f806 | nt_euler_phi_compute_v1 | digits_weighted_mod | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"ZERO_BINOM_N"
] | 3 | 0.005 | 2026-02-08T13:33:13.985504Z | {
"verified": true,
"answer": 7936,
"timestamp": "2026-02-08T13:33:13.990567Z"
} | 0bd7ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 1618
},
"timestamp": "2026-02-15T18:15:01.639Z",
"answer": 7936
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b3ca2a | nt_sum_divisors_mod_v1_1742523217_3452 | Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 9464$ and there exist positive integers $a \leq 1188$, $b \leq 1180$ satisfying $t = 3a + 5b$. Let $N$ be the number of positive integers $n \leq |T|$ that are relatively prime to $30$. Compute the remainder when the sum of the divisors of $N$ is divided b... | 9,360 | 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=1188)), Geq(left=Var(name='b'), right=Const(val... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C4"
] | 067e5d | nt_sum_divisors_mod_v1 | null | 7 | 0 | [
"C4",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T05:52:20.508480Z | {
"verified": true,
"answer": 9360,
"timestamp": "2026-02-08T05:52:20.510697Z"
} | 502617 | 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": 5066
},
"timestamp": "2026-02-12T16:30:02.143Z",
"answer": 9360
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
1ffba4 | lin_form_endings_v1_655260480_3007 | Let $a = 105$ and $b = 60$. Define $g = \gcd(a, b)$. Let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 32$ and $B = 8$. Define
$$
T = a' \cdot A + b' \cdot B - a' \cdot b'.
$$
Let
$$
S = a \cdot A + b \cdot B - a - b + 1.
$$
Compute $S - T$. | 3,448 | graphs = [
Graph(
let={
"a_coeff": Const(105),
"b_coeff": Const(60),
"A_val": Const(32),
"B_val": Const(8),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T17:07:21.901707Z | {
"verified": true,
"answer": 3448,
"timestamp": "2026-02-08T17:07:21.904978Z"
} | 7e77f1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 615
},
"timestamp": "2026-02-16T09:02:20.898Z",
"answer": 3464
},
{
"id": 11,... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
a9c3f0 | lte_diff_endings_v1_1125832087_161 | Let $a = 1883$ and $b = 8$. Let $p = 5$ and $K = 7$. Define $d = a - b$, and let $v_p(d)$ be the largest integer $k$ such that $p^k$ divides $d$. Let $m = K - v_p(d)$ and let $p^m$ be the corresponding power of $p$. Given $N = 12051609$, compute the value of $\left\lfloor \frac{N}{p^m} \right\rfloor$. | 96,412 | graphs = [
Graph(
let={
"a_val": Const(1883),
"b_val": Const(8),
"p_val": Const(5),
"K_val": Const(7),
"N_val": Const(12051609),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 4 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T02:54:55.402401Z | {
"verified": true,
"answer": 96412,
"timestamp": "2026-02-08T02:54:55.402989Z"
} | 43499a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 527
},
"timestamp": "2026-02-17T15:48:55.099Z",
"answer": 96412
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
f7c86d | nt_num_divisors_compute_v1_655260480_1777 | Let $n = 15376$. Determine the value of the number of positive divisors of $n$. | 15 | graphs = [
Graph(
let={
"n": Const(15376),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.009 | 2026-02-08T16:22:14.055957Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T16:22:14.065272Z"
} | 5b5249 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 395
},
"timestamp": "2026-02-16T07:17:59.526Z",
"answer": 15
},
{
"id": 11,
"... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
9c80f9 | antilemma_cartesian_v1_124444284_1270 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 24, inclusive, and $b$ is an integer from 1 to 28, inclusive. Compute $x$. | 672 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(24)), right=IntegerRange(start=Const(1), end=Const(28)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T03:48:19.462756Z | {
"verified": true,
"answer": 672,
"timestamp": "2026-02-08T03:48:19.463775Z"
} | b3d474 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 264
},
"timestamp": "2026-02-10T05:21:26.448Z",
"answer": 672
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
0f3736 | antilemma_v7_kummer_677425708_160 | Let $x$ be the largest integer $k$ such that $2^k$ divides $\binom{585}{234}$. Compute the remainder when $44121 \cdot x$ is divided by $74672$. | 54,280 | graphs = [
Graph(
let={
"_n": Const(234),
"x": MaxKDivides(target=Binom(n=Const(585), k=Ref("_n")), base=Const(2)),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(74672)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | antilemma_v7_kummer | null | 7 | 0 | [
"V7"
] | 1 | 0.001 | 2026-02-08T03:06:49.719436Z | {
"verified": true,
"answer": 54280,
"timestamp": "2026-02-08T03:06:49.720098Z"
} | 6e0730 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 689
},
"timestamp": "2026-02-08T20:20:09.421Z",
"answer": 54280
},
{
"i... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
}
] | {
"lo": -6.51,
"mid": -0.53,
"hi": 4.75
} | ||
f6e712 | algebra_poly_eval_v1_151522320_1033 | Let $y = \sum_{k=1}^{3} k$. Define $\text{result} = 7y^2 - 5y - 6$. Let $n = 74064$. Compute the remainder when $n \cdot \text{result}$ is divided by $97457$. | 14,876 | graphs = [
Graph(
let={
"_n": Const(74064),
"y": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": Sum(Mul(Const(7), Pow(Ref("y"), Const(2))), Mul(Const(-5), Ref("y")), Const(-6)),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), modulus=... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_poly_eval_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T03:43:16.877224Z | {
"verified": true,
"answer": 14876,
"timestamp": "2026-02-08T03:43:16.879194Z"
} | 8e5a4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 805
},
"timestamp": "2026-02-10T15:33:00.459Z",
"answer": 14876
},
{
"i... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
c78c50 | nt_sum_divisors_mod_v1_1125832087_1582 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 113400$ and $10$ divides the $k$-th Fibonacci number. Define $M = 11483$ and let $\sigma$ be the sum of all positive divisors of $n$. Let $r$ be the remainder when $\sigma$ is divided by $M$. Compute the remainder when $20338 \cdot r$ is divided by... | 15,564 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(113400)), Divides(divisor=Const(10), dividend=Fibonacci(arg=Var(name='n')))))),
"M": Const(11483),
"sigma": SumDivisors(n=Ref("n")),
... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_divisors_mod_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T03:48:59.855015Z | {
"verified": true,
"answer": 15564,
"timestamp": "2026-02-08T03:48:59.857365Z"
} | e5fedf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 2229
},
"timestamp": "2026-02-10T15:57:19.466Z",
"answer": 15564
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
a6b141 | comb_count_permutations_fixed_v1_898971024_998 | Let $n$ be the smallest prime divisor of 454597 that is at least 2. Compute the value of $$
\binom{n}{9} \cdot !(n - 9),
$$
where $!k$ denotes the number of derangements of $k$ elements. | 55 | graphs = [
Graph(
let={
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(454597))))),
"k": Const(9),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=R... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.004 | 2026-02-08T15:49:44.851395Z | {
"verified": true,
"answer": 55,
"timestamp": "2026-02-08T15:49:44.855565Z"
} | bdf6e7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 662
},
"timestamp": "2026-02-16T15:47:13.222Z",
"answer": 55
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a5105a | alg_poly3_sum_v1_1218484723_2272 | Consider all ordered pairs $(a, b)$ of integers with $1 \le a \le 40$ and $1 \le b \le \left|\{ (a_1, b_1) : 1 \le a_1 \le 40,\, 1 \le b_1 \le 40,\, 17b_1^{4} = \bigl|\{ v : 32 \le v \le 800,\, \text{there exist integers } a_1, b_1 \text{ with } 1 \le a_1 \le 5,\, 1 \le b_1 \le 5 \text{ such that } 2a_1^{2} + 12a_1b_1 ... | 73,020 | graphs = [
Graph(
let={
"_n": Const(40),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY4_COUNT"
] | a605ae | alg_poly3_sum_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.016 | 2026-02-25T04:05:44.301224Z | {
"verified": true,
"answer": 73020,
"timestamp": "2026-02-25T04:05:44.317432Z"
} | e5c5a0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 354,
"completion_tokens": 2670
},
"timestamp": "2026-03-29T03:52:47.322Z",
"answer": 73020
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
72f438 | nt_max_prime_below_v1_124444284_5833 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 18$, and $\gcd(p, q) = 1$. Let $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $m \leq n \leq 11881$. | 11,867 | graphs = [
Graph(
let={
"upper": Const(11881),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.815 | 2026-02-08T06:53:49.026672Z | {
"verified": true,
"answer": 11867,
"timestamp": "2026-02-08T06:53:52.841828Z"
} | c4b669 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2614
},
"timestamp": "2026-02-13T06:05:20.874Z",
"answer": 11867
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a8ba3b | nt_sum_divisors_mod_v1_124444284_9206 | Let $n$ be the number of positive integers less than or equal to 1469 that are relatively prime to 21. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by 10891. | 2,880 | graphs = [
Graph(
let={
"_n": Const(1469),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"M": Const(10891),
"sigma": SumDivisors(n=Ref("n")),
... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.003 | 2026-02-08T12:17:53.356913Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T12:17:53.359571Z"
} | b48d9c | 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": 750
},
"timestamp": "2026-02-15T00:05:10.860Z",
"answer": 2880
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
aaa1a4 | algebra_quadratic_discriminant_v1_458359167_2845 | Let $m = 2560$. Define $n$ to be the number of integers $j$ such that $0 \le j \le m$ and $\binom{2560}{j}$ is odd.
Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 31500$, $\gcd(p, q) = 1$, and $p < q$.
Compute the value of $(-6)^2 - n \cdot a \cdot ... | 356 | graphs = [
Graph(
let={
"_m": Const(2560),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Const(2560), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"a"... | NT | null | COMPUTE | sympy | V8 | [
"V8/COPRIME_PAIRS"
] | cea98a | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.002 | 2026-02-08T06:48:10.925696Z | {
"verified": true,
"answer": 356,
"timestamp": "2026-02-08T06:48:10.928012Z"
} | 3356ab | 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": 2252
},
"timestamp": "2026-02-13T04:49:05.084Z",
"answer": 356
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"le... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
b9e220 | sequence_lucas_compute_v1_151522320_2240 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 29$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 7$, and $t = 5a + 2b$. Define $Q$ to be the remainder when $44121$ times the $n$-th Lucas number is divided by $50096$. Compute $Q$. | 46,861 | graphs = [
Graph(
let={
"_n": Const(50096),
"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=3)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.2 | 2026-02-08T04:42:29.128181Z | {
"verified": true,
"answer": 46861,
"timestamp": "2026-02-08T04:42:29.327798Z"
} | b2bf18 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1850
},
"timestamp": "2026-02-11T21:47:49.717Z",
"answer": 46861
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
920424 | comb_binomial_compute_v1_1470522791_677 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 12816$ and $\binom{12816}{j}$ is odd. Compute $\binom{n}{9}$. | 11,440 | graphs = [
Graph(
let={
"_n": Const(12816),
"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(12816), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"k... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_binomial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T13:11:20.457392Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T13:11:20.460071Z"
} | 6f5df3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1130
},
"timestamp": "2026-02-24T17:23:19.464Z",
"answer": 11440
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
725616 | nt_lcm_compute_v1_865884756_2152 | Let $a = 1180$. Let $b$ be the number of integers $t$ with $21 \leq t \leq 8166$ for which there exist positive integers $a'$ and $b'$ such that $1 \leq a' \leq 444$, $1 \leq b' \leq 251$, and $t = 15a' + 6b'$. Define $c = 30976$ and let $\ell = \operatorname{lcm}(a, b)$. Find the remainder when $c - \ell$ is divided b... | 31,604 | graphs = [
Graph(
let={
"a": Const(1180),
"b": 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=444)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_lcm_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T16:35:07.746296Z | {
"verified": true,
"answer": 31604,
"timestamp": "2026-02-08T16:35:07.748796Z"
} | 51a6a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 4737
},
"timestamp": "2026-02-17T08:00:29.603Z",
"answer": 31604
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a66ece | lin_form_endings_v1_349078426_1612 | Let $a = 6$ and $b = 8$. Let $L$ be the least common multiple of $a$ and $b$. Let $k = 13365$ and define $s = k \cdot L$. Compute the remainder when $s$ is divided by $80518$. | 79,206 | graphs = [
Graph(
let={
"a_coeff": Const(6),
"b_coeff": Const(8),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(13365),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(80518),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:45:55.321319Z | {
"verified": true,
"answer": 79206,
"timestamp": "2026-02-08T13:45:55.323099Z"
} | 7b32ff | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 297
},
"timestamp": "2026-02-16T05:07:31.283Z",
"answer": 19940
},
{
"id": 11... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
8291f9 | nt_count_divisors_in_range_v1_784195855_6620 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 937024$. Define $T$ to be the set of all positive integers $t$ for which there exist positive integers $a$ and $b$ with $1 \le a \le 49$, $1 \le b \le 48$, $28 \le t \le 453$, and $t = 2a + 7b + 19$. Let $m$ be the minimum value of $x ... | 1,914 | graphs = [
Graph(
let={
"n": Const(1260),
"a": Const(16),
"b": 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=Co... | NT | null | COUNT | sympy | B3 | [
"B3",
"LIN_FORM"
] | 70a683 | nt_count_divisors_in_range_v1 | negation_mod | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.015 | 2026-02-08T08:45:54.127184Z | {
"verified": true,
"answer": 1914,
"timestamp": "2026-02-08T08:45:54.141840Z"
} | d4bc0e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 4521
},
"timestamp": "2026-02-13T21:06:42.103Z",
"answer": 1914
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma":... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
0d4c53 | diophantine_fbi2_count_v1_1978505735_7407 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $k$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$.\\
Let $T$ be the set of all integers $d$ such that $3 \leq d \leq 199$, $d$ divides $k$, $\frac{k}{d} \geq 6$, and $\frac{k}{d} \leq 202$. (Assume $199$ is... | 23 | graphs = [
Graph(
let={
"_n": Const(202),
"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(176400)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 3 | 0.06 | 2026-02-08T20:15:03.525638Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T20:15:03.585951Z"
} | cfce62 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 2090
},
"timestamp": "2026-02-19T00:10:48.766Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"l... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9b0b1a | geo_count_lattice_rect_v1_784195855_5675 | Compute the number of lattice points in the rectangle $[0, 111] \times [0, 140]$. | 15,792 | graphs = [
Graph(
let={
"a": Const(111),
"b": Const(140),
"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 | 2026-02-08T08:02:15.017318Z | {
"verified": true,
"answer": 15792,
"timestamp": "2026-02-08T08:02:15.018767Z"
} | 7591a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 266
},
"timestamp": "2026-02-24T08:43:47.003Z",
"answer": 15792
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||||
c118c4 | nt_count_intersection_v1_1431428450_436 | Let $N$ be the number of integers $t$ such that $44 \leq t \leq 15113$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 76$, $1 \leq b \leq 665$, and $t = 15a + 21b + 8$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq N$, $11$ divides $n$, and $\gcd(n, 10) = 1$. | 182 | 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=76)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.307 | 2026-02-08T13:27:30.321206Z | {
"verified": true,
"answer": 182,
"timestamp": "2026-02-08T13:27:30.628564Z"
} | 911c3b | 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": 2432
},
"timestamp": "2026-02-15T16:17:53.147Z",
"answer": 182
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ef58ab | nt_count_coprime_and_v1_1918700295_852 | Let $k_1$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 16896$ and $\binom{16896}{j} \equiv 1 \pmod{2}$. Let $k_2 = 9$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 55002$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Compute the number of elements in $S$. Find the value ... | 18,334 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(55002),
"k1": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16896)), Eq(Mod(value=Binom(n=Const(16896), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='non... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_coprime_and_v1 | null | 6 | 0 | [
"V8"
] | 1 | 8.921 | 2026-02-08T03:32:26.891588Z | {
"verified": true,
"answer": 18334,
"timestamp": "2026-02-08T03:32:35.812771Z"
} | 98df72 | 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": 2137
},
"timestamp": "2026-02-10T14:46:15.126Z",
"answer": 18334
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
aabca8 | comb_bell_compute_v1_1978505735_2166 | Let $p$ and $q$ be positive integers such that $pq = 771750$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such ordered pairs $(p, q)$. Define $r = B_n$, the $n$-th Bell number. Compute $51984 - r$. | 47,844 | 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=771750)), 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 | 2026-02-08T16:42:16.304641Z | {
"verified": true,
"answer": 47844,
"timestamp": "2026-02-08T16:42:16.307043Z"
} | 8ddb23 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1282
},
"timestamp": "2026-02-17T11:12:54.173Z",
"answer": 47844
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5f3047 | diophantine_fbi2_min_v1_124444284_8082 | Let $k = 60$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1225$. Define $\sigma = \min\{x + y \mid (x,y) \in S\}$. Now consider the set of all positive integers $d$ such that $d \mid k$, $7 \leq d \leq \sigma$, and $\frac{k}{d} \geq 5$. Compute the minimum value of such $d$. | 10 | graphs = [
Graph(
let={
"k": Const(60),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1225)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.035 | 2026-02-08T09:33:25.587771Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T09:33:25.623270Z"
} | 42a319 | 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": 1025
},
"timestamp": "2026-02-14T04:43:06.329Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V8",
"stat... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
276a9b | lin_form_endings_v1_677425708_2420 | Let $A$ be the number of integers $t$ such that $50 \leq t \leq 970$ and there exist positive integers $a \leq 29$ and $b \leq 13$ satisfying $t = 20a + 30b$. Let $B = 11742 \cdot A$. Compute the remainder when $B$ is divided by $87136$. | 22,890 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=29)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:02:07.873558Z | {
"verified": true,
"answer": 22890,
"timestamp": "2026-02-08T05:02:07.874294Z"
} | 436e7c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 8838
},
"timestamp": "2026-02-24T02:36:09.279Z",
"answer": 22890
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
e28eb7 | alg_qf_psd_min_v1_601307018_5033 | Let $S = \left\{ v : v \geq 2,\ v \leq 1066,\ \text{there exist integers } a, b \text{ with } 1 \leq a, b \leq 8 \text{ such that } 20a^2 - 28ab + 10b^2 = v \right\}$. Find the minimum value of
$$
2814a^2 + 7638b^2 + 15276bc + 402ab + 10251c^2 - 2412ac
$$
over all positive integers $a, b, c$ with $1 \leq a \leq |S|$, $... | 33,969 | graphs = [
Graph(
let={
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(2)), Leq... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_min_v1 | null | 5 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 1.105 | 2026-03-10T05:42:20.113690Z | {
"verified": true,
"answer": 33969,
"timestamp": "2026-03-10T05:42:21.218325Z"
} | f80d79 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 9560
},
"timestamp": "2026-04-19T00:46:51.482Z",
"answer": 33969
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -6.2,
"mid": -2.86,
"hi": 0.46
} | ||
64f862 | antilemma_sum_equals_v1_784195855_471 | Let $n = 95$. Let $S$ be the set of all ordered pairs of positive integers $(i, j)$ such that $i + j = 95$ and $1 \leq i, j \leq 95$. Let $x$ be the number of elements in $S$. Multiply $x$ by 37351 and find the remainder when the result is divided by 92934. | 72,436 | graphs = [
Graph(
let={
"_n": Const(95),
"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(95)), 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 | 0.026 | 2026-02-08T04:24:18.238878Z | {
"verified": true,
"answer": 72436,
"timestamp": "2026-02-08T04:24:18.265346Z"
} | 94b4c3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 4363
},
"timestamp": "2026-02-24T00:32:18.374Z",
"answer": 72436
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
190bc2 | modular_count_residue_v1_1874849503_1590 | Let $m = 5$ and let $r$ be the smallest integer $d \ge 2$ that divides $735$. Let $N$ be the number of positive integers $n$ such that $1 \le n \le 46225$ and $n \equiv r \pmod{m}$. Compute the remainder when $33776 \cdot N$ is divided by $78785$. | 34,165 | graphs = [
Graph(
let={
"_n": Const(78785),
"upper": Const(46225),
"m": Const(5),
"r": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(735))))),
"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 | 4.163 | 2026-02-08T13:59:28.885871Z | {
"verified": true,
"answer": 34165,
"timestamp": "2026-02-08T13:59:33.049011Z"
} | 3b39d5 | 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": 2515
},
"timestamp": "2026-02-10T05:36:18.061Z",
"answer": 34165
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
e6c424 | comb_bell_compute_v1_397696148_1108 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 56$ and the $k$-th Fibonacci number is divisible by $13$. Compute the $n$-th Bell number. Find the value of this Bell number. | 4,140 | graphs = [
Graph(
let={
"_n": Const(13),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(56)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Bell(Ref("n")),
},
go... | NT | COMB | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | comb_bell_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T12:20:53.232351Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T12:20:53.233460Z"
} | 19e2cf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1491
},
"timestamp": "2026-02-15T00:27:28.532Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
c1738f | comb_binomial_compute_v1_397696148_1230 | Let $n$ be the number of nonnegative integers $j \leq 68616$ for which $\binom{68616}{j}$ is odd. Let $k = 8$. Compute the remainder when $44121 \cdot \binom{n}{k}$ is divided by $85783$. | 39,593 | graphs = [
Graph(
let={
"_n": Const(68616),
"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(68616), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"k... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_binomial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T12:25:34.722867Z | {
"verified": true,
"answer": 39593,
"timestamp": "2026-02-08T12:25:34.723931Z"
} | ae4444 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 4354
},
"timestamp": "2026-02-24T15:42:04.073Z",
"answer": 39593
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
0cae63 | geo_visible_lattice_v1_397696148_697 | Let $n = 100$. Compute the number of lattice points $(x, y)$ such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Multiply this number by $11494$, and find the remainder when the result is divided by $99511$. | 7,745 | graphs = [
Graph(
let={
"n": Const(100),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(11494), Ref("result")), modulus=Const(99511)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 2.269 | 2026-02-08T11:42:21.442344Z | {
"verified": true,
"answer": 7745,
"timestamp": "2026-02-08T11:42:23.711317Z"
} | 148b3a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2977
},
"timestamp": "2026-02-24T14:30:44.374Z",
"answer": 7745
},
{
"i... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
7321e3 | antilemma_k3_v1_677425708_4281 | Let $m = 8032$ and $n = 11$. Define $\displaystyle x = \sum_{d \mid m} \phi(d)$, and then define $\displaystyle y = \sum_{d \mid x} \phi(d)$. Let $z$ be the sum of all real solutions $t$ to the equation $t^2 - 5929t + 100504 = 0$. Compute the remainder when $y^2 + 11y + z$ is divided by $80701$. Find the value of this ... | 46,505 | graphs = [
Graph(
let={
"_m": Const(8032),
"_n": Const(11),
"x": SumOverDivisors(n=SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Ref("_n"), ... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"K3/K3",
"K3"
] | cde176 | antilemma_k3_v1 | quadratic_mod | 6 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.003 | 2026-02-08T06:31:40.044008Z | {
"verified": true,
"answer": 46505,
"timestamp": "2026-02-08T06:31:40.046961Z"
} | d56e97 | 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": 1081
},
"timestamp": "2026-02-13T01:32:44.840Z",
"answer": 46505
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a7c86b_n | alg_poly4_min_v1_1419126231_1852 | An engineer tunes two parameters $a$ and $b$, each an integer from 1 to 188, to minimize the energy consumption of a reactor modeled by $1693710b^4 - 2230740a b^3 + 1115370a^2 b^2 + 20655a^4 - 247860a^d b$, where $d$ is the smallest integer $\geq 2$ dividing $315$. What is the minimum possible energy value? | 20,655 | ALG | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_poly4_min_v1 | null | 6 | null | [
"MIN_PRIME_FACTOR"
] | 1 | 0.09 | 2026-02-25T11:24:22.810706Z | null | 7eab78 | a7c86b | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 2746
},
"timestamp": "2026-03-31T05:08:33.680Z",
"answer": 20655
},
{
"... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
739b2b | comb_count_permutations_fixed_v1_784195855_7482 | Compute $\binom{5}{0} \cdot !5$, where $!5$ denotes the number of derangements of $5$ elements. | 44 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_count_permutations_fixed_v1 | null | 2 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.029 | 2026-02-08T09:20:21.840740Z | {
"verified": true,
"answer": 44,
"timestamp": "2026-02-08T09:20:21.869526Z"
} | 97a0aa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 322
},
"timestamp": "2026-02-24T11:08:23.180Z",
"answer": 44
},
{
"id":... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma":... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
0ec11b | nt_num_divisors_compute_v1_124444284_3835 | Let $n = 46656$. Compute the number of positive divisors of $n$. | 49 | graphs = [
Graph(
let={
"n": Const(46656),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"MAX_PRIME_BELOW/MOBIUS_SUM/DIVISOR_PARITY",
"MAX_PRIME_BELOW/DIVISOR_PARITY"
] | 26ae09 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"DIVISOR_PARITY",
"MAX_PRIME_BELOW",
"MOBIUS_SUM"
] | 4 | 0.037 | 2026-02-08T05:37:59.596405Z | {
"verified": true,
"answer": 49,
"timestamp": "2026-02-08T05:37:59.632932Z"
} | dabcd1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 350
},
"timestamp": "2026-02-12T11:23:43.910Z",
"answer": 49
},
{
... | 1 | [
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
479315 | geo_count_lattice_rect_v1_655260480_3586 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 512$ and $0 \leq y \leq 158$. | 81,567 | graphs = [
Graph(
let={
"a": Const(512),
"b": Const(158),
"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 | 2026-02-08T17:27:27.669446Z | {
"verified": true,
"answer": 81567,
"timestamp": "2026-02-08T17:27:27.670140Z"
} | ad3868 | 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": 459
},
"timestamp": "2026-02-18T02:30:25.080Z",
"answer": 81567
},
{
... | 1 | [] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||||
d5ffe0 | comb_count_partitions_v1_458359167_3264 | Let $m = 83794$ and $c = 67933$. Let $n$ be the number of integers $t$ with $9 \le t \le 53$ such that there exist integers $a$, $b$ with $1 \le a \le 9$, $1 \le b \le 5$, and $t = 2a + 7b$. Let $N = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function. Let $P$ be the number of integer partitions of $N$. ... | 10,697 | graphs = [
Graph(
let={
"_m": Const(83794),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left=V... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/K3"
] | c7df50 | comb_count_partitions_v1 | null | 7 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T08:15:12.827300Z | {
"verified": true,
"answer": 10697,
"timestamp": "2026-02-08T08:15:12.828814Z"
} | 89bc8a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 2761
},
"timestamp": "2026-02-13T16:20:17.280Z",
"answer": 10697
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cc28d9 | comb_binomial_compute_v1_1742523217_4082 | Let $m = 1251$. Let $n_1$ be the number of positive integers $n$ such that $1 \le n \le m$, $9$ divides $n$, and $\gcd(n, 14) = 1$. Let $n$ be the number of positive integers $n$ such that $1 \le n \le n_1$ and
$$
n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}.
$$
Compute $\binom{n}{5}$. | 792 | graphs = [
Graph(
let={
"_m": Const(1251),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
"n": CountOverSet(set... | NT | null | COMPUTE | sympy | C5 | [
"C5/L3C"
] | 5ea002 | comb_binomial_compute_v1 | null | 6 | 0 | [
"C5",
"L3C"
] | 2 | 0.003 | 2026-02-08T06:59:25.334219Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T06:59:25.337025Z"
} | 0ee2ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1306
},
"timestamp": "2026-02-13T06:49:36.950Z",
"answer": 792
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
07f1a5 | diophantine_product_count_v1_1520064083_1439 | For each integer $k$ from $1$ to $15$, compute $\phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Let $k$ be the sum of these values. Let $\text{result}$ be the number of positive integers $x$ such that $1 \leq x \leq 85$, $x$ divides $k$, and $\frac{k}{x} \leq 85$. Find the sm... | 12 | graphs = [
Graph(
let={
"k": Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(15), Var("k"))))),
"upper": Const(85),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), ... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | diophantine_product_count_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.006 | 2026-02-08T03:59:59.114499Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T03:59:59.120352Z"
} | eb4e25 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 1262
},
"timestamp": "2026-02-10T16:31:49.933Z",
"answer": 12
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
4d470a | lin_form_endings_v1_1742523217_4172 | Let $a = 21$ and $b = 15$. Define $l$ to be the least common multiple of $a$ and $b$. Let $s = 10539 \cdot l$. Compute the remainder when $s$ is divided by $54941$. | 7,775 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(15),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(10539),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(54941),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T07:02:43.435897Z | {
"verified": true,
"answer": 7775,
"timestamp": "2026-02-08T07:02:43.436276Z"
} | a74cf6 | 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": 606
},
"timestamp": "2026-02-13T07:55:05.908Z",
"answer": 7775
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5934d9 | diophantine_product_count_v1_809748730_100 | Let $k = 840$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 34596$. Let $s$ be the minimum value of $x + y$ as $(x,y)$ ranges over $P$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq s$, $x$ divides $k$, and $\frac{840}{x} \leq s$. Let $r$ be the number ... | 37,786 | graphs = [
Graph(
let={
"k": Const(840),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(34596)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.015 | 2026-02-08T11:19:17.516923Z | {
"verified": true,
"answer": 37786,
"timestamp": "2026-02-08T11:19:17.531775Z"
} | 1fbaa3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 2250
},
"timestamp": "2026-02-14T11:45:36.472Z",
"answer": 37786
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7ef7b6_n | alg_poly_orbit_legendre_v1_1218484723_3270 | A cryptographic protocol uses a function $f(x) = 3x^4 + 3x^3 - x^2 - 5x - 5 \bmod 29$ and exponentiation modulo 29. Starting with a seed $a$, it computes $N = a^{14} \bmod 29$, then $M = f(a)$, $R = M^{14} \bmod 29$, and $S = N + R$. Then it computes $T = f(M)$. A seed is valid if $T = a$, $S$ is divisible by 3, and $M... | 1,014 | ALG | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 6 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.04 | 2026-02-25T04:58:32.600938Z | null | 9f3d01 | 7ef7b6 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 19028
},
"timestamp": "2026-03-30T19:55:43.612Z",
"answer": 1014
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
df1c87 | antilemma_cartesian_v1_655260480_6009 | Let $S$ be the set of all ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 39$ and $1 \leq b \leq 40$. Let $N$ be the number of elements in $S$. Compute the value of $$
N + \left(2^{N \bmod 15}\right) \bmod 64063.
$$ | 1,561 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(39)), right=IntegerRange(start=Const(1), end=Const(40)))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(15))), modulus=Const(64063))),
},... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T18:46:40.346813Z | {
"verified": true,
"answer": 1561,
"timestamp": "2026-02-08T18:46:40.347616Z"
} | ee7a7d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 502
},
"timestamp": "2026-02-25T00:29:51.621Z",
"answer": 1561
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -7.4,
"hi": -4.8
} | ||
10ede6 | geo_visible_lattice_v1_677425708_4286 | Let $n = 90$. A visible lattice point is an ordered pair $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $V$ be the number of visible lattice points for this $n$. Compute the remainder when $42271 \cdot V$ is divided by $94498$. Find the value of this remainder. | 25,325 | graphs = [
Graph(
let={
"n": Const(90),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(42271), Ref("result")), modulus=Const(94498)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 1.796 | 2026-02-08T06:31:43.281541Z | {
"verified": true,
"answer": 25325,
"timestamp": "2026-02-08T06:31:45.077685Z"
} | b72d69 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 9307
},
"timestamp": "2026-02-24T06:28:59.530Z",
"answer": 25325
},
{
"... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
7fe0dd | modular_min_modexp_v1_677425708_3116 | Let $a = 2$ and $n = 72900$. Let $b$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 6889$. Let $u$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = n$. Let $r$ be the smallest positive integer $x$ such that $1 \le ... | 33,610 | graphs = [
Graph(
let={
"_n": Const(72900),
"a": Const(2),
"b": 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(6889)))), exp... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_min_modexp_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.123 | 2026-02-08T05:30:01.238977Z | {
"verified": true,
"answer": 33610,
"timestamp": "2026-02-08T05:30:01.362080Z"
} | 2b694c | 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": 6096
},
"timestamp": "2026-02-12T09:54:56.682Z",
"answer": 33610
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
eb7c3f | comb_count_derangements_v1_1218484723_5271 | Let $n = \sum_{k=0}^{2} 2^k$. Compute the remainder when $44121D_n$ is divided by $96847$, where $D_n$ denotes the number of derangements of $n$ elements. | 61,466 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(0), end=Const(2), expr=Pow(Ref("_n"), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(96847)),
},
... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T06:55:12.260357Z | {
"verified": true,
"answer": 61466,
"timestamp": "2026-02-25T06:55:12.261705Z"
} | 960eab | 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": 1851
},
"timestamp": "2026-03-29T20:15:20.648Z",
"answer": 61466
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
f66b91 | diophantine_product_count_v1_397696148_1529 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Let $k$ be the minimum value of $x + y$ as $(x, y)$ ranges over $P$. Determine the number of positive integers $x$ such that $1 \leq x \leq 382$, $x$ divides $k$, and $\frac{k}{x} \leq 382$. Compute the value of $$
(44121 \cd... | 3,752 | graphs = [
Graph(
let={
"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(129600)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(3... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.027 | 2026-02-08T12:38:02.168604Z | {
"verified": true,
"answer": 3752,
"timestamp": "2026-02-08T12:38:02.195953Z"
} | 4dd590 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 2694
},
"timestamp": "2026-02-15T03:03:29.410Z",
"answer": 3752
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e954f3 | comb_count_surjections_v1_1978505735_7012 | Let $n = 6$ and $k = 2$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ is the Stirling number of the second kind. Let $P$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $m$ be the number of elements in $P$. Compute the value of the Bell number $B_{|\te... | 877 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(11)))),
"n": Const(6),
"k": Const(2),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1"
] | 47d042 | comb_count_surjections_v1 | bell_mod | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T19:59:50.936113Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T19:59:50.938459Z"
} | a55045 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 893
},
"timestamp": "2026-02-18T23:47:20.028Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
593358 | alg_qf_psd_orbit_v1_1218484723_6947 | Let $U = |\{ (a_1, b_1) : 1 \le a_1, b_1 \le 30,\ -128a_1^3b_1 -128a_1b_1^3 + 192a_1^2b_1^2 + 32a_1^4 + 32b_1^4 = 8192 \}|$. Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \le a \le b \le c \le 52$ such that $52a^2 - 52ab + 52b^2 - 52ac - 52bc + U \cdot c^2 = 99372$. | 22 | graphs = [
Graph(
let={
"_n": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(52)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(52)), Geq(Var("c"), Const(1)), Leq(Var("c"... | ALG | null | COUNT | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"POLY4_COUNT"
] | 1 | 0.26 | 2026-02-25T08:23:01.050258Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-25T08:23:01.310354Z"
} | 15d49c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 5251
},
"timestamp": "2026-03-30T03:20:15.271Z",
"answer": 38
},
{
"i... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
173728 | alg_poly_orbit_legendre_v1_1218484723_4520 | For an integer $a$ with $0 \leq a \leq 106488$, define $N = a^{41} \bmod 83$, $M = (a^3 - 5a) \bmod 83$, $R = M^{41} \bmod 83$, $S = N + R$, and $T = (M^3 - 5M) \bmod 83$. Find the number of such $a$ for which $T = a$, $S \equiv 0 \pmod{3}$, and $M \neq a$. | 7,698 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-5), Var("a"))), modulus=Const(83)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-5), Ref("p1"))), modulus=Const(83)),
"leg0": ModExp(base=Var("a"), exp=Const(41), mod=Const(83)),
... | NT | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 6 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.013 | 2026-02-25T06:11:11.185698Z | {
"verified": true,
"answer": 7698,
"timestamp": "2026-02-25T06:11:11.198672Z"
} | 753e10 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 27619
},
"timestamp": "2026-03-29T16:05:56.838Z",
"answer": 7698
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"status": "ok"
},
{
"lemma": "V1",
"status": ... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
694ba3 | comb_sum_binomial_row_v1_124444284_1168 | Let $n = 15$. Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. Compute $|S|^n$. | 32,768 | graphs = [
Graph(
let={
"n": Const(15),
"result": Pow(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=12)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T03:43:00.440416Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T03:43:00.441558Z"
} | d55783 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 473
},
"timestamp": "2026-02-10T03:52:08.577Z",
"answer": 32768
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
a00e7a | antilemma_k2_v1_124444284_2668 | Let $n = 58564$. Define
$$
x = \sum_{k=1}^{118} \phi(k) \left\lfloor \frac{\sum_{d \mid 118} \phi(d)}{k} \right\rfloor.
$$
Let $D$ be the number of digits in $|x|$. Compute
$$
\sum_{i=0}^{D-1} \left( \text{the } i\text{-th digit of } |x| \right) \cdot (i+1)^2 + n.
$$ | 58,685 | graphs = [
Graph(
let={
"_n": Const(58564),
"x": Summation(var="k", start=Const(1), end=Const(118), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=118), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
"Q": Sum(Summation(var="i", start=Sub(C... | NT | COMB | COMPUTE | sympy | IDENTITY_SUB_SELF | [
"IDENTITY_SUB_SELF",
"IDENTITY_DIV_SELF",
"K3/K2",
"K2"
] | d9046a | antilemma_k2_v1 | null | 6 | 0 | [
"IDENTITY_DIV_SELF",
"IDENTITY_SUB_SELF",
"K2",
"K3"
] | 4 | 0.003 | 2026-02-08T04:52:12.315456Z | {
"verified": true,
"answer": 58685,
"timestamp": "2026-02-08T04:52:12.318249Z"
} | 75c601 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 1867
},
"timestamp": "2026-02-11T22:18:24.729Z",
"answer": 58685
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "IDENTITY_SUB_SELF",
"status": "ok"
},
{
"lemma": "K14",
"status... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f61e51 | comb_count_derangements_v1_1470522791_550 | Let $n$ be the number of positive integers $j$ such that $1 \leq j \leq 8$ and $j^5 \leq 32768$. Compute the subfactorial of $n$, denoted $!n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(8)), Leq(Pow(Var("j"), Ref("_n")), Const(32768))), domain='positive_integers')),
"result": Subfactorial(arg=Ref(name='n')),
... | COMB | null | COUNT | sympy | C3 | [
"C3"
] | 8a214c | comb_count_derangements_v1 | null | 3 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T13:05:37.854832Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T13:05:37.855938Z"
} | b83fcd | 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": 1013
},
"timestamp": "2026-02-24T17:16:18.720Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
1a55a6 | nt_count_divisible_v1_1742523217_685 | Let $n = 1925$ and $N = 53824$. Determine the largest integer $k$ such that $3^k$ divides $\binom{4813}{1925}$. Find the number of positive integers $m$ such that $1 \le m \le 53824$ and $m$ is divisible by this value of $k$. | 7,689 | graphs = [
Graph(
let={
"_n": Const(1925),
"upper": Const(53824),
"divisor": MaxKDivides(target=Binom(n=Const(4813), k=Ref("_n")), base=Const(3)),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("u... | NT | null | COUNT | sympy | V7 | [
"V7"
] | 0672d4 | nt_count_divisible_v1 | null | 6 | 0 | [
"V7"
] | 1 | 1.667 | 2026-02-08T03:10:23.304923Z | {
"verified": true,
"answer": 7689,
"timestamp": "2026-02-08T03:10:24.971761Z"
} | ef414f | 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": 2378
},
"timestamp": "2026-02-09T21:15:41.092Z",
"answer": 7689
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
616ba3 | modular_count_residue_v1_48377204_1191 | Let $m$ be the number of integers $j$ such that $0 \leq j \leq 2096$ and $\binom{2096}{j}$ is odd. Determine the number of positive integers $n$ such that $1 \leq n \leq 72900$ and $n \equiv 6 \pmod{m}$. | 9,112 | graphs = [
Graph(
let={
"upper": Const(72900),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2096)), Eq(Mod(value=Binom(n=Const(2096), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | modular_count_residue_v1 | null | 5 | 0 | [
"V8"
] | 1 | 2.438 | 2026-02-08T15:55:56.308693Z | {
"verified": true,
"answer": 9112,
"timestamp": "2026-02-08T15:55:58.747151Z"
} | 7af5cf | 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": 941
},
"timestamp": "2026-02-24T19:22:13.546Z",
"answer": 9112
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
6ed983 | nt_euler_phi_compute_v1_1353956133_661 | Let $n=55555$, and let $\varphi(n)$ denote the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
Let $S$ be the set of all ordered pairs $(x_1,x_2)$ of positive integers such that $x_1$ and $x_2$ are odd and $x_1+x_2=14$. Let $m$ be the number of elements in $S$.
Define
$$A=\sum_... | 44,266 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(55555),
"result": EulerPhi(n=Ref("n")),
"Q": Sum(Summation(var="i", start=Summation(var="k", start=Const(0), end=Const(7), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=CountOverSet(set=SolutionsSet(var=Tuple(ele... | COMB | NT | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 2d1cee | nt_euler_phi_compute_v1 | digits_weighted_mod | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"ONE_FACTORIAL_0"
] | 3 | 0.007 | 2026-02-08T11:46:55.948959Z | {
"verified": true,
"answer": 44266,
"timestamp": "2026-02-08T11:46:55.955824Z"
} | 2d429e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 292,
"completion_tokens": 1311
},
"timestamp": "2026-02-14T18:56:34.624Z",
"answer": 44266
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORI... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d5f0d2 | nt_count_intersection_v1_1742523217_955 | Let $N = 50000$, $a = 7$, and $b = 1 + 2 + 3 + 4 + 5$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$, $7$ divides $n$, and $\gcd(n, b) = 1$. | 3,810 | graphs = [
Graph(
let={
"N": Const(50000),
"a": Const(7),
"b": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(diviso... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_intersection_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 2.028 | 2026-02-08T03:22:03.449518Z | {
"verified": true,
"answer": 3810,
"timestamp": "2026-02-08T03:22:05.477985Z"
} | bfee3e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1214
},
"timestamp": "2026-02-10T01:06:55.203Z",
"answer": 3810
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
ace5b0 | nt_count_phi_equals_v1_151522320_6 | Let $N = \sum_{k=1}^{92} \phi(k) \left\lfloor \frac{92}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n$ such that $1 \leq n \leq N$ and $\phi(n) = 102$. | 2 | graphs = [
Graph(
let={
"_n": Const(92),
"upper": Summation(var="k", start=Const(1), end=Const(92), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"k": Const(102),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("... | NT | null | COUNT | sympy | LIN_FORM | [
"K2"
] | 6897ab | nt_count_phi_equals_v1 | null | 7 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 1.195 | 2026-02-08T02:55:08.230596Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T02:55:09.425551Z"
} | fbba57 | 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": 11487
},
"timestamp": "2026-02-23T19:53:49.612Z",
"answer": 2
},
{
"id"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -1.86,
"mid": 0.76,
"hi": 3.03
} | ||
681547 | modular_min_linear_v1_1440796553_1441 | Let $a = 17964$ and $m = 30215$. Let $S$ be the set of all integers $n$ with $1 \leq n \leq 14717$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $b$ be the number of elements in $S$. Let $T$ be the set of all integers $x$ with $1 \leq x \leq m$ such that $17964x \equiv b \pmod{30215}$. Let $... | 15,865 | graphs = [
Graph(
let={
"_n": Const(73838),
"a": Const(17964),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(14717)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modul... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | 73f8b0 | modular_min_linear_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 7.281 | 2026-02-08T14:00:20.916120Z | {
"verified": true,
"answer": 15865,
"timestamp": "2026-02-08T14:00:28.197135Z"
} | ef1d28 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 7338
},
"timestamp": "2026-02-15T23:01:01.082Z",
"answer": 15865
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
81a347 | alg_poly3_count_v1_1218484723_4069 | Let $Q$ be the number of ordered triples $(a, b, c)$ of positive integers with $1 \le a, b, c \le 40$ such that
$$15660abc + 21750c^{3} + \min\{x + y : (x, y),\ x > 0,\ y > 0,\ xy = 1703025\} \cdot b^{2}c - 1566ab^{2} + 174b^{3} + 23490a^{2}c \\
\quad + 3654b \cdot c^{\left|\{ p : p > 0,\ \text{there exists an integer ... | 10 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(40),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Geq(Var... | NT | null | COUNT | sympy | K2 | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | alg_poly3_count_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"K2"
] | 3 | 10.133 | 2026-02-25T05:43:24.478242Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-25T05:43:34.611067Z"
} | 31c281 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 324,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T13:39:31.805Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status":... | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
2d9614 | comb_count_partitions_v1_124444284_9095 | Let $p_1, p_2, \dots, p_m$ be the list of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 72$, $\gcd(p, q) = 1$, and $p < q$, listed in increasing order. Let $N$ be the number of prime numbers $n$ such that $m \le n \le 181$. Let $P$ be the number of integer partitions of $N$. Find th... | 36,246 | graphs = [
Graph(
let={
"_m": Const(181),
"_n": Const(82876),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(l... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COUNT_PRIMES"
] | c35fa2 | comb_count_partitions_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"COUNT_PRIMES"
] | 2 | 0.002 | 2026-02-08T12:12:34.301763Z | {
"verified": true,
"answer": 36246,
"timestamp": "2026-02-08T12:12:34.303655Z"
} | c59e68 | 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": 3420
},
"timestamp": "2026-02-14T23:24:43.338Z",
"answer": 36246
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b11e8c | nt_max_prime_below_v1_1742523217_2811 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m = |P|$. Determine the largest prime number $n$ such that $m \leq n \leq 55225$. | 55,219 | graphs = [
Graph(
let={
"upper": Const(55225),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.596 | 2026-02-08T05:24:01.360630Z | {
"verified": true,
"answer": 55219,
"timestamp": "2026-02-08T05:24:04.957127Z"
} | b9f00c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 2146
},
"timestamp": "2026-02-12T08:22:59.183Z",
"answer": 55219
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
55f611 | comb_count_derangements_v1_2051736721_4290 | Let $n$ be the number of positive integers $j$ such that $1 \le j \le 7$ and $j^4 \le 2401$. Compute the number of derangements of a set of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(4)), Const(2401))), domain='positive_integers')),
"result": Subfactorial(arg=Ref(name='n')),
... | COMB | null | COUNT | sympy | C3 | [
"C3"
] | 8a214c | comb_count_derangements_v1 | null | 3 | 0 | [
"C3"
] | 1 | 0.002 | 2026-02-08T17:52:16.118376Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T17:52:16.120139Z"
} | 74d77a | 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": 802
},
"timestamp": "2026-02-18T10:00:41.175Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
caffc3 | antilemma_cartesian_v1_655260480_3854 | Compute the number of ordered pairs $(x, y)$ where $x$ is an integer from 1 to 37, inclusive, and $y$ is an integer from 1 to 41, inclusive. | 1,517 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(37)), right=IntegerRange(start=Const(1), end=Const(41)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T17:34:42.402250Z | {
"verified": true,
"answer": 1517,
"timestamp": "2026-02-08T17:34:42.403260Z"
} | 4f23e9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 860
},
"timestamp": "2026-02-24T22:49:20.270Z",
"answer": 1517
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
244cda | lin_form_endings_v1_168721529_529 | Let $a = 63$ and $b = 45$. Let $k = 2$, and let $\ell$ be the least common multiple of $a$ and $b$. Define $s = k\ell + a + b$. Let $t = 17818 \cdot s$. Compute the remainder when $t$ is divided by $67527$. | 49,446 | graphs = [
Graph(
let={
"a_coeff": Const(63),
"b_coeff": Const(45),
"k_val": Const(2),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:05:30.808390Z | {
"verified": true,
"answer": 49446,
"timestamp": "2026-02-08T13:05:30.809539Z"
} | 60be38 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 656
},
"timestamp": "2026-02-09T05:58:22.729Z",
"answer": 49446
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -2,
"mid": 1.85,
"hi": 5.2
} | ||
6d7ac8 | nt_count_with_divisor_count_v1_865884756_1507 | Let $m=5$. Let $n$ be the number of integers $t$ for which there exist integers $a$ and $b$ such that $1\le a\le 20$, $1\le b\le 27$, $21\le t\le 462$, and
$$t=15a+6b.$$
Let $N$ be the set of all integers $n$ with $2\le n\le 3$ that are prime, and let
$$D=\sum_{k=1}^{\sum_{n\in N} n} \varphi(k)\left\lfloor\frac{m}{k}\... | 5,162 | graphs = [
Graph(
let={
"_m": Const(5),
"_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=20)), Geq(left=Var(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B1",
"SUM_PRIMES/K2"
] | 706d36 | nt_count_with_divisor_count_v1 | negation_mod | 7 | 0 | [
"B1",
"K2",
"LIN_FORM",
"SUM_PRIMES"
] | 4 | 3.922 | 2026-02-08T16:05:01.230144Z | {
"verified": true,
"answer": 5162,
"timestamp": "2026-02-08T16:05:05.151755Z"
} | e9e36d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 4019
},
"timestamp": "2026-02-16T21:38:28.814Z",
"answer": 5162
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
71f4da | geo_count_lattice_triangle_v1_124444284_7857 | Consider the triangle with vertices at $(144, 81)$, $(169, 200)$, and $(0, 0)$. Let $A$ be twice the area of this triangle. Let $B$ be the number of lattice points on the boundary of the triangle, computed as the sum of the greatest common divisors of the absolute differences in coordinates along each edge. Compute $\f... | 7,551 | graphs = [
Graph(
let={
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=200)), Mul(Const(value=169), Sub(left=Const(value=0), right=Const(value=81))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(value=81))), GCD(a=Abs(arg=Su... | ALG | NT | COUNT | sympy | V5 | [
"V5"
] | 79df37 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"V5"
] | 1 | 0.005 | 2026-02-08T09:23:51.749879Z | {
"verified": true,
"answer": 7551,
"timestamp": "2026-02-08T09:23:51.754401Z"
} | 484db4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1009
},
"timestamp": "2026-02-14T03:43:08.413Z",
"answer": 7551
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5ef203_n | geo_count_lattice_triangle_v1_1218484723_2768 | A robot computes three values from sensor inputs: it multiplies 128 by 111 and adds 77 times -89, taking the absolute value to get $M$. Then it computes $R$ as the sum of GCDs from differences in signal strengths: $\gcd(128,89)$, $\gcd(|128-77|, |111-89|)$, and $\gcd(77,111)$. It then calculates $S = (M + 2 - R)/2$. Wh... | 48,307 | GEOM | null | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 3 | null | null | null | 0.002 | 2026-02-25T04:28:07.930312Z | null | 7e656e | 5ef203 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 815
},
"timestamp": "2026-03-30T19:00:25.278Z",
"answer": 48307
},
{
"i... | 1 | [] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |||
5ba743 | antilemma_sum_equals_v1_1918700295_2383 | Let $n = 32$. Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 30$, $1 \leq j \leq 30$, and $i + j = n$. Let $x = |S|$. Compute the remainder when $81413 \cdot x$ is divided by $61614$. | 19,645 | graphs = [
Graph(
let={
"_n": Const(32),
"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(30)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.008 | 2026-02-08T07:51:21.820211Z | {
"verified": true,
"answer": 19645,
"timestamp": "2026-02-08T07:51:21.828321Z"
} | 514c02 | 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": 901
},
"timestamp": "2026-02-24T08:32:23.748Z",
"answer": 19645
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
9b6629 | nt_count_coprime_and_v1_48377204_104 | Let $k_1 = 5$ and let $k_2$ be the largest prime number between 2 and 8, inclusive. Determine the number of positive integers $n_1$ such that $1 \leq n_1 \leq 39060$, $\gcd(n_1, 5) = 1$, and $\gcd(n_1, k_2) = 1$. | 26,784 | graphs = [
Graph(
let={
"upper": Const(39060),
"k1": Const(5),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 7.812 | 2026-02-08T15:14:08.383331Z | {
"verified": true,
"answer": 26784,
"timestamp": "2026-02-08T15:14:16.194997Z"
} | c3ecb9 | 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": 904
},
"timestamp": "2026-02-16T01:47:41.179Z",
"answer": 26784
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
660c06 | nt_count_digit_sum_v1_784195855_8574 | Let $m = 22$. Consider the set of all positive integers $n$ such that $1 \leq n \leq m$ and $n \equiv 0 \pmod{22}$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y$ equals the sum of the elements in this set. Define $n_0$ to be the maximum value of $xy$ over all such pairs $(x, y)... | 6,000 | graphs = [
Graph(
let={
"_m": Const(22),
"_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")), SumOverSet(set=SolutionsSet(var=Var("n"), condit... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/B1/B3"
] | cf3329 | nt_count_digit_sum_v1 | null | 7 | 0 | [
"B1",
"B3",
"SUM_DIVISIBLE"
] | 3 | 3.877 | 2026-02-08T16:11:47.472577Z | {
"verified": true,
"answer": 6000,
"timestamp": "2026-02-08T16:11:51.349562Z"
} | 503221 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 1520
},
"timestamp": "2026-02-16T22:24:24.552Z",
"answer": 6000
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3cd94a | nt_lcm_compute_v1_865884756_526 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 665856$. Let $a$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $b = 1555$. Define $L = \mathrm{lcm}(a, b)$. Let $C$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq ... | 68,519 | 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(665856)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(1555)... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | bd6782 | nt_lcm_compute_v1 | negation_mod | 4 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.004 | 2026-02-08T15:29:17.471460Z | {
"verified": true,
"answer": 68519,
"timestamp": "2026-02-08T15:29:17.475818Z"
} | 94fedc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2111
},
"timestamp": "2026-02-16T06:25:02.169Z",
"answer": 68519
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2cda86 | diophantine_sum_product_min_v1_1125832087_69 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 278784$. Let $T$ be the set of all values $x + y$ for $(x, y) \in S$, and let $m$ be the minimum value in $T$. Let $U$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq m$ and $\binom{1056}{j}$ is odd. Let $n$ be the... | 44,121 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(1056),
"S": Const(5),
"P": Const(4),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), CountOverSet(set=SolutionsSet(var=Var("j"), condit... | ALG | COMB | EXTREMUM | sympy | B3 | [
"B3/V8"
] | 4fad5b | diophantine_sum_product_min_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.005 | 2026-02-08T02:51:10.499618Z | {
"verified": true,
"answer": 44121,
"timestamp": "2026-02-08T02:51:10.504907Z"
} | c7c238 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 2321
},
"timestamp": "2026-02-10T11:41:39.424Z",
"answer": 44121
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
66f046 | diophantine_fbi2_count_v1_168721529_1043 | Let $n = 64$. Define $w = \sum_{d \mid n} \mu(d)$, where $\mu$ denotes the M\"obius function. Let $k = 360$. Consider the set of all positive integers $d$ such that $d \geq 6$, $d \leq v$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 203$, where $v$ is the largest integer such that $11^v$ divides $161051^{41}$. Let $r... | 19,663 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(64),
"w": SumOverDivisors(n=Ref(name='n'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"k": Const(360),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), ... | NT | null | COUNT | sympy | LIOUVILLE_MINUS_ONE | [
"LIOUVILLE_MINUS_ONE",
"MOBIUS_SUM",
"K14"
] | 126ed1 | diophantine_fbi2_count_v1 | null | 5 | 2 | [
"K14",
"LIOUVILLE_MINUS_ONE",
"MOBIUS_SUM"
] | 3 | 0.032 | 2026-02-08T13:26:00.788381Z | {
"verified": true,
"answer": 19663,
"timestamp": "2026-02-08T13:26:00.820776Z"
} | f81da2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 2188
},
"timestamp": "2026-02-09T12:55:22.949Z",
"answer": 19663
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
140165 | geo_count_lattice_rect_v1_1520064083_6090 | Let $a = 99$ and $b = 326$. Define $R$ as the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $r$ be the remainder when $|R|$ is divided by $11$. Compute the $r$-th Bell number. | 4,140 | graphs = [
Graph(
let={
"a": Const(99),
"b": Const(326),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 5 | 0 | null | null | 0.007 | 2026-02-08T07:51:05.994030Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T07:51:06.000808Z"
} | 4987aa | 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": 645
},
"timestamp": "2026-02-24T08:32:17.512Z",
"answer": 4140
},
{
"id... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
6a4569 | nt_sum_gcd_range_mod_v1_865884756_6623 | Let $N$ be the number of positive integers $n \leq 41004$ such that $9$ divides $n$ and $\gcd(n, 35) = 1$. Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 8100$. Define $S = \sum_{n_1=1}^{N} \gcd(n_1, k)$. Find the remainder when $S$ is divided by $10601$. | 4,973 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(41004)), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(35)), Const(1))))),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(va... | NT | null | COMPUTE | sympy | C5 | [
"C5",
"B3"
] | 2a47df | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B3",
"C5"
] | 2 | 0.146 | 2026-02-08T19:19:58.047453Z | {
"verified": true,
"answer": 4973,
"timestamp": "2026-02-08T19:19:58.193768Z"
} | 4b210b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 3021
},
"timestamp": "2026-02-18T21:59:25.859Z",
"answer": 4973
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab109f | antilemma_k2_v1_1520064083_4153 | Let $c = 2$. Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 78x + 1496 = 0$. Let $m = 12$. Define $x = \sum_{k=1}^{m} k$, and then define $\mathcal{S} = \sum_{k=1}^{x} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $\mathcal{S}$. | 3,081 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(12),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_c")), Mul(Const(-78), Var("x")), Const(1496)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Summation(var=... | NT | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2",
"VIETA_SUM/K2",
"K2"
] | bbc4ec | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"SUM_ARITHMETIC",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T06:07:17.034423Z | {
"verified": true,
"answer": 3081,
"timestamp": "2026-02-08T06:07:17.036556Z"
} | c8f6e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 837
},
"timestamp": "2026-02-12T20:07:51.702Z",
"answer": 3081
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
be07b3 | nt_sum_over_divisible_v1_1874849503_481 | Let $ n = 156 $. Define $ S $ as the set of all ordered pairs of positive integers $ (x, y) $ such that $ x + y = n $. Let $ u $ be the maximum value of $ xy $ over all such pairs. Find the sum of all positive integers $ k $ such that $ k \leq u $ and $ k $ is divisible by 200. | 93,000 | graphs = [
Graph(
let={
"_n": Const(156),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y"))))... | NT | null | SUM | sympy | V8 | [
"B1"
] | 5b950e | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"B1",
"V8"
] | 2 | 2.552 | 2026-02-08T13:06:10.692279Z | {
"verified": true,
"answer": 93000,
"timestamp": "2026-02-08T13:06:13.243918Z"
} | 7f1b35 | 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": 806
},
"timestamp": "2026-02-09T17:32:19.222Z",
"answer": 93000
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
ab3229 | nt_count_coprime_v1_458359167_4328 | Let $k = \sum_{i=1}^{5} \varphi(i) \left\lfloor \frac{5}{i} \right\rfloor$, where $\varphi(i)$ denotes Euler's totient function. Let $N = 26896$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$ and $\gcd(n, k) = 1$. | 14,345 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(26896),
"k": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_coprime_v1 | null | 4 | 0 | [
"K2"
] | 1 | 2.069 | 2026-02-08T11:41:53.625012Z | {
"verified": true,
"answer": 14345,
"timestamp": "2026-02-08T11:41:55.693982Z"
} | 7e2590 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 640
},
"timestamp": "2026-02-16T03:09:27.978Z",
"answer": 17930
},
{
"id": 11... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
f0604e | nt_sum_divisors_compute_v1_1742523217_426 | Let $ n_1 $ be the sum of all positive integers at most 22 that are divisible by 22. Let $ t = \Omega(\phi(2)) $, where $ \phi $ is Euler's totient function and $ \Omega(n) $ counts the number of prime factors of $ n $ with multiplicity. Let $ w = \sum_{d \mid n_1} \mu(d) $, where $ \mu $ is the Möbius function. Define... | 36,673 | graphs = [
Graph(
let={
"_n": Const(22),
"n2": EulerPhi(n=Const(2)),
"t": BigOmega(n=Ref(name='n2')),
"n1": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(22)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Co... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/MOBIUS_SUM",
"BIG_OMEGA_ZERO",
"ONE_PHI_2"
] | 424577 | nt_sum_divisors_compute_v1 | null | 6 | 2 | [
"BIG_OMEGA_ZERO",
"MOBIUS_SUM",
"ONE_PHI_2",
"SUM_DIVISIBLE"
] | 4 | 0.002 | 2026-02-08T03:01:53.125640Z | {
"verified": true,
"answer": 36673,
"timestamp": "2026-02-08T03:01:53.128137Z"
} | e0a070 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2324
},
"timestamp": "2026-02-09T17:49:09.116Z",
"answer": 36673
},
{
"... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"statu... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} |
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