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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
d88960 | algebra_poly_eval_v1_1419126231_787 | Let $F_n$ denote the $n$-th Fibonacci number. Let $S = \{6a + 15b \mid 1 \leq a \leq 11,\ 1 \leq b \leq 13,\ 21 \leq 6a + 15b \leq 261\}$. Let $t$ be the number of positive integers $n$ with $1 \leq n \leq |S|$ such that $13 \mid F_n$. Compute $39204 - (4t^2 - 5t - 2)$. | 38,777 | graphs = [
Graph(
let={
"_m": Const(39204),
"_n": Const(13),
"t": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t1"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(nam... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_FIB_DIVISIBLE"
] | 95eec8 | algebra_poly_eval_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-25T10:16:38.377234Z | {
"verified": true,
"answer": 38777,
"timestamp": "2026-02-25T10:16:38.380411Z"
} | 73c8a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 5367
},
"timestamp": "2026-03-30T09:59:33.967Z",
"answer": 38777
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
7b5203 | nt_count_phi_equals_v1_124444284_9426 | Let $n = 55$. Define $u$ to be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 102$. Define $k$ as the sum $\sum_{j=1}^{55} \phi(j) \left\lfloor \frac{55}{j} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $S$ be the set of all positive integers $m$ with $1 \leq m... | 1 | graphs = [
Graph(
let={
"_n": Const(55),
"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")), Const(102)))), expr=Mul(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | B1 | [
"B1",
"K2"
] | 7fde97 | nt_count_phi_equals_v1 | null | 6 | 0 | [
"B1",
"K2"
] | 2 | 0.22 | 2026-02-08T12:26:54.838883Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T12:26:55.059324Z"
} | 6b8684 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 3708
},
"timestamp": "2026-02-15T01:42:49.378Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ"... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
60bdc9 | comb_count_partitions_v1_153355830_1712 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 39$, $1 \le i \le 38$, and $1 \le j \le 39$. Compute the number of integer partitions of $n$. (An integer partition of a positive integer $m$ is a way of writing $m$ as a sum of positive integers, disregarding order.) | 26,015 | graphs = [
Graph(
let={
"_n": Const(39),
"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(38)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_partitions_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.008 | 2026-02-08T06:35:14.399222Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T06:35:14.407122Z"
} | 35dc7f | 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": 1714
},
"timestamp": "2026-02-24T06:31:47.527Z",
"answer": 26015
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
1ce707 | comb_count_partitions_v1_124444284_4039 | Let $n$ be the number of positive integers at most $291$ that are divisible by $3$ and relatively prime to $10$. Determine the value of the number of integer partitions of $n$. | 31,185 | graphs = [
Graph(
let={
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(291)), Divides(divisor=Ref("_n"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"result": Partition(arg... | NT | COMB | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | comb_count_partitions_v1 | null | 3 | 0 | [
"C5"
] | 1 | 0.001 | 2026-02-08T05:43:42.796272Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T05:43:42.797308Z"
} | 05c36a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 1727
},
"timestamp": "2026-02-12T13:10:18.082Z",
"answer": 31185
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
898697_n | alg_sym_quad_system_v1_1218484723_2742 | An engineer is testing a model for interaction energy between two particles of types A and B. For integers $a$ and $b$ between $1$ and $8$, the energy is given by
\[
E(a,b) = -20ab + 4a^{2} + 29b^{2}.
\]
Let $M$ be the smallest energy value $E(a,b)$ that occurs for such integer choices.
The engineer also designs a rec... | 7,305 | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN/B3",
"B3/B3"
] | cf9e4b | alg_sym_quad_system_v1 | null | 7 | null | [
"B3",
"QF_PSD_MIN"
] | 2 | 0.025 | 2026-02-25T04:27:32.148270Z | null | b6f595 | 898697 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 461,
"completion_tokens": 21166
},
"timestamp": "2026-03-30T18:59:49.506Z",
"answer": 7305
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
e709af | modular_sum_quadratic_residues_v1_2051736721_1602 | Let $p = 173$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Let $S$ be the set of all values of $x + y$ as $(x, y)$ ranges over these pairs. Let $m$ be the minimum value in $S$. Compute the value of $$\frac{p(p - 1)}{m} \mod 78532.$$
Find the remainder when this value is mult... | 38,763 | graphs = [
Graph(
let={
"p": Const(173),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), 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")), ... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:07:15.618148Z | {
"verified": true,
"answer": 38763,
"timestamp": "2026-02-08T16:07:15.620583Z"
} | d81372 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1318
},
"timestamp": "2026-02-16T21:15:31.751Z",
"answer": 38763
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
79d2de | nt_sum_divisors_mod_v1_971394319_64 | Let $n$ be the number of integers $t$ such that $18 \le t \le 741$ and there exist positive integers $a$ and $b$ with $1 \le a \le 235$, $1 \le b \le 52$, and $t = 2a + 5b + 11$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11821$. | 2,418 | 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=235)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.158 | 2026-02-08T12:49:04.133716Z | {
"verified": true,
"answer": 2418,
"timestamp": "2026-02-08T12:49:04.292125Z"
} | e514c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 3493
},
"timestamp": "2026-02-15T05:40:32.910Z",
"answer": 2418
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
016e6f | antilemma_k3_v1_717093673_1005 | Let $n = 9157$. Compute the remainder when $44121$ times the sum of $\phi(d)$ over all positive divisors $d$ of $n$ is divided by $99947$. | 30,223 | graphs = [
Graph(
let={
"_n": Const(9157),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(99947)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:47:25.633802Z | {
"verified": true,
"answer": 30223,
"timestamp": "2026-02-08T15:47:25.634439Z"
} | 4d6f8c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 1851
},
"timestamp": "2026-02-16T14:00:15.294Z",
"answer": 30223
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0d3882 | diophantine_sum_product_min_v1_1742523217_471 | Let $\phi(n)$ denote Euler's totient function. Let $n_{\text{max}}$ be the largest prime number less than or equal to $19$. Let $P$ be the number of ordered pairs $(i,j)$ with $1 \le i \le 3$ and $1 \le j \le 23$ such that $\gcd(i,j) = \phi(2)$. Determine the value of $x$, where $x$ is the smallest positive integer sat... | 3 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(19)), IsPrime(Var("n"))))),
"S": Const(20),
"P": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=V... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COUNT_COPRIME_GRID",
"ONE_PHI_1",
"ONE_PHI_2"
] | bc99e9 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID",
"MAX_PRIME_BELOW",
"ONE_PHI_1",
"ONE_PHI_2"
] | 4 | 0.006 | 2026-02-08T03:04:15.711674Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T03:04:15.718108Z"
} | e69ef4 | 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": 1169
},
"timestamp": "2026-02-09T18:23:25.377Z",
"answer": 3
},
{
"id":... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
bb78fd | nt_count_coprime_v1_1125832087_2024 | Let $k = 46$. Compute the number of positive integers $n \leq 34596$ such that $\gcd(n, k) = 1$. | 16,546 | graphs = [
Graph(
let={
"upper": Const(34596),
"k": Const(46),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
},
goal=Ref("result"),
... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/B1"
] | 844731 | nt_count_coprime_v1 | null | 3 | 0 | [
"B1",
"SUM_ARITHMETIC"
] | 2 | 4.583 | 2026-02-08T04:17:23.009364Z | {
"verified": true,
"answer": 16546,
"timestamp": "2026-02-08T04:17:27.592066Z"
} | 9bf69f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1065
},
"timestamp": "2026-02-10T16:05:18.251Z",
"answer": 16546
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
3c7c63 | alg_poly3_count_v1_1419126231_1940 | Let $V = \left|\left\{ v \mid 5 \le v \le 16385,\ \exists\, a,b \in \mathbb{Z}^+\ \text{with}\ 1 \le a,b \le 26\ \text{such that}\ 5a^2 + 25b^2 - 20ab = v \right\}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le V$ and $1 \le b \le 416$ such that $27a^3 = 80621568$. | 416 | graphs = [
Graph(
let={
"_n": Const(27),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(5)), Leq(Var("v"), Const(16385... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_poly3_count_v1 | null | 6 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 2.125 | 2026-02-25T11:29:17.347514Z | {
"verified": true,
"answer": 416,
"timestamp": "2026-02-25T11:29:19.472440Z"
} | 6123b2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T14:40:22.228Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
f5000b_n | comb_count_surjections_v1_601307018_1078 | A puzzle designer creates modules that group $n$ unique tiles into exactly 5 non-empty, unlabeled clusters. The number $n$ is computed by summing $\varphi(d) \cdot \lfloor 3/d \rfloor$ for $d = 1$ to $3$. For each such grouping, there are $5!$ ways to assign cluster labels. How many labeled clusterings are possible? | 1,800 | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"K2"
] | 6897ab | comb_count_surjections_v1 | null | 3 | null | [
"COUNT_SUM_EQUALS",
"K2"
] | 2 | 0.069 | 2026-03-10T01:39:40.646603Z | null | bae925 | f5000b | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 910
},
"timestamp": "2026-03-29T14:50:48.862Z",
"answer": 1800
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
cd9ef4 | nt_count_divisible_v1_1742523217_371 | Let $T$ be the set of all integers $t$ such that $10 \leq t \leq 60$ and $t = 6a + 4b$ for some integers $a$ and $b$ with $1 \leq a \leq 8$ and $1 \leq b \leq 3$. Let $d$ be the number of elements in $T$. Find the number of positive integers $n$ with $1 \leq n \leq 60025$ such that $n$ is divisible by $d$. Compute this... | 2,501 | graphs = [
Graph(
let={
"upper": Const(60025),
"divisor": 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=8)), Ge... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.878 | 2026-02-08T03:00:05.940745Z | {
"verified": true,
"answer": 2501,
"timestamp": "2026-02-08T03:00:07.818624Z"
} | f675ed | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1336
},
"timestamp": "2026-02-09T02:19:19.957Z",
"answer": 2501
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
84fa1b | geo_visible_lattice_v1_717093673_230 | Let $n = 77$. Define a visible lattice point as an ordered pair of positive integers $(x, y)$ such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the number of visible lattice points.
Find the value of $Q$. | 3,663 | graphs = [
Graph(
let={
"n": Const(77),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.222 | 2026-02-08T15:15:20.621803Z | {
"verified": true,
"answer": 3663,
"timestamp": "2026-02-08T15:15:20.844027Z"
} | b1b221 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T20:30:55.296Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
7ecc45 | comb_bell_compute_v1_1918700295_3930 | Let $n = 9$. Define $s$ to be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 3481$. Let $P$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = s$. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set o... | 57,457 | 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(3481)))), expr=Sum(Var("x"), Var("y")))),
"n": Const(9),
... | COMB | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 6cdf3d | comb_bell_compute_v1 | negation_mod | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T09:03:24.792001Z | {
"verified": true,
"answer": 57457,
"timestamp": "2026-02-08T09:03:24.795546Z"
} | 43ec97 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1668
},
"timestamp": "2026-02-24T10:20:32.581Z",
"answer": 57457
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQU... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
d8f284 | antilemma_k2_v1_655260480_6253 | Let $n = 273$. Compute the value of
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{273}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 37,401 | graphs = [
Graph(
let={
"_n": Const(273),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(273), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 3 | 0 | [
"K13",
"K2"
] | 2 | 0.003 | 2026-02-08T18:56:08.901602Z | {
"verified": true,
"answer": 37401,
"timestamp": "2026-02-08T18:56:08.904141Z"
} | 4b960e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 950
},
"timestamp": "2026-02-18T20:32:39.723Z",
"answer": 37401
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
21649b | modular_modexp_compute_v1_124444284_738 | Let $a = 11$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 9604$. Define $e$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $m = 47524$. Compute the remainder when $a^e$ is divided by $m$. | 21,769 | graphs = [
Graph(
let={
"a": Const(11),
"e": 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(9604)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.007 | 2026-02-08T03:29:18.525859Z | {
"verified": true,
"answer": 21769,
"timestamp": "2026-02-08T03:29:18.532394Z"
} | 2c6ac6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 4588
},
"timestamp": "2026-02-09T21:18:20.142Z",
"answer": 21769
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
d128cb | lin_form_endings_v1_124444284_1174 | Let $a = 36$ and $b = 48$. Define $s$ to be the greatest common divisor of $a$ and $b$. Let $k = 171$. Compute the value of $\left\lfloor \frac{k}{\gcd(k, s)} \right\rfloor$, then multiply this value by 19374. Find the remainder when the result is divided by 89406. Determine the value of this remainder. | 31,446 | graphs = [
Graph(
let={
"a_coeff": Const(36),
"b_coeff": Const(48),
"k_val": Const(171),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:43:17.990259Z | {
"verified": true,
"answer": 31446,
"timestamp": "2026-02-08T03:43:17.990905Z"
} | 171a02 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 589
},
"timestamp": "2026-02-10T03:57:01.692Z",
"answer": 31446
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
0da531 | v1_endings_v1_1742523217_87 | Let $n = 76477$. Define $v_3(n!)$ to be the largest integer $k$ such that $3^k$ divides $n!$, and define $v_7(n!)$ analogously as the largest integer $k$ such that $7^k$ divides $n!$. Let $a$ be the remainder when $v_3(n!)$ is divided by $1000$, and let $b$ be the remainder when $v_7(n!)$ is divided by $100$. Compute $... | 23,242 | graphs = [
Graph(
let={
"n_val": Const(76477),
"p1_val": Const(3),
"p2_val": Const(7),
"n_fact": Factorial(Ref("n_val")),
"vp1": MaxKDivides(target=Ref("n_fact"), base=Ref("p1_val")),
"vp2": MaxKDivides(target=Ref("n_fact"), base=Ref("p... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 5 | null | [
"V1"
] | 1 | 0 | 2026-02-08T02:52:24.054528Z | {
"verified": true,
"answer": 23242,
"timestamp": "2026-02-08T02:52:24.054953Z"
} | 162eb2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1112
},
"timestamp": "2026-02-09T13:41:25.163Z",
"answer": 23341
},
{
... | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "... | {
"lo": 4.13,
"mid": 6.95,
"hi": 10
} | ||
1bca84 | antilemma_k2_v1_971394319_1291 | Compute $$\sum_{k=1}^{338} \phi(k) \left\lfloor \frac{\sum_{d \mid 338} \phi(d)}{k} \right\rfloor,$$ where $\phi$ denotes Euler's totient function. | 57,291 | graphs = [
Graph(
let={
"_n": Const(338),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=338), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.008 | 2026-02-08T13:35:44.070900Z | {
"verified": true,
"answer": 57291,
"timestamp": "2026-02-08T13:35:44.078860Z"
} | 24b5fe | 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": 745
},
"timestamp": "2026-02-15T18:45:41.577Z",
"answer": 57291
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ad7e64 | modular_inverse_v1_1978505735_893 | Let $m = 77$. Let $K$ be the set of all positive integers $k$ such that $1 \leq k \leq 222299$ and $m$ divides $k$. Let $t$ be the number of elements in $K$. Let $U$ be the set of all prime numbers $n$ such that $2 \leq n \leq t$. Let $u$ be the number of elements in $U$. Find the smallest positive integer $x$ such tha... | 33 | graphs = [
Graph(
let={
"_m": Const(77),
"_n": Const(2),
"a": Const(127),
"m": Const(419),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("k"), condit... | NT | null | EXTREMUM | sympy | C2 | [
"C2/COUNT_PRIMES"
] | 7e2e72 | modular_inverse_v1 | null | 7 | 0 | [
"C2",
"COUNT_PRIMES"
] | 2 | 0.042 | 2026-02-08T15:40:07.655963Z | {
"verified": true,
"answer": 33,
"timestamp": "2026-02-08T15:40:07.697501Z"
} | 022d06 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1925
},
"timestamp": "2026-02-16T11:33:42.685Z",
"answer": 33
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ce9b2e | nt_sum_over_divisible_v1_1439011603_451 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 82621$ and $n$ is divisible by $193$. Let $\text{result}$ be the sum of all elements of $A$. Let $c$ be the sum of $\phi(d)$ over all positive divisors $d$ of $3721$, where $\phi$ is Euler's totient function. Compute the remainder when $c - \text{... | 24,583 | graphs = [
Graph(
let={
"_n": Const(51270),
"upper": Const(82621),
"divisor": Const(193),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Co... | NT | null | SUM | sympy | K3 | [
"K3"
] | 91dc2d | nt_sum_over_divisible_v1 | negation_mod | 3 | 0 | [
"K3"
] | 1 | 5.197 | 2026-02-08T15:30:11.451814Z | {
"verified": true,
"answer": 24583,
"timestamp": "2026-02-08T15:30:16.648999Z"
} | 8bfc43 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1367
},
"timestamp": "2026-02-16T07:46:44.943Z",
"answer": 24583
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
45e4bb | antilemma_sum_equals_v1_124444284_577 | Let $n$ be the number of integers $t$ such that there exist positive integers $a$ and $b$ satisfying $1 \le a \le 8$, $1 \le b \le 9$, $20 \le t \le 174$, and $t = 6a + 14b$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 64$ and $1 \le j \le 64$ such that $i + j = n$. Let $Q = 50176 + \s... | 50,203 | 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=8)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 979f4d | antilemma_sum_equals_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.009 | 2026-02-08T03:22:35.160908Z | {
"verified": true,
"answer": 50203,
"timestamp": "2026-02-08T03:22:35.169458Z"
} | 5b65db | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 353,
"completion_tokens": 3384
},
"timestamp": "2026-02-09T19:22:12.039Z",
"answer": 50203
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lem... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
188ffa | nt_count_digit_sum_v1_2051736721_5862 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 144$. Let $P$ be the maximum value of $xy$ over all such pairs. Let $T$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = P$. Let $Q$ be the minimum value of $x_1 + y_1$ over all such pairs. Let... | 11,600 | graphs = [
Graph(
let={
"_n": Const(144),
"upper": Const(210681),
"target_sum": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Min... | NT | null | COUNT | sympy | B3 | [
"B3/B3",
"B1/B3"
] | db7887 | nt_count_digit_sum_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 7.173 | 2026-02-08T18:50:18.895316Z | {
"verified": true,
"answer": 11600,
"timestamp": "2026-02-08T18:50:26.068308Z"
} | 4d286b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 7450
},
"timestamp": "2026-02-18T19:57:24.965Z",
"answer": 11600
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
220dca | comb_count_partitions_v1_1820931509_712 | Let $S$ be the set of all integers $t$ such that $27 \leq t \leq 159$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 9$, and $t = 21a + 6b$. Let $n$ be the number of elements in $S$. Let $p(n)$ denote the number of integer partitions of $n$. Find the remainder when $65075 \cdot p(n)$ is div... | 29,347 | graphs = [
Graph(
let={
"_n": Const(94208),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:50:07.741169Z | {
"verified": true,
"answer": 29347,
"timestamp": "2026-02-08T11:50:07.743667Z"
} | 375a6c | 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": 11756
},
"timestamp": "2026-02-24T14:50:01.524Z",
"answer": 29347
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
cad0de | modular_sum_quadratic_residues_v1_2051736721_238 | Let $m = 74529$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. For each such pair, compute $x + y$, and let $s_{\min}$ be the smallest such sum. Let $p$ be the largest prime number $n$ such that $2 \le n \le s_{\min}$. Compute $\frac{p(p-1)}{4}$. | 73,035 | graphs = [
Graph(
let={
"_m": Const(74529),
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(a... | NT | null | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T15:18:33.537953Z | {
"verified": true,
"answer": 73035,
"timestamp": "2026-02-08T15:18:33.541209Z"
} | c6db30 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1220
},
"timestamp": "2026-02-16T04:14:03.069Z",
"answer": 73035
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
01fbad | sequence_lucas_compute_v1_717093673_3374 | Let $m = 4356$. Determine the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$; denote this number by $n$. Find the number of positive integers $k$ such that $1 \leq k \leq n$ and $k$ is divisible by 121. Compute the Lucas number indexed by this count. | 5,778 | graphs = [
Graph(
let={
"_m": Const(4356),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | ALG | NT | COMPUTE | sympy | COMB1 | [
"COMB1/C2"
] | dc963c | sequence_lucas_compute_v1 | null | 4 | 0 | [
"C2",
"COMB1"
] | 2 | 0.003 | 2026-02-08T17:30:43.894313Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T17:30:43.896816Z"
} | a9aaf2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1382
},
"timestamp": "2026-02-18T03:55:46.580Z",
"answer": 5778
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
41861b | modular_sum_quadratic_residues_v1_809748730_576 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 360$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Let $p$ be the number of integers $t$ with $27 \leq t \leq 122... | 37,733 | graphs = [
Graph(
let={
"_m": 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=360)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B1/LIN_FORM"
] | 07ef38 | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"B1",
"COPRIME_PAIRS",
"LIN_FORM"
] | 3 | 0.004 | 2026-02-08T11:36:10.347875Z | {
"verified": true,
"answer": 37733,
"timestamp": "2026-02-08T11:36:10.351435Z"
} | f2ca84 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 3899
},
"timestamp": "2026-02-14T17:01:42.119Z",
"answer": 37733
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a920d5 | sequence_lucas_compute_v1_601307018_3822 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 35$ such that $32b^2 - 64ab + 32a^2 = \min\{ x + y \mid x > 0, y > 0, xy = 5308416 \}$. Let $Q = L_n$, where $L_n$ denotes the $n$-th Lucas number. Compute $Q$. | 64,079 | graphs = [
Graph(
let={
"_m": Const(32),
"_n": Const(35),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Leq(Var("a"), Var("b"... | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"B3/QF_PSD_ORBIT"
] | cb4069 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"B3",
"POLY_ORBIT_HENSEL",
"QF_PSD_ORBIT"
] | 3 | 2.062 | 2026-03-10T04:24:58.587614Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-03-10T04:25:00.649350Z"
} | d47056 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1877
},
"timestamp": "2026-03-29T10:07:29.477Z",
"answer": 64079
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
8d1a6f | geo_count_lattice_rect_v1_153355830_2886 | Let $a = 27$ and $b = 107$. Define $L$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Compute $|L|$. | 3,024 | graphs = [
Graph(
let={
"a": Const(27),
"b": Const(107),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0 | 2026-02-08T07:27:30.941394Z | {
"verified": true,
"answer": 3024,
"timestamp": "2026-02-08T07:27:30.941742Z"
} | 3c1067 | 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": 384
},
"timestamp": "2026-02-24T08:05:25.308Z",
"answer": 3024
},
{
"id... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
7277a8 | nt_min_phi_inverse_v1_1742523217_12 | Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1225$. Let $\ell$ be the minimum value of $x + y$ over all such pairs. Let $k = 20$. Let $n$ be the smallest positive integer such that $1 \leq n \leq \ell$ and $\phi(n) = k$. Determine the value of $n$. | 25 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1225)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(20)... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"B3"
] | 0cd20d | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.055 | 2026-02-08T02:50:17.590071Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T02:50:17.644638Z"
} | fa5e77 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1885
},
"timestamp": "2026-02-08T19:55:17.826Z",
"answer": 25
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -4.35,
"mid": -2.09,
"hi": 0.05
} | ||
b21f5d | comb_count_permutations_fixed_v1_458359167_1409 | Let $m = 770$ and $n = 11$. Define $k$ to be the number of nonnegative integers $j$ such that $j \leq \sum_{d \mid m} \phi(d)$ and $\binom{m}{j}$ is odd. Let $r = \binom{n}{k} \cdot !(n - k)$, where $!t$ denotes the number of derangements of $t$ elements. Compute the remainder when $44121 \cdot r$ is divided by $92735$... | 535 | graphs = [
Graph(
let={
"_m": Const(770),
"_n": Const(92735),
"n": Const(11),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), SumOverDivisors(n=Const(value=770), var='d', expr=EulerPhi(n=Var(name='d')))), E... | NT | COMB | COUNT | sympy | K3 | [
"K3/V8"
] | b9331d | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"K3",
"V8"
] | 2 | 0.002 | 2026-02-08T04:35:39.891728Z | {
"verified": true,
"answer": 535,
"timestamp": "2026-02-08T04:35:39.893855Z"
} | ac6d21 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1075
},
"timestamp": "2026-02-10T17:20:07.240Z",
"answer": 535
},
{
"i... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f07399 | nt_num_divisors_compute_v1_655260480_2698 | Let $n$ be the number of integers $t$ such that $27 \leq t \leq 3157$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 163$, $1 \leq b \leq 999$, and $t = 7a + 2b + 18$. Compute the number of positive integer divisors of $n$. | 6 | 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=163)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | COMB1 | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-08T16:54:59.566140Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T16:54:59.577981Z"
} | 9145df | 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": 5175
},
"timestamp": "2026-02-17T15:19:11.543Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f32ece | sequence_lucas_compute_v1_677425708_4028 | Let $ n $ be the largest prime number such that $ 2 \leq n \leq 20 $. Let $ L_n $ denote the $ n $-th Lucas number, defined by $ L_1 = 1 $, $ L_2 = 3 $, and $ L_k = L_{k-1} + L_{k-2} $ for $ k \geq 3 $. Compute the remainder when $ 44121 \cdot L_n $ is divided by $ 54302 $. Determine the value of this remainder. | 9,237 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(20)), IsPrime(Var("n"))))),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), ... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T06:08:31.569199Z | {
"verified": true,
"answer": 9237,
"timestamp": "2026-02-08T06:08:31.569999Z"
} | 81f5df | 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": 1489
},
"timestamp": "2026-02-12T19:38:41.294Z",
"answer": 9237
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d3c039 | nt_count_digit_sum_v1_1978505735_5149 | Let $n$ be a positive integer such that $1 \leq n \leq 10267$ and the sum of the decimal digits of $n$ is $27$. Let $A$ be the number of such integers $n$.
Let $B$ be the largest prime number less than or equal to $2027$.
Compute $B - A$. | 1,807 | graphs = [
Graph(
let={
"_n": Const(2027),
"upper": Const(10267),
"target_sum": Const(27),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | nt_count_digit_sum_v1 | negation_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 4.219 | 2026-02-08T18:48:14.005591Z | {
"verified": true,
"answer": 1807,
"timestamp": "2026-02-08T18:48:18.224227Z"
} | 2a88ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 6150
},
"timestamp": "2026-02-18T19:50:59.785Z",
"answer": 1807
},
{... | 1 | [
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
520dcd | modular_modexp_compute_v1_1248542787_99 | Let $a$ be the number of integers $t$ such that $7 \leq t \leq 59$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 5$, and $t = 4a + 3b$.
Let $e$ be the sum of all real solutions $x$ to the equation $x^2 - 5329x - 220170 = 0$.
Define $m = 13689$ and let $r = a^e \bmod m$, that is, t... | 55,910 | graphs = [
Graph(
let={
"_n": Const(74883),
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(left=V... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"LIN_FORM",
"ONE_PHI_1"
] | 094305 | modular_modexp_compute_v1 | null | 7 | 0 | [
"LIN_FORM",
"ONE_PHI_1",
"VIETA_SUM"
] | 3 | 1.255 | 2026-02-08T02:57:10.954081Z | {
"verified": true,
"answer": 55910,
"timestamp": "2026-02-08T02:57:12.209107Z"
} | debb1f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 7946
},
"timestamp": "2026-02-09T12:27:34.763Z",
"answer": 38094
},
{
... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": 3.31,
"mid": 6.77,
"hi": 10
} | ||
143578 | antilemma_k3_v1_124444284_10363 | Let $ N = 83440 $. Define $ x $ to be the sum of Euler's totient function $ \phi(d) $ over all positive divisors $ d $ of $ N $. Let $ r $ be the remainder when $ |x| $ is divided by 11. Compute the Bell number $ B_r $, which counts the number of partitions of a set of $ r $ elements. Find the value of $ B_r $. | 52 | graphs = [
Graph(
let={
"_n": Const(83440),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.006 | 2026-02-08T13:01:36.430089Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T13:01:36.436141Z"
} | 11ab20 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 974
},
"timestamp": "2026-02-15T09:01:56.734Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c11743 | comb_count_surjections_v1_1915831931_1676 | Let $a$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 10$ and $1 \le j \le 10$ such that $i + j = 11$. Let $k$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = a$. Define
$$
r = k! \cdot S(5, k),
$$
where $S(5, k)$ denotes the Stirling number of the sec... | 25,480 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(11)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(10))))),
"n":... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1"
] | 5b2e59 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.017 | 2026-02-08T16:22:05.904226Z | {
"verified": true,
"answer": 25480,
"timestamp": "2026-02-08T16:22:05.921181Z"
} | 965c1f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 676
},
"timestamp": "2026-02-24T20:48:26.035Z",
"answer": 25480
},
{
"... | 1 | [
{
"lemma": "COMB1",
"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": "V8",
"sta... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
43feaf | nt_count_gcd_equals_v1_1520064083_5251 | Let $k$ be the number of positive integers $n$ with $1 \leq n \leq 3761$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $d = 11$, and let $\text{result}$ be the number of positive integers $n$ with $1 \leq n \leq 17161$ such that $\gcd(n, k) = d$. Compute the remainder when $44121 \cdot \tex... | 18,070 | graphs = [
Graph(
let={
"_n": Const(63920),
"upper": Const(17161),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(3761)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), mo... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 1.89 | 2026-02-08T06:42:09.609029Z | {
"verified": true,
"answer": 18070,
"timestamp": "2026-02-08T06:42:11.498888Z"
} | 9029de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1776
},
"timestamp": "2026-02-13T03:25:58.591Z",
"answer": 18070
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
2185e9 | nt_min_crt_v1_717093673_37 | Find the smallest positive integer $n$ such that $1 \leq n \leq 56$, $n \equiv 4 \pmod{7}$, and $n \equiv 0 \pmod{8}$. | 32 | graphs = [
Graph(
let={
"m": Const(7),
"k": Const(8),
"a": Const(4),
"b": Const(0),
"upper": Const(56),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | NT | null | EXTREMUM | sympy | C2 | [
"MOBIUS_COPRIME",
"COPRIME_PAIRS",
"V7"
] | b55f31 | nt_min_crt_v1 | null | 3 | 0 | [
"C2",
"COPRIME_PAIRS",
"MOBIUS_COPRIME",
"V7"
] | 4 | 0.049 | 2026-02-08T15:09:29.831501Z | {
"verified": true,
"answer": 32,
"timestamp": "2026-02-08T15:09:29.880742Z"
} | b5042d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 576
},
"timestamp": "2026-02-16T05:16:37.340Z",
"answer": 32
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
875fa2 | geo_count_lattice_triangle_v1_397696148_1849 | Let $ A $ be the area of the triangle with vertices at $ (200,100) $, $ (210,120) $, and $ (0,0) $, multiplied by 2. Let $ B $ be the sum of the greatest common divisors of the absolute differences in coordinates along each side of the triangle:
$$
\gcd(|200|, |100|) + \gcd(|210 - 200|, |120 - 100|) + \gcd(|0 - 210|, ... | 1,431 | graphs = [
Graph(
let={
"_n": Const(100),
"area_2x": Abs(arg=Sum(Mul(Const(value=200), Const(value=120)), Mul(Const(value=210), Sub(left=Const(value=0), right=Const(value=100))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=200)), b=Abs(arg=Ref(name='_n'))), GCD(a=Abs(arg=... | ALG | NT | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.004 | 2026-02-08T12:48:31.699567Z | {
"verified": true,
"answer": 1431,
"timestamp": "2026-02-08T12:48:31.704023Z"
} | d4d45c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 410
},
"timestamp": "2026-02-16T04:06:45.671Z",
"answer": -69
},
{
"id": 11,
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
eed5ff | nt_min_coprime_above_v1_717093673_3756 | Let $S$ be the set of all ordered pairs $(a,b)$ such that $a$ is an integer with $1 \le a \le 6$ and $b$ is an integer with $1 \le b \le 53$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all integers $n$ such that $82369 < n \le 82697$ and $\gcd(n, m) = 1$. Determine the value of the smallest element... | 82,373 | graphs = [
Graph(
let={
"start": Const(82369),
"upper": Const(82697),
"modulus": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(53)))),
"result": MinOverSet(set=SolutionsSet(var=V... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_min_coprime_above_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.057 | 2026-02-08T17:49:41.104768Z | {
"verified": true,
"answer": 82373,
"timestamp": "2026-02-08T17:49:41.161897Z"
} | 606810 | 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": 892
},
"timestamp": "2026-02-18T08:56:27.645Z",
"answer": 82373
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
aba4e3 | antilemma_v7_kummer_1116507919_268 | Let $m = 4000$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = 2500$. Let $k$ be the number of positive integers at most $m$ that are divisible by 100. Determine the largest integer $x$ such that $3^x$ divides $\binom{s}{k}$. | 2 | graphs = [
Graph(
let={
"_m": Const(4000),
"_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(2500)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | C2 | [
"C2/V7",
"B3/V7",
"V7"
] | e64a46 | antilemma_v7_kummer | null | 7 | 0 | [
"B3",
"C2",
"V7"
] | 3 | 0.002 | 2026-02-08T02:30:12.821874Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T02:30:12.823457Z"
} | aa504e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1340
},
"timestamp": "2026-02-08T19:20:18.449Z",
"answer": 2
},
{
"id":... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
00fa8e | comb_count_permutations_fixed_v1_1742523217_1352 | Let $n_2 = 8$. Define $$
c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$ Let $n_1 = 11 + c$. Define $$
e = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$ Let $n = 6 + e$. Compute $\binom{n}{1} \cdot !(n - 1)$, where $!m$ denotes the number of derangements of $m$ elements. | 264 | graphs = [
Graph(
let={
"n2": Const(8),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sum(Const(11), Ref("c")),
"e": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T03:41:21.444361Z | {
"verified": true,
"answer": 264,
"timestamp": "2026-02-08T03:41:21.445316Z"
} | cca1fb | 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": 571
},
"timestamp": "2026-02-10T15:20:09.538Z",
"answer": 264
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"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... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
a30590 | nt_count_divisible_and_v1_1820931509_491 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 10265616$. Let $m$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Determine the number of positive integers $n$ such that $1 \le n \le m$, $n$ is divisible by 9, and $n$ is divisible by 12. Compute the remainder when $... | 14,546 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(10265616)))), expr=Sum(Var("x"), Var("y")))),
"d1": Cons... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.221 | 2026-02-08T11:40:24.939751Z | {
"verified": true,
"answer": 14546,
"timestamp": "2026-02-08T11:40:25.160433Z"
} | 41f8fb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3773
},
"timestamp": "2026-02-14T17:58:53.544Z",
"answer": 14546
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c4cb18 | modular_modexp_compute_v1_48377204_1670 | Let $a$ be the number of positive integers $n$ with $1 \le n \le 44$ such that $n$ is even and $\gcd(n, 21) = 1$. Let $e = \sum_{k=1}^{123} k$. Define $r = a^e \bmod 25200$. Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 3694084$. Let $c$ be the minimum value of $x + y$ over all s... | 51,231 | graphs = [
Graph(
let={
"_m": Const(60996),
"_n": Const(2),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(44)), Divides(divisor=Ref("_n"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3",
"SUM_ARITHMETIC",
"C5"
] | 2349bd | modular_modexp_compute_v1 | negation_mod | 7 | 0 | [
"B3",
"C5",
"SUM_ARITHMETIC"
] | 3 | 0.004 | 2026-02-08T16:18:09.097472Z | {
"verified": true,
"answer": 51231,
"timestamp": "2026-02-08T16:18:09.101284Z"
} | eefa39 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2675
},
"timestamp": "2026-02-17T00:55:28.100Z",
"answer": 51231
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
12377d | nt_min_coprime_above_v1_1978505735_719 | Let $a = 27889$ and $m = 271$. Find the smallest integer $n$ such that $n > a$, $n \leq 28170$, and $\gcd(n, m) = 1$. Denote this integer by $r$. Let $d_0$ be the smallest divisor of $16965341$ that is at least $2$. Compute $$\left( r \bmod d_0 \right) + 1009 \cdot \left( r \bmod 397 \right),$$ and find the remainder w... | 50,461 | graphs = [
Graph(
let={
"start": Const(27889),
"upper": Const(28170),
"modulus": Const(271),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | nt_min_coprime_above_v1 | two_moduli | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.046 | 2026-02-08T15:34:29.639143Z | {
"verified": true,
"answer": 50461,
"timestamp": "2026-02-08T15:34:29.685498Z"
} | 893882 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 4045
},
"timestamp": "2026-02-16T08:18:21.825Z",
"answer": 50461
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
57cb39 | nt_count_divisible_and_v1_124444284_165 | Let $d_1$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 450$, $\gcd(p, q) = 1$, and $p < q$. Let $d_2 = 6$. Determine the number of positive integers $n$ such that $1 \leq n \leq 34860$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 2,905 | graphs = [
Graph(
let={
"upper": Const(34860),
"d1": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=450)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisible_and_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.215 | 2026-02-08T03:02:06.890798Z | {
"verified": true,
"answer": 2905,
"timestamp": "2026-02-08T03:02:08.105778Z"
} | 223e97 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 811
},
"timestamp": "2026-02-09T14:10:33.805Z",
"answer": 2905
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -3.55,
"mid": 0.8,
"hi": 4.81
} | ||
aa5b69 | comb_count_derangements_v1_601307018_368 | Let $n = (8 + t) \cdot v$, where $t = \sum_{k=0}^{1} (-1)^k \binom{1}{k}$, $s = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, $R = \binom{11}{11} - 1 + s$, and $v = \sum_{k=0}^{R} (-1)^k \binom{R}{k}$. Compute the number of derangements of $n$ elements, $D_n$. | 14,833 | graphs = [
Graph(
let={
"u": Const(6),
"n3": Sum(Ref("u"), Const(1)),
"s": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"n2": Const(1),
"t": Summation(var="k1", start=Const(0... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | ba7829 | comb_count_derangements_v1 | null | 3 | 3 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 2 | 0.004 | 2026-03-10T00:54:22.379651Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-03-10T00:54:22.383569Z"
} | 154ca0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1291
},
"timestamp": "2026-03-28T22:54:12.561Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -4.31,
"mid": -1.92,
"hi": 0.62
} | ||
af895a | diophantine_product_count_v1_124444284_4426 | Let $n = 246$ and $k = 360$. Define $\text{upper}$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Define $\text{result}$ to be the number of positive integers $x$ such that $1 \leq x \leq \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \leq \text{upper}$. Compute the... | 90,581 | graphs = [
Graph(
let={
"_n": Const(246),
"k": Const(360),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2'))... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | diophantine_product_count_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.007 | 2026-02-08T06:01:12.612803Z | {
"verified": true,
"answer": 90581,
"timestamp": "2026-02-08T06:01:12.620223Z"
} | c6cd96 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 1769
},
"timestamp": "2026-02-12T18:16:45.721Z",
"answer": 90581
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a7be44 | antilemma_k2_v1_1125832087_2229 | Compute the value of
$$
\sum_{k=1}^{109} \varphi(k) \left\lfloor \frac{109}{k} \right\rfloor,
$$
where $\varphi$ denotes Euler's totient function. | 5,995 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Div(Const(82), Const(82)), end=Const(109), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(109), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"IDENTITY_DIV_SELF",
"K2"
] | 39e678 | antilemma_k2_v1 | null | 5 | 0 | [
"IDENTITY_DIV_SELF",
"K13",
"K2"
] | 3 | 0.002 | 2026-02-08T04:25:30.047629Z | {
"verified": true,
"answer": 5995,
"timestamp": "2026-02-08T04:25:30.049337Z"
} | e1315c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 691
},
"timestamp": "2026-02-10T16:44:51.227Z",
"answer": 5995
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
25112e_n | alg_sym_quad_system_v1_1419126231_864 | Three musicians tune their instruments so that the squares of their frequencies $a$, $b$, and $c$ (positive integers) satisfy $a^2 + b^2 + c^2 = ab + bc + ca$, and their combined pitch adjustment follows $7a + 8b + 6c = 1113$. For each valid tuning, they compute the sum of cubes of the frequencies. What is the remainde... | 1,903 | ALG | null | COMPUTE | sympy | ONE_PHI_1 | [
"ABS_INEQ"
] | 1c5bb8 | alg_sym_quad_system_v1 | null | 6 | null | [
"ABS_INEQ",
"ONE_PHI_1"
] | 2 | 5.358 | 2026-02-25T10:20:11.206873Z | null | d37246 | 25112e | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 690
},
"timestamp": "2026-03-31T04:04:49.737Z",
"answer": 1903
},
{
"id... | 1 | [
{
"lemma": "ABS_INEQ",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
7f978a_n | modular_product_range_v1_601307018_602 | A biologist labels a sequence of specimens from day $p$ to day $326$, where $p$ is the largest prime number no greater than $161$. Each day, the label is multiplied into a cumulative code. At the end, the code is reduced modulo $10663$. What is the resulting value? | 8,638 | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_product_range_v1 | null | 4 | null | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-03-10T01:07:55.298730Z | null | 7c266f | 7f978a | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T14:18:52.933Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"... | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
cb6733 | comb_count_derangements_v1_1520064083_3671 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 154350$, $\gcd(p, q) = 1$, and $p < q$. Let $r = !n$ denote the subfactorial of $n$. Compute the remainder when $44121 \cdot r$ is divided by $58733$. | 43,707 | graphs = [
Graph(
let={
"_n": Const(58733),
"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=154350)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T05:47:39.062300Z | {
"verified": true,
"answer": 43707,
"timestamp": "2026-02-08T05:47:39.063868Z"
} | 09e90a | 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": 1592
},
"timestamp": "2026-02-12T14:32:58.288Z",
"answer": 43707
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
1b5a27 | alg_qf_psd_sum_v1_1218484723_692 | Find the remainder when $$\sum_{\substack{1 \leq a \leq 355 \\ 1 \leq b \leq 355}} \left( 29b^2 + \left|\left\{ v : 0 \leq v \leq \min\{x+y : x>0, y>0, xy=11075584\} \text{ and } \exists\, a,b \in \mathbb{Z},\, 1 \leq a,b \leq 17 \text{ such that } 26a^2 - 52ab + 26b^2 = v \right\}\right| \cdot a^2 + 36ab \right)$$ is ... | 8,080 | graphs = [
Graph(
let={
"_m": Const(355),
"_n": Const(29),
"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(355)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref... | ALG | null | COMPUTE | sympy | B3 | [
"B3/QF_PSD_DISTINCT"
] | b8e9cb | alg_qf_psd_sum_v1 | null | 6 | 0 | [
"B3",
"QF_PSD_DISTINCT"
] | 2 | 0.252 | 2026-02-25T02:26:13.262964Z | {
"verified": true,
"answer": 8080,
"timestamp": "2026-02-25T02:26:13.515033Z"
} | 3d3ad7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 27206
},
"timestamp": "2026-03-28T23:55:59.963Z",
"answer": 8080
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
bab787 | lte_diff_endings_v1_784195855_1337 | Let $a = 51$, $b = 11$, $p = 2$, $K = 6$, and $N = 508217$. Let $\text{diff} = a - b$, and let $v_p(\text{diff})$ be the largest integer $k$ such that $p^k$ divides $\text{diff}$. Define $m = K - v_p(\text{diff})$ and let $p^m$ be $p$ raised to the power $m$. Compute the greatest integer less than or equal to $N$ divid... | 63,527 | graphs = [
Graph(
let={
"a_val": Const(51),
"b_val": Const(11),
"p_val": Const(2),
"K_val": Const(6),
"N_val": Const(508217),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_va... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 5 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T04:59:11.471035Z | {
"verified": true,
"answer": 63527,
"timestamp": "2026-02-08T04:59:11.471751Z"
} | dbb755 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 248
},
"timestamp": "2026-02-18T14:44:40.632Z",
"answer": 63527
}
] | 2 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
89c853 | nt_count_coprime_v1_1918700295_709 | Let $k = 43$ and let the upper bound be $88888$. Determine the number of positive integers $n$ such that $1 \leq n \leq 88888$ and $\gcd(n, 43) = \phi(2)$, where $\phi$ denotes Euler's totient function. Compute this number. | 86,821 | graphs = [
Graph(
let={
"upper": Const(88888),
"k": Const(43),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), EulerPhi(n=Const(2)))))),
},
goal=Ref("... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_count_coprime_v1 | null | 3 | 0 | [
"ONE_PHI_2"
] | 1 | 11.56 | 2026-02-08T03:23:51.160920Z | {
"verified": true,
"answer": 86821,
"timestamp": "2026-02-08T03:24:02.720742Z"
} | 0fd4bf | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 350
},
"timestamp": "2026-02-17T23:34:44.281Z",
"answer": 86821
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": ... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
0acd3c | comb_sum_binomial_row_v1_971394319_823 | Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $12$, where $\phi$ is Euler's totient function. Compute $2^n$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(12),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | K3 | [
"K3"
] | 54c41e | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T13:19:11.187142Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T13:19:11.188704Z"
} | a0cca4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 242
},
"timestamp": "2026-02-16T04:30:58.001Z",
"answer": 4096
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
31bfbe | alg_qf_psd_orbit_v1_601307018_7310 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 254$ such that $26a^2 - 20ab + 26b^2 = 848250$. | 5 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(25)), Leq(Var("v"), Const(7225)... | ALG | null | COUNT | sympy | B3_DIFF | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_orbit_v1 | null | 7 | 0 | [
"B3_DIFF",
"QF_PSD_DISTINCT"
] | 2 | 0.889 | 2026-03-10T07:54:32.991650Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-03-10T07:54:33.880668Z"
} | be5179 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 14774
},
"timestamp": "2026-04-19T06:25:12.260Z",
"answer": 5
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
149869 | nt_count_digit_sum_v1_1248542787_56 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Let $s_{\text{min}}$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Determine the number of positive integers $n$ such that $1 \leq n \leq 99999$ and the sum of the decimal digits of $n$ is equal to $s_{\text{min}}... | 5,875 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(144)))), expr=Sum(Var("x"), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_digit_sum_v1 | null | 5 | 0 | [
"B3"
] | 1 | 4.262 | 2026-02-08T02:55:59.043970Z | {
"verified": true,
"answer": 5875,
"timestamp": "2026-02-08T02:56:03.305676Z"
} | dee6e1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1596
},
"timestamp": "2026-02-08T23:57:05.978Z",
"answer": 5875
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 0.75,
"mid": 2.37,
"hi": 3.9
} | ||
0bec3b | comb_factorial_compute_v1_1742523217_83 | Let $T$ be the set of all integers $t$ with $5 \leq t \leq 22$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 8$ and $1 \leq b \leq 2$, such that $t = 2a + 3b$. Let $n$ be the number of elements in $T$. Now let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$... | 40,320 | 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=8)), Geq(left=Var(name='b'), right=Const(value=... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_factorial_compute_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T02:52:15.551392Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T02:52:15.553275Z"
} | b82bb2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 868
},
"timestamp": "2026-02-09T13:41:11.987Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
c071cb | sequence_lucas_compute_v1_898971024_116 | Let $A$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 737$ and $\gcd(n_1, 20) = 1$. Let $B$ be the number of positive integers $n_2$ such that $1 \leq n_2 \leq A$, $5$ divides $n_2$, and $\gcd(n_2, m) = 1$, where $m$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integ... | 15,127 | graphs = [
Graph(
let={
"_c": Const(20),
"_m": Const(5),
"_n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(737)), Eq(GCD(a=Var("n1"), b=Ref("_c")), Const(1))))),
"n": CountOverSet(set=SolutionsSet(v... | NT | null | COMPUTE | sympy | B3 | [
"B3/C5",
"C4/C5"
] | 6d1010 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"B3",
"C4",
"C5"
] | 3 | 0.01 | 2026-02-08T15:12:03.034814Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T15:12:03.045047Z"
} | 7dfda4 | 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": 1302
},
"timestamp": "2026-02-16T02:38:32.606Z",
"answer": 15127
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
df522d | geo_count_lattice_rect_v1_1874849503_619 | Let $a = 32$ and $b = 60$. Define a lattice point as a point $(x, y)$ in the coordinate plane where both $x$ and $y$ are integers. Determine the number of lattice points in the rectangle defined by $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute this number. | 2,013 | graphs = [
Graph(
let={
"a": Const(32),
"b": Const(60),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T13:13:18.830662Z | {
"verified": true,
"answer": 2013,
"timestamp": "2026-02-08T13:13:18.832276Z"
} | 61bee6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 239
},
"timestamp": "2026-02-09T19:05:31.418Z",
"answer": 2013
},
{
"id... | 1 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
3be489 | comb_count_permutations_fixed_v1_865884756_6164 | Let $m = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $s = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Define $n = 6m$ and $k = 4s$. Let $R = \binom{n}{k} \cdot !(n - k)$, where $!d$ denotes the number of derangements of $d$ elements.
Compute $R$. | 15 | graphs = [
Graph(
let={
"n2": Const(0),
"m": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"n1": Const(0),
"s": Summation(var="k2", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T19:02:01.002719Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T19:02:01.004279Z"
} | 1bb40b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 688
},
"timestamp": "2026-02-25T00:58:17.333Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||
689d28 | diophantine_product_count_v1_1439011603_2391 | Let $k$ be the number of integers $t$ with $15 \leq t \leq 1278$ for which there exist positive integers $a \leq 40$ and $b \leq 153$ such that $t = 9a + 6b$. Determine the number of positive integers $x \leq 27$ such that $x$ divides $k$ and $\frac{k}{x} \leq 27$. | 2 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=40)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.035 | 2026-02-08T16:45:30.236366Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:45:30.271673Z"
} | 910657 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 3647
},
"timestamp": "2026-02-17T11:36:31.836Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bf1a88 | comb_sum_binomial_row_v1_1742523217_1211 | Let $n$ be the number of integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \le a \le 3$, $1 \le b \le 4$, $15 \le t \le 51$, and $t = 9a + 6b$. Let $k$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Compute $k^n$. | 2,048 | 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=3)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T03:32:06.952784Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T03:32:06.957641Z"
} | c1a4e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1875
},
"timestamp": "2026-02-10T05:06:53.778Z",
"answer": 2048
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"s... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
3ce864 | geo_count_lattice_triangle_v1_1520064083_4008 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 2097$, $9$ divides $n$, and $\gcd(n, 14) = 1$. Define
$$
A = \left| 361 \cdot N - 81 \cdot 300 \right|.
$$
Consider the triangle with vertices at $(0, 0)$, $(361, 300)$, and $(81, 100)$. Let $B$ be the sum of the greatest common divisors of the abs... | 30,184 | graphs = [
Graph(
let={
"_m": Const(81),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2097)), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
"area_2x": Abs(arg=Su... | NT | null | COUNT | sympy | C5 | [
"C5/B1"
] | fb17e9 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B1",
"C5"
] | 2 | 0.008 | 2026-02-08T06:01:14.642240Z | {
"verified": true,
"answer": 30184,
"timestamp": "2026-02-08T06:01:14.650381Z"
} | ce62e6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 2890
},
"timestamp": "2026-02-12T18:05:23.089Z",
"answer": 30184
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f58fff | antilemma_cartesian_v1_655260480_2923 | Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 10$ and $1 \leq b \leq 15$. Compute the remainder when $72343 \cdot x$ is divided by $75850$. | 4,900 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(15)))),
"_c": Const(72343),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(75850)),
},
goa... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T17:03:48.859367Z | {
"verified": true,
"answer": 4900,
"timestamp": "2026-02-08T17:03:48.860135Z"
} | 4b580a | 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": 916
},
"timestamp": "2026-02-17T18:15:24.856Z",
"answer": 4900
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
51cb10 | comb_count_surjections_v1_1218484723_711 | Let $k = 3$ 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. | 540 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Summation(var="k1", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Ref("_n"), Var("k1"))))),
"k": Const(3),
"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 | 3 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-25T02:27:18.598402Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-25T02:27:18.599852Z"
} | 16212b | 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": 729
},
"timestamp": "2026-03-10T01:05:41.584Z",
"answer": 540
},
{
"id"... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.42,
"hi": -2.84
} | ||
895790 | antilemma_k2_v1_865884756_5620 | Let $m = 307$. Compute
$$
\sum_{d \mid m} \phi(d),
$$
where $\phi(d)$ denotes Euler's totient function and the sum is over all positive divisors $d$ of $m$. Denote this sum by $n$. Now compute
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{307}{k} \right\rfloor.
$$
Find the value of this sum. | 47,278 | graphs = [
Graph(
let={
"_m": Const(307),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(307), Var("k"))))),
},
goal=Re... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 7 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.002 | 2026-02-08T18:44:10.526993Z | {
"verified": true,
"answer": 47278,
"timestamp": "2026-02-08T18:44:10.528913Z"
} | f4faef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1343
},
"timestamp": "2026-02-18T18:57:43.955Z",
"answer": 47278
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0195c4 | geo_count_lattice_triangle_v1_677425708_2096 | Let $A$ be twice the area of the triangle with vertices at $(0,0)$, $(103,66)$, and $(64,169)$, which is $|103 \cdot 169 + 64 \cdot (-66)|$. Let $B$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along the three edges: $\gcd(103,66) + \gcd(|64-103|, |t - 66|) + \gcd(... | 7,507 | graphs = [
Graph(
let={
"_m": Const(77687),
"_n": Summation(var="k", start=Const(1), end=Const(11), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(11), Var("k"))))),
"area_2x": Abs(arg=Sum(Mul(Const(value=103), Const(value=169)), Mul(Const(value=64), Sub(left=Const(value=... | NT | null | COUNT | sympy | K2 | [
"K2/LIN_FORM"
] | a96dc0 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-08T04:47:17.823108Z | {
"verified": true,
"answer": 7507,
"timestamp": "2026-02-08T04:47:17.834715Z"
} | 1afd9d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 321,
"completion_tokens": 5521
},
"timestamp": "2026-02-10T05:55:29.245Z",
"answer": 18568
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
186ef6 | nt_count_divisible_and_v1_784195855_5910 | Let $d_1 = 6$ and $d_2 = \sum_{k=1}^4 k$. Compute the number of positive integers $n$ such that $n \leq 45540$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 1,518 | graphs = [
Graph(
let={
"upper": Const(45540),
"d1": Const(6),
"d2": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(M... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 1.538 | 2026-02-08T08:11:12.101923Z | {
"verified": true,
"answer": 1518,
"timestamp": "2026-02-08T08:11:13.639570Z"
} | dcde33 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 421
},
"timestamp": "2026-02-15T19:44:13.996Z",
"answer": 1518
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status"... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
b1caff | nt_min_with_divisor_count_v1_458359167_515 | Let $C$ be the number of integers $j$ with $0 \leq j \leq 2584$ such that $\binom{2584}{j}$ is odd. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = C + 9$. Let $T$ be the set of all values of $x + y$ as $(x, y)$ ranges over $S$. Let $d$ be the minimum element of $T$. Let $n$ be the... | 48 | graphs = [
Graph(
let={
"upper": Const(44521),
"div_count": 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")), Sum(CountOverSet(set=SolutionsSet(v... | NT | null | EXTREMUM | sympy | B3 | [
"V8/B3"
] | b4fc86 | nt_min_with_divisor_count_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 2.39 | 2026-02-08T03:23:14.574545Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T03:23:16.964743Z"
} | ca8112 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 1399
},
"timestamp": "2026-02-10T13:22:41.826Z",
"answer": 48
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
b0ff93 | comb_count_surjections_v1_865884756_5322 | Let $n = 7$ and $k = 4$. Define $S(n, k)$ to be the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets. Compute the remainder when $40^2 - k! \cdot S(n, k)$ is divided by $88075$. | 81,275 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(40)), right=IntegerRange(start=Const(1), ... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 009729 | comb_count_surjections_v1 | negation_mod | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T18:31:51.177443Z | {
"verified": true,
"answer": 81275,
"timestamp": "2026-02-08T18:31:51.179049Z"
} | 718e23 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1597
},
"timestamp": "2026-02-18T17:49:27.011Z",
"answer": 81275
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
261190 | modular_count_residue_v1_458359167_1190 | Let $r$ be the largest prime number such that $2 \leq r \leq 22$. Compute the number of positive integers $n$ such that $1 \leq n \leq 60000$ and $n \equiv r \pmod{21}$. | 2,857 | graphs = [
Graph(
let={
"upper": Const(60000),
"m": Const(21),
"r": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(22)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 7.914 | 2026-02-08T04:29:09.674011Z | {
"verified": true,
"answer": 2857,
"timestamp": "2026-02-08T04:29:17.587606Z"
} | 3b31e1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 378
},
"timestamp": "2026-02-11T20:54:51.962Z",
"answer": 2862
},
{
"id": 11,... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
7e2cff | diophantine_product_count_v1_717093673_1813 | Let $k = 120$ and $u = 12$. Define $A$ to be the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Let $r$ be the number of elements in $A$. Now let $B$ be the set of all integers $t$ such that $25 \leq t \leq 3285$ and there exist positive integers $a \leq 553$ an... | 3,251 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(120),
"upper": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 341932 | diophantine_product_count_v1 | digits_weighted_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.012 | 2026-02-08T16:20:36.954751Z | {
"verified": true,
"answer": 3251,
"timestamp": "2026-02-08T16:20:36.966460Z"
} | 37966a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 3469
},
"timestamp": "2026-02-17T01:33:05.018Z",
"answer": 3251
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0f9637 | nt_lcm_compute_v1_124444284_3697 | Let $a = 686$. Let $b$ be the number of positive integers $j$ such that $1 \leq j \leq 2968$ and $j^3 \leq 26145183232$. Let $\text{result} = \text{lcm}(a, b)$. Compute the remainder when $88523 \cdot \text{result}$ is divided by $65084$. | 6,148 | graphs = [
Graph(
let={
"a": Const(686),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(2968)), Leq(Pow(Var("j"), Const(3)), Const(26145183232))), domain='positive_integers')),
"result": LCM(a=Ref("a"), b=Ref("b... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | nt_lcm_compute_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T05:32:51.650569Z | {
"verified": true,
"answer": 6148,
"timestamp": "2026-02-08T05:32:51.651605Z"
} | bfac45 | 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": 1668
},
"timestamp": "2026-02-12T10:28:59.783Z",
"answer": 6148
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0d2e48 | sequence_fibonacci_compute_v1_784195855_1866 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 31$ for which there exist positive integers $a \leq 8$ and $b \leq 5$ such that $t = 2a + 3b$. Compute the $n$-th Fibonacci number. | 75,025 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:22:30.487180Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T05:22:30.488354Z"
} | 087edc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1779
},
"timestamp": "2026-02-12T06:58:16.884Z",
"answer": 75025
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c68d99 | nt_count_divisible_and_v1_898971024_657 | Let $d_1 = 6$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Define $d_2$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $Q$ be the number of positive integers $n$ such that $1 \leq n \leq 109620$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$... | 3,654 | graphs = [
Graph(
let={
"upper": Const(109620),
"d1": Const(6),
"d2": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25)))),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 3 | 0 | [
"B3"
] | 1 | 6.591 | 2026-02-08T15:34:40.408970Z | {
"verified": true,
"answer": 3654,
"timestamp": "2026-02-08T15:34:47.000390Z"
} | 9abae5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 480
},
"timestamp": "2026-02-16T06:09:44.058Z",
"answer": 3654
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
bdcc06 | nt_count_gcd_equals_v1_1978505735_6636 | Let $N$ be the number of positive integers $n$ such that $n \leq 16900$ and $\gcd(n, 228) = 76$. Let $S$ be the sum of all positive integers $n_1$ such that $n_1 \leq 240$ and $n_1$ is divisible by 10. Let $A$ be the sum of $(i+1)^2$ times the $i$th decimal digit of $|N|$ for $i$ from 0 to the number of digits of $|N|$... | 3,033 | graphs = [
Graph(
let={
"upper": Const(16900),
"k": Const(228),
"d": Const(76),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | d92c90 | nt_count_gcd_equals_v1 | digits_weighted_mod | 5 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 1.235 | 2026-02-08T19:43:14.603442Z | {
"verified": true,
"answer": 3033,
"timestamp": "2026-02-08T19:43:15.838704Z"
} | 53400c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1314
},
"timestamp": "2026-02-18T23:20:51.434Z",
"answer": 3033
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4d5869 | nt_num_divisors_compute_v1_397696148_1525 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 34$. For each pair, compute the product $xy$, and let $n$ be the maximum value among these products. Let $d$ be the number of positive divisors of $n$. Compute the remainder when $48359 \cdot d$ is divided by $93185$. | 51,892 | graphs = [
Graph(
let={
"_n": Const(93185),
"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(34)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T12:37:02.119334Z | {
"verified": true,
"answer": 51892,
"timestamp": "2026-02-08T12:37:02.121235Z"
} | 453ee1 | 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": 560
},
"timestamp": "2026-02-15T03:00:37.490Z",
"answer": 51892
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
85f147 | nt_sum_divisors_compute_v1_1520064083_3340 | Let $a = 26244$. Compute the sum of all positive divisors of $a$, and denote this sum by $s$. Let $b = 81745$. Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $t$ be the number of elements in $P$. Compute the remainder ... | 69,015 | graphs = [
Graph(
let={
"_n": Const(81745),
"n": Const(26244),
"result": SumDivisors(n=Ref("n")),
"Q": Sum(Ref("result"), Mod(value=Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 64a51e | nt_sum_divisors_compute_v1 | mod_exp | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T05:35:56.402089Z | {
"verified": true,
"answer": 69015,
"timestamp": "2026-02-08T05:35:56.403204Z"
} | 0822cf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1174
},
"timestamp": "2026-02-12T10:51:13.009Z",
"answer": 69015
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
debaa8 | diophantine_fbi2_min_v1_1978505735_3341 | Let $k = 240$, $a = 4$, $b = 4$, and $u = 250$. Define $r$ to be the smallest integer $d$ such that $5 \leq d \leq 250$, $d$ divides $240$, and $\frac{240}{d} \geq 5$.
Let $Q = 8 - r$.
Compute $Q$. | 3 | graphs = [
Graph(
let={
"k": Const(240),
"a": Const(4),
"b": Const(4),
"upper": Const(250),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=R... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.114 | 2026-02-08T17:34:15.212930Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T17:34:15.326844Z"
} | af8614 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 372
},
"timestamp": "2026-02-16T11:23:49.686Z",
"answer": -40
},
{
"id": 11,
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
7f33de | comb_sum_binomial_row_v1_151522320_754 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Compute $|S|^{16}$. | 65,536 | graphs = [
Graph(
let={
"n": Const(16),
"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=216)), Eq(left=GCD(a=Var(name='p'), b=Va... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T03:29:43.295358Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T03:29:43.296271Z"
} | 7b5341 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 904
},
"timestamp": "2026-02-10T15:00:06.496Z",
"answer": 65536
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"sta... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6dbceb | modular_min_linear_v1_784195855_3634 | Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16900$. Let $m = 52976$ and $b = 40648$. Define $S$ as the set of all positive integers $x$ such that $1 \leq x \leq m$ and $$a x \equiv b \pmod{m}.$$ Let $r$ be the smallest element of $S$. Compute $69169 - r$. | 60,455 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16900)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(40648)... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_min_linear_v1 | null | 6 | 0 | [
"B3"
] | 1 | 2.114 | 2026-02-08T06:33:09.210921Z | {
"verified": true,
"answer": 60455,
"timestamp": "2026-02-08T06:33:11.324874Z"
} | 22da23 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 2334
},
"timestamp": "2026-02-13T01:55:01.955Z",
"answer": 60455
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0cc3dd | geo_visible_lattice_v1_548369836_187 | Let $n = 100$. Define $r$ to be the number of ordered pairs $(x, y)$ of integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the value of $$
Q = \sum_{k=1}^{r} \tau(k),$$ where $\tau(k)$ denotes the number of positive divisors of $k$. | 53,988 | graphs = [
Graph(
let={
"n": Const(100),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Summation(var="n", start=Div(Const(65), Const(65)), end=Abs(arg=Ref(name='result')), expr=NumDivisors(n=Var("n"))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF"
] | b48fad | geo_visible_lattice_v1 | null | 6 | 0 | [
"IDENTITY_DIV_SELF"
] | 1 | 0.198 | 2026-02-08T02:48:14.576634Z | {
"verified": true,
"answer": 53988,
"timestamp": "2026-02-08T02:48:14.774717Z"
} | 1da94c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T16:24:09.285Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
}
] | {
"lo": 4.89,
"mid": 6.21,
"hi": 7.78
} | ||
ab1576 | comb_count_derangements_v1_153355830_2642 | Let $m = 120$. Define $A$ to be the set of all positive integers $n$ such that $1 \leq n \leq m$ and $30$ divides the $n$-th Fibonacci number. Let $k = |A|$. Let $B$ be the set of all positive integers $d$ such that $d \geq k$ and $d$ divides $1001$. Let $n$ be the smallest element of $B$. Compute the number of derange... | 1,854 | graphs = [
Graph(
let={
"_m": Const(120),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Divides(divisor=Const(30), dividend=Fibonacci(arg=Var(name='n')))))),
"n": MinOverSet(set=SolutionsSet(var=Var("d")... | NT | COMB | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MIN_PRIME_FACTOR"
] | 0c6279 | comb_count_derangements_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T07:15:14.338144Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T07:15:14.340927Z"
} | 2d1a4a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 1329
},
"timestamp": "2026-02-13T09:13:58.863Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"st... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
e09ff3 | modular_sum_quadratic_residues_v1_458359167_230 | Let $m = 14$. Define $n$ to be the number of integers $t$ such that $16 \leq t \leq 9294$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 1014$, $1 \leq b \leq 321$, and $t = 6a + 10b$. Let $p$ be the number of positive integers $k$ such that $1 \leq k \leq n$ and $m$ divides $F_k$, the $k$-th Fibonac... | 1,140 | graphs = [
Graph(
let={
"_m": Const(14),
"_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=1014)), Geq(left=V... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/COUNT_FIB_DIVISIBLE"
] | 95eec8 | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T03:05:14.365870Z | {
"verified": true,
"answer": 1140,
"timestamp": "2026-02-08T03:05:14.369201Z"
} | bdbdda | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 6337
},
"timestamp": "2026-02-10T12:57:36.311Z",
"answer": 1140
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"sta... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6f0e85 | modular_mod_compute_v1_1978505735_5153 | Let $m$ be the number of positive integers $n$ such that $1 \leq n \leq 54607$, $7$ divides $n$, and $\gcd(n, 6) = 1$.
Compute the remainder when $-37636$ is divided by $m$. | 1,379 | graphs = [
Graph(
let={
"_n": Const(6),
"a": Const(-37636),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(54607)), Divides(divisor=Const(7), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | modular_mod_compute_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T18:48:18.832474Z | {
"verified": true,
"answer": 1379,
"timestamp": "2026-02-08T18:48:18.834227Z"
} | 6a3b11 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 1460
},
"timestamp": "2026-02-18T19:49:09.044Z",
"answer": 1379
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1c4207 | comb_count_permutations_fixed_v1_809748730_487 | Let $n$ be the number of integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 2$, $1 \le b \le 5$, $14 \le t \le 40$, and $t = 10a + 4b$. Let $k$ be the smallest integer $d \ge 2$ such that $d$ divides $49049$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!(n - k)$ denotes the number of d... | 240 | 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=2)), Geq(left=Var(na... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T11:32:35.839904Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T11:32:35.842559Z"
} | 699501 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1336
},
"timestamp": "2026-02-14T15:37:11.298Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
24d984 | comb_count_partitions_v1_1874849503_1121 | Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 38x - 7035 = 0$. Compute the number of integer partitions of $n$. | 26,015 | graphs = [
Graph(
let={
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-38), Var("x")), Const(-7035)), Const(0)))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | comb_count_partitions_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T13:38:26.490181Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T13:38:26.492023Z"
} | b7e9ac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 809
},
"timestamp": "2026-02-10T01:23:25.124Z",
"answer": 26015
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"st... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
617dc5 | comb_binomial_compute_v1_2051736721_4348 | Let $n$ be the smallest divisor of $1356277$ that is at least $2$. Let $k = 5$. Compute $\binom{n}{k}$, and denote this value as $r$. Let $d_1$ be the smallest divisor of $1356277$ that is at least $2$. Compute $d_1 - r$, and find the remainder when this difference is divided by $86362$. Determine the value of this rem... | 85,088 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1356277))))),
"k": Const(5),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(v... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | fd27b3 | comb_binomial_compute_v1 | negation_mod | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T17:55:31.519190Z | {
"verified": true,
"answer": 85088,
"timestamp": "2026-02-08T17:55:31.521548Z"
} | 780160 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1291
},
"timestamp": "2026-02-18T10:09:15.236Z",
"answer": 85088
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7a4a30 | antilemma_sum_equals_v1_1520064083_6295 | Consider all integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le 4$, $1\le b\le 3$, $10\le t\le 34$, and
$$t=4a+6b.$$
Let $m$ be the number of such integers $t$.
Let $n$ be the number of ordered pairs $(u,v)$ of integers with $1\le u\le 4$ and $1\le v\le 13$.
Let $x$ be the number of ordered... | 877 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM/COUNT_CARTESIAN",
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 194720 | antilemma_sum_equals_v1 | bell_mod | 5 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.028 | 2026-02-08T08:00:28.987019Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T08:00:29.015075Z"
} | a24123 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 330,
"completion_tokens": 740
},
"timestamp": "2026-02-24T08:43:32.400Z",
"answer": 877
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
ce47db | alg_poly4_sum_v1_1419126231_1853 | Let $m$ be the smallest divisor of $51937997$ that is at least $2$. Compute the remainder when $\sum_{a=1}^{m} \sum_{b=1}^{79} (32a^4 - 96a^3b + 120a^2b^2 - 72ab^3 + 17b^4)$ is divided by $77509$. | 28,574 | graphs = [
Graph(
let={
"_n": Const(2),
"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"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divid... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_poly4_sum_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.025 | 2026-02-25T11:24:22.939445Z | {
"verified": true,
"answer": 28574,
"timestamp": "2026-02-25T11:24:22.963976Z"
} | 9ac587 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 15961
},
"timestamp": "2026-03-30T14:20:24.895Z",
"answer": 28574
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
f6d096 | nt_sum_divisors_mod_v1_784195855_4884 | Let $n$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers satisfying $xy = 396900$. Let $\sigma$ denote the sum of the positive divisors of $n$, and let $M = 10357$. Compute the remainder when $\sigma$ is divided by $M$. | 4,368 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10357... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T07:27:13.395524Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T07:27:13.396894Z"
} | 0e5c14 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1506
},
"timestamp": "2026-02-13T10:35:59.902Z",
"answer": 4368
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
fbffa0 | comb_count_derangements_v1_1080341949_399 | For each integer $j$ with $0\le j\le 36865$, consider the binomial coefficient $\binom{36865}{j}$. Let $n$ be the number of integers $j$ in this range for which $\binom{36865}{j}\equiv 1\pmod{2}$.
Let $!n$ denote the number of derangements of $n$ elements (that is, permutations of $n$ elements with no fixed points). L... | 58,260 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(36865)), Eq(Mod(value=Binom(n=Const(36865), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | B3 | [
"B3",
"V8"
] | 7c01c3 | comb_count_derangements_v1 | negation_mod | 8 | 0 | [
"B3",
"V8"
] | 2 | 0.002 | 2026-02-08T13:28:48.577227Z | {
"verified": true,
"answer": 58260,
"timestamp": "2026-02-08T13:28:48.579481Z"
} | 4ce42f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 2146
},
"timestamp": "2026-02-24T18:28:21.663Z",
"answer": 58260
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
766e94 | diophantine_sum_product_min_v1_458359167_4619 | Let $S$ be the number of integers $n$ such that $1 \leq n \leq 40$ and the sum of the decimal digits of $n$ is even. Let $P$ be the number of integers $t$ such that $9 \leq t \leq 113$ and there exist positive integers $a \leq 46$ and $b \leq 3$ for which $t = 2a + 7b$. Determine the smallest positive integer $x$ such ... | 16,013 | graphs = [
Graph(
let={
"_n": Const(67760),
"S": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(40)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"P": CountOverSet(set=SolutionsSet(var=Var("t"),... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"L3B"
] | f85b0e | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.01 | 2026-02-08T11:55:42.840847Z | {
"verified": true,
"answer": 16013,
"timestamp": "2026-02-08T11:55:42.850985Z"
} | be9e8f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 2454
},
"timestamp": "2026-02-14T21:16:48.158Z",
"answer": 16013
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ceac8c | geo_count_lattice_rect_v1_53965629_8 | Let $a = 120$ and $b = 29$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$.
A lattice point is a point $(x, y)$ where both $x$ and $y$ are integers. The rectangle includes all points such that $0 \le x \le a$ and $0 \le y \le b$.
Compute the number of such points. | 3,630 | graphs = [
Graph(
let={
"a": Const(120),
"b": Const(29),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T11:12:50.016603Z | {
"verified": true,
"answer": 3630,
"timestamp": "2026-02-08T11:12:50.017111Z"
} | f1b218 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 261
},
"timestamp": "2026-02-09T10:44:36.141Z",
"answer": 3630
},
{
"id... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
44303a | comb_bell_compute_v1_655260480_1526 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1470$, $\gcd(p, q) = 1$, and $p < q$. Compute the Bell number $B_n$, which is the number of partitions of a set of size $n$. | 4,140 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=1470)), 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 | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T16:12:33.273182Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:12:33.274677Z"
} | cf9cfd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 2060
},
"timestamp": "2026-02-16T22:48:07.257Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
40142a | antilemma_sum_factor_cartesian_v1_677425708_1748 | Compute the sum of $i \cdot j$ over all ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 20$ and $1 \leq j \leq 16$. | 28,560 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=Const(1), end=Const(16)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 2 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:24:47.421497Z | {
"verified": true,
"answer": 28560,
"timestamp": "2026-02-08T04:24:47.422415Z"
} | aa6b3b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 207
},
"timestamp": "2026-02-10T00:20:09.370Z",
"answer": 28560
},
{
"i... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"sta... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} |
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