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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
16b1d5 | modular_min_linear_v1_1431428450_759 | Let $a$ be the sum of all real solutions $x$ to the equation $x^2 - 8434x - 143667 = 0$. Let $b = 10159$ and $m = 14093$. Determine the smallest positive integer $x$ such that $1 \leq x \leq m$ and $ax \equiv b \pmod{m}$. Find the value of this integer. | 11,429 | graphs = [
Graph(
let={
"_n": Const(2),
"a": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-8434), Var("x")), Const(-143667)), Const(0)))),
"b": Const(10159),
"m": Const(14093),
"result": MinOverSet(... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_min_linear_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.56 | 2026-02-08T13:40:12.681421Z | {
"verified": true,
"answer": 11429,
"timestamp": "2026-02-08T13:40:13.241143Z"
} | 394b1f | 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": 2663
},
"timestamp": "2026-02-15T19:51:12.225Z",
"answer": 11429
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9db249 | nt_sum_totient_over_divisors_v1_1874849503_739 | Let $n_1$ be the largest prime number between $2$ and $6$, inclusive. Define $w$ to be the number of distinct prime factors of $n_1$. Let $p = 2$, and let $v$ be the remainder when $\left( (p - \sum_{d \mid \gcd(9,14)} \mu(d))! + 1 \right)$ is divided by $p$. Let $n = 91677$, and let $\text{result}$ be the sum of $\phi... | 9,324 | graphs = [
Graph(
let={
"n1": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6)), IsPrime(Var("n"))))),
"w": SmallOmega(n=Ref(name='n1')),
"p": Const(2),
"v": Mod(value=Sum(Factorial(Sub(Ref("p"), SumOverDi... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/OMEGA_ONE",
"MOBIUS_COPRIME",
"WILSON"
] | 8d2f63 | nt_sum_totient_over_divisors_v1 | null | 6 | 2 | [
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME",
"OMEGA_ONE",
"WILSON"
] | 4 | 0.017 | 2026-02-08T13:16:27.376554Z | {
"verified": true,
"answer": 9324,
"timestamp": "2026-02-08T13:16:27.393541Z"
} | 6aa8ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 991
},
"timestamp": "2026-02-09T20:26:40.247Z",
"answer": 9324
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "OMEGA_ONE",
"st... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
ba3c27 | nt_min_coprime_above_v1_397696148_2402 | Let $ A $ be the set of integers $ n $ such that $ 75625 < n \le 75710 $ and $ \gcd(n, 75) = 1 $. Let $ a $ be the smallest element of $ A $. Let $ b $ be the largest prime number less than or equal to $ 7002 $. Compute $ (a \bmod 317) + b \cdot (a \bmod 313) $, and find the remainder when this quantity is divided by $... | 40,373 | graphs = [
Graph(
let={
"_n": Const(65550),
"start": Const(75625),
"upper": Const(75710),
"modulus": Const(75),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var(... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_min_coprime_above_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.013 | 2026-02-08T13:09:24.353925Z | {
"verified": true,
"answer": 40373,
"timestamp": "2026-02-08T13:09:24.367198Z"
} | 573427 | 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": 2282
},
"timestamp": "2026-02-15T12:45:46.437Z",
"answer": 40373
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a33fbf | comb_factorial_compute_v1_1218484723_6904 | Let $n$ be the minimum value of $10a^2 - 32ab + 32b^2$ over all positive integers $a, b$ with $1 \le a, b \le 20$. Let $M = n!$. Find the remainder when $38809 - M$ is divided by $56706$. | 55,195 | graphs = [
Graph(
let={
"_n": Const(38809),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)))), expr=Sum(Mul(Const(-32), Var("a"... | COMB | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | comb_factorial_compute_v1 | null | 4 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.001 | 2026-02-25T08:21:38.169635Z | {
"verified": true,
"answer": 55195,
"timestamp": "2026-02-25T08:21:38.171099Z"
} | e367f6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 4959
},
"timestamp": "2026-03-30T03:04:26.218Z",
"answer": 55195
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
3207bc | diophantine_fbi2_count_v1_153355830_2273 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $A$ be the set of positive integers $d$ such that $2 \le d \le 129$, $d$ divides $k$, $\frac{k}{d} \ge 2$, and $\frac{k}{d} \le t_{\text{max}}$, where $t_{\text{max}}$ is the number of integers $t$ ... | 20 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr... | NT | null | COUNT | sympy | VIETA_SUM | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"VIETA_SUM"
] | 3 | 0.096 | 2026-02-08T07:01:29.397888Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T07:01:29.493391Z"
} | b9147e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 5007
},
"timestamp": "2026-02-13T07:25:45.443Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lem... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7e2171 | diophantine_fbi2_min_v1_677425708_3368 | Let $m$ be the number of prime numbers between 2 and 11, inclusive. Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 32400$. Let $u$ be the number of integers $t$ with $18 \leq t \leq 780$ for which there exist positive integers $a \leq 10$ and $b \leq 85$ suc... | 6,646 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_c")), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"_n": Const(2),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/LIN_FORM",
"B3"
] | c20eb1 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B3",
"COUNT_PRIMES",
"LIN_FORM"
] | 3 | 0.017 | 2026-02-08T05:40:37.163004Z | {
"verified": true,
"answer": 6646,
"timestamp": "2026-02-08T05:40:37.180033Z"
} | 83c3bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2925
},
"timestamp": "2026-02-12T12:21:30.457Z",
"answer": 6646
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e77c04 | antilemma_k2_v1_655260480_3488 | Let $n = 311$. Define $s$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient function. Compute the value of
$$
\sum_{k=1}^{s} \phi(k) \left\lfloor \frac{311}{k} \right\rfloor.
$$ | 48,516 | graphs = [
Graph(
let={
"_m": Const(311),
"_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(311), Var("k"))))),
},
goal=Re... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.002 | 2026-02-08T17:24:29.404299Z | {
"verified": true,
"answer": 48516,
"timestamp": "2026-02-08T17:24:29.406765Z"
} | 47d3d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 851
},
"timestamp": "2026-02-18T01:35:01.745Z",
"answer": 48516
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d82574 | nt_count_divisible_and_v1_784195855_5171 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 6$. Define $d_1$ to be the maximum value of $xy$ over all such pairs. Let $d_2 = 12$. Let $N$ be the number of positive integers $n$ with $1 \leq n \leq 58320$ such that
\[
n \equiv \sum_{d \mid \gcd(99, M)} \mu(d) \pmod{d_1}
\]
and... | 1,620 | graphs = [
Graph(
let={
"_n": Const(99),
"upper": Const(58320),
"d1": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), ... | NT | null | COUNT | sympy | L3C | [
"L3C/MOBIUS_COPRIME",
"B1"
] | 2fee23 | nt_count_divisible_and_v1 | null | 7 | 0 | [
"B1",
"L3C",
"MOBIUS_COPRIME"
] | 3 | 1.967 | 2026-02-08T07:42:33.891276Z | {
"verified": true,
"answer": 1620,
"timestamp": "2026-02-08T07:42:35.858486Z"
} | af2b98 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 307,
"completion_tokens": 603
},
"timestamp": "2026-02-20T04:52:12.421Z",
"answer": 1620
}
] | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
4c8566 | nt_count_intersection_v1_655260480_2842 | Let $a$ be the largest prime number at most 6. Let $N = 20000$. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \leq N$, $a$ divides $n_1$, and $\gcd(n_1, 18) = 1$. | 1,333 | graphs = [
Graph(
let={
"N": Const(20000),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6)), IsPrime(Var("n"))))),
"b": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_intersection_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.368 | 2026-02-08T17:01:58.132577Z | {
"verified": true,
"answer": 1333,
"timestamp": "2026-02-08T17:01:59.500547Z"
} | 1176da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1038
},
"timestamp": "2026-02-17T18:10:00.961Z",
"answer": 1333
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e12108 | nt_count_divisors_in_range_v1_2051736721_1190 | Let $D$ be the set of all positive divisors $d_1$ of $1358360$ such that $1 \leq d_1 \leq 1160$. Let $b$ be the sum of $\phi(d)$ over all $d \in D$, where $\phi$ denotes Euler's totient function. Let $n = 27720$, $a = 1$, and let $R$ be the set of all positive divisors $d_2$ of $n$ such that $a \leq d_2 \leq b$. Let $q... | 60 | graphs = [
Graph(
let={
"n": Const(27720),
"a": Const(1),
"b": SumOverDivisors(n=MaxOverSet(set=SolutionsSet(var=Var(name='d1'), condition=And(Geq(left=Var(name='d1'), right=Const(value=1)), Leq(left=Var(name='d1'), right=Const(value=1160)), Divides(divisor=Var(name='d1')... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/K3"
] | 97a225 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"K3",
"MAX_DIVISOR"
] | 2 | 0.028 | 2026-02-08T15:52:59.717558Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T15:52:59.745489Z"
} | 9c7ba3 | 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": 3389
},
"timestamp": "2026-02-16T15:59:45.073Z",
"answer": 60
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a7d506 | modular_sum_quadratic_residues_v1_2051736721_5985 | Let $p = 461$. Define $\text{result} = \frac{p(p-1)}{4}$. Let $S$ be the set of all positive integers $n$ such that $2 \leq n \leq 316$ and $n$ is prime. Let $D$ be the set of all positive divisors $d$ of 99221 such that $1 \leq d \leq \max(S)$. Compute the remainder when
$$
\text{result} \bmod 317 + 3001 \cdot \left(\... | 57,829 | graphs = [
Graph(
let={
"_m": Const(59273),
"_n": Const(317),
"p": Const(461),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=Sum(Mod(value=Ref("result"), modulus=Ref("_n")), Mul(Const(3001), Mod(value=Ref("result")... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_DIVISOR"
] | c7ab7c | modular_sum_quadratic_residues_v1 | two_moduli | 6 | 0 | [
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T18:53:44.593652Z | {
"verified": true,
"answer": 57829,
"timestamp": "2026-02-08T18:53:44.596714Z"
} | 888faa | 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": 1365
},
"timestamp": "2026-02-18T20:17:00.908Z",
"answer": 57829
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4bc4ea | nt_count_intersection_v1_124444284_618 | Let $N = 5000$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq N$, $3$ divides $n$, and $\gcd(n, 14) = d$, where $d = \sum_{k \mid \gcd(15,22)} \mu(k)$ and $\mu$ denotes the Möbius function.
Compute the number of elements in $S$. | 714 | graphs = [
Graph(
let={
"N": Const(5000),
"a": Const(3),
"b": Const(14),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Re... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_intersection_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 0.9 | 2026-02-08T03:24:21.969349Z | {
"verified": true,
"answer": 714,
"timestamp": "2026-02-08T03:24:22.869313Z"
} | 6d9909 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1257
},
"timestamp": "2026-02-09T19:50:01.189Z",
"answer": 714
},
{
"id... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemm... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
4d3eef | comb_count_surjections_v1_1218484723_5322 | Let $k$ be the number of integers $a$ with $0 \le a \le 72$ such that
$$(\,(a^{2} + a -34 \bmod 73)^{2} + (a^{2} + a -34 \bmod 73) -34 \bmod 73\,)^{2} + (\,(a^{2} + a -34 \bmod 73)^{2} + (a^{2} + a -34 \bmod 73) -34 \bmod 73\,) -34 \bmod 73 = a,$$
$$(a^{36} \bmod 73) + (a^{2} + a -34 \bmod 73^{36} \bmod 73) + (\,(a^{2}... | 150 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(72)), Eq(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-34)), mo... | COMB | NT | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE"
] | 7c2be8 | comb_count_surjections_v1 | null | 7 | 0 | [
"POLY_ORBIT_LEGENDRE"
] | 1 | 0.004 | 2026-02-25T06:56:18.266607Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-25T06:56:18.270651Z"
} | 428c1d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 441,
"completion_tokens": 14010
},
"timestamp": "2026-03-29T20:31:41.205Z",
"answer": 1
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
42bbbf | geo_count_lattice_rect_v1_1431428450_1265 | Compute the number of lattice points in the rectangle $[0, 222] \times [0, 89]$, including the boundary. | 20,070 | graphs = [
Graph(
let={
"a": Const(222),
"b": Const(89),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T13:59:10.421281Z | {
"verified": true,
"answer": 20070,
"timestamp": "2026-02-08T13:59:10.422375Z"
} | bafef3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 217
},
"timestamp": "2026-02-24T19:25:31.283Z",
"answer": 20070
},
{
"i... | 1 | [] | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||||
5d328b | nt_count_coprime_v1_865884756_1005 | Let $k = 49$ and $N = 84100$. Define $A$ to be the set of all positive integers $n$ such that $1 \le n \le N$ and $\gcd(n, k) = 1$. Let $r$ be the remainder when $44121 \cdot |A|$ is divided by $88255$. Find the value of $r$. | 60,971 | graphs = [
Graph(
let={
"upper": Const(84100),
"k": Const(49),
"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))))),
"Q": Mod(value=Mul(Const(4412... | NT | null | COUNT | sympy | K14 | [
"K14/C5/MOBIUS_COPRIME"
] | 27d800 | nt_count_coprime_v1 | null | 3 | 0 | [
"C5",
"K14",
"MOBIUS_COPRIME"
] | 3 | 11.935 | 2026-02-08T15:43:25.394477Z | {
"verified": true,
"answer": 60971,
"timestamp": "2026-02-08T15:43:37.329837Z"
} | 2da718 | 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": 2811
},
"timestamp": "2026-02-16T12:02:52.709Z",
"answer": 60971
},
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fa4c98 | nt_count_divisors_in_range_v1_865884756_4376 | Let $n$ be the number of positive integers $n_1 \leq 13860$ such that $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{11}$. Compute the number of positive divisors $d$ of $n$ such that $7 \leq d \leq 107$. | 21 | graphs = [
Graph(
let={
"_n": Const(13860),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"L3C"
] | 73f8b0 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"L3C",
"MAX_DIVISOR"
] | 2 | 0.363 | 2026-02-08T17:54:35.938960Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T17:54:36.302434Z"
} | 6629ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 3223
},
"timestamp": "2026-02-18T09:46:53.704Z",
"answer": 21
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1be8cd | diophantine_product_count_v1_168721529_535 | Let $k = \sum_{i=1}^{15} i$. Compute the number of positive integers $x$ such that $1 \leq x \leq 113$, $x$ divides $k$, and $\frac{k}{x} \leq 113$. Let $N$ be this number. Let $Q$ be the sum of $26896$ and $\sum_{i=0}^{d-1} d_i (i+1)^2$, where $d$ is the number of digits in $N$ and $d_i$ is the $i$-th digit of $N$ (st... | 26,904 | graphs = [
Graph(
let={
"_n": Const(26896),
"k": Summation(var="k", start=Const(1), end=Const(15), expr=Var("k")),
"upper": Const(113),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Di... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_product_count_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.008 | 2026-02-08T13:05:56.866000Z | {
"verified": true,
"answer": 26904,
"timestamp": "2026-02-08T13:05:56.874248Z"
} | 7b4046 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 1199
},
"timestamp": "2026-02-09T06:02:35.569Z",
"answer": 26904
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "o... | {
"lo": -2,
"mid": 1.85,
"hi": 5.2
} | ||
b7bf57 | nt_count_phi_equals_v1_1978505735_1176 | Let $S$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 60$, $1 \le b \le 350$, $9 \le t \le 1700$, and $t = 5a + 4b$. Let $u$ be the number of elements in $S$. Compute the number of positive integers $n$ such that $1 \le n \le u$ and $\phi(n) = 372$. | 2 | graphs = [
Graph(
let={
"upper": 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=60)), Geq(left=Var(name='b'), right=Const(va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_phi_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.144 | 2026-02-08T15:52:50.498163Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:52:50.642271Z"
} | 097389 | 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": 5768
},
"timestamp": "2026-02-16T14:54:06.522Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
59671e | sequence_count_fib_divisible_v1_865884756_144 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 197136$. Define $s_0$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $D$ be the set of all positive integers $d_1$ such that $1 \leq d_1 \leq s_0$ and $d_1$ divides $816072$. Define $u$ to be the maximum element o... | 29 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(M... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 33b851 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.066 | 2026-02-08T15:12:32.348233Z | {
"verified": true,
"answer": 29,
"timestamp": "2026-02-08T15:12:32.413966Z"
} | d68f5c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 3620
},
"timestamp": "2026-02-11T11:05:13.895Z",
"answer": 0
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "... | {
"lo": 1.94,
"mid": 5.23,
"hi": 8.52
} | ||
48c948 | comb_bell_compute_v1_548369836_277 | Let $n = 9$. Define $B_n$ to be the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Let $S$ be the set of all nonnegative integers $j$ such that
\begin{itemize}
\item $j \geq \sum_{d \mid 28} \mu(d)$,
\item $j \leq 60399$, and
\item $\binom{60399}{j} \equiv \sum_{d \mid \gcd(11,13)} \... | 74,086 | graphs = [
Graph(
let={
"_n": Const(87041),
"n": Const(9),
"result": Bell(Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), SumOverDivisors(n=Const(value=28), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("j"), Cons... | NT | COMB | COMPUTE | sympy | V8 | [
"V8",
"MOBIUS_COPRIME",
"MOBIUS_SUM"
] | fe0397 | comb_bell_compute_v1 | negation_mod | 7 | 0 | [
"MOBIUS_COPRIME",
"MOBIUS_SUM",
"V8"
] | 3 | 0.004 | 2026-02-08T02:50:20.683922Z | {
"verified": true,
"answer": 74086,
"timestamp": "2026-02-08T02:50:20.687560Z"
} | ee3a5b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 2074
},
"timestamp": "2026-02-08T20:17:39.613Z",
"answer": 74086
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"... | {
"lo": -2.08,
"mid": 1.77,
"hi": 4.93
} | ||
e82676 | comb_bell_compute_v1_784195855_8788 | Let $a = 3$ and $b = 3$. Define $n_2 = a + b$ and
$$
m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = 7$ and
$$
w = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Define $n = 9 + m + w$. Compute the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. | 21,147 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(3),
"n2": Sum(Ref("a"), Ref("b")),
"m": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(7),
"w": Summat... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_bell_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T16:19:02.390181Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T16:19:02.391562Z"
} | 20a0b2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 575
},
"timestamp": "2026-02-24T20:37:09.767Z",
"answer": 21147
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
991223 | diophantine_fbi2_count_v1_1918700295_3818 | Let $n = 84$. Consider the Cartesian product of the sets $\{1, 2, \dots, 20\}$ and $\{1, 2, \dots, 21\}$, and let $k$ be the number of elements in this product. Define $D$ to be the set of all integers $d$ such that $5 \leq d \leq n$, $d$ divides $k$, and the quotient $k/d$ satisfies $5 \leq k/d \leq 84$. Let $r$ be th... | 64,128 | graphs = [
Graph(
let={
"_n": Const(84),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=Const(1), end=Const(21)))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.023 | 2026-02-08T08:57:47.931276Z | {
"verified": true,
"answer": 64128,
"timestamp": "2026-02-08T08:57:47.954418Z"
} | 1654df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1320
},
"timestamp": "2026-02-13T22:46:21.880Z",
"answer": 64128
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e1006f | diophantine_fbi2_count_v1_124444284_3701 | Let $k = 1260$. Compute the number of positive integers $d$ such that $5 \leq d \leq 132$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 130$. | 20 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(1260),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(132)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div... | NT | null | COUNT | sympy | B3 | [
"K13"
] | 8d970a | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"B3",
"K13"
] | 2 | 0.033 | 2026-02-08T05:32:52.332524Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T05:32:52.365983Z"
} | ae469f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 2551
},
"timestamp": "2026-02-12T10:30:06.271Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.32,
"hi": 6.32
} | ||
aef5fa | geo_count_lattice_triangle_v1_1874849503_684 | Let the area of a triangle with vertices at $(0,1)$, $(121,128)$, and $(128,0)$ be denoted by $A$. The quantity $2A$ is given by
$$
|121 \cdot 128 + 128 \cdot (-1) + 0|.
$$
Let $b$ be the sum of the greatest common divisors of the absolute differences in coordinates along each edge of the triangle, specifically
$$
\gcd... | 7,616 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=121), Const(value=128)), Mul(Const(value=128), Sub(left=Const(value=0), right=Const(value=1))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=121)), b=Abs(arg=Const(value=1))), GCD(a=Abs(arg=Sub(left=Const(value=128), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 6 | 0 | null | null | 0.005 | 2026-02-08T13:15:11.708565Z | {
"verified": true,
"answer": 7616,
"timestamp": "2026-02-08T13:15:11.713878Z"
} | ef984c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 1915
},
"timestamp": "2026-02-09T19:48:45.932Z",
"answer": 8188
},
{
... | 1 | [] | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||||
b9e283 | nt_lcm_compute_v1_1353956133_99 | Let $T$ be the set of all integers $t$ with $15 \leq t \leq 4266$ for which there exist positive integers $a \leq 386$ and $b \leq 132$ such that $t = 9a + 6b$. Let $a = |T|$ and $b = 975$. Define $L = \mathrm{lcm}(a, b)$. Compute the value of
$$
\sum_{i=0}^{\mathrm{num\_digits}(L) - 1} \mathrm{digit}_i(L) \cdot (i+1)... | 40,632 | graphs = [
Graph(
let={
"_n": Const(2),
"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=386)), Geq(left=Var(... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_lcm_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:18:56.236402Z | {
"verified": true,
"answer": 40632,
"timestamp": "2026-02-08T11:18:56.238757Z"
} | 5c1a96 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 4776
},
"timestamp": "2026-02-14T11:33:29.252Z",
"answer": 40632
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d6519e | antilemma_k3_v1_153355830_2874 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $83353$. Find the remainder when $8100 - x$ is divided by $93518$. | 18,265 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=83353), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(8100), Ref("x")), modulus=Const(93518)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T07:27:27.435652Z | {
"verified": true,
"answer": 18265,
"timestamp": "2026-02-08T07:27:27.436117Z"
} | cd193c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 1133
},
"timestamp": "2026-02-13T10:24:57.007Z",
"answer": 18265
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
004776 | nt_gcd_compute_v1_168721529_408 | Let $m=53361$.
Let $N$ be the number of integers $t$ for which there exist integers $a$ and $b$ such that $1\le a\le6$, $1\le b\le10$, $14\le t\le76$, and
$$t=7a+3b+4.$$
Let $n_1$ be the greatest prime number $n$ such that
$$n\ge A\quad\text{and}\quad n\le N,$$
where $A$ is the number of positive integers $p$ for whi... | 86,757 | graphs = [
Graph(
let={
"_m": Const(53361),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=V... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW/OMEGA_ONE",
"LIN_FORM/MAX_PRIME_BELOW/OMEGA_ONE",
"COPRIME_PAIRS/DIVISOR_PARITY"
] | 6a6a7f | nt_gcd_compute_v1 | null | 7 | 2 | [
"COPRIME_PAIRS",
"DIVISOR_PARITY",
"LIN_FORM",
"MAX_PRIME_BELOW",
"OMEGA_ONE"
] | 5 | 0.008 | 2026-02-08T13:02:30.609757Z | {
"verified": true,
"answer": 86757,
"timestamp": "2026-02-08T13:02:30.617528Z"
} | 440ce1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 409,
"completion_tokens": 2902
},
"timestamp": "2026-02-09T04:42:21.554Z",
"answer": 86757
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": 1.49,
"mid": 4.54,
"hi": 7.77
} | ||
64847f | comb_count_surjections_v1_865884756_6367 | Let $n = 8$ and $k = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $R$ be the absolute value of this result.
Let $T$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4$. Compute the number of elements in $T$.
Let $d_i$ d... | 43,448 | graphs = [
Graph(
let={
"n": Const(8),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 43779f | comb_count_surjections_v1 | digits_weighted_mod | 6 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T19:10:04.958318Z | {
"verified": true,
"answer": 43448,
"timestamp": "2026-02-08T19:10:04.962597Z"
} | 127f1d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 2566
},
"timestamp": "2026-02-18T21:27:31.610Z",
"answer": 43448
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
43bac8 | nt_count_divisible_and_v1_655260480_2139 | Let $d_1$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $d_2 = 12$. Compute the number of positive integers $n$ such that $1 \leq n \leq 91296$, $d_1$ divides $n$, and $d_2$ divides $n$. Let $Q$ be the remainder when $60552$ times this count is divided by $... | 71,847 | graphs = [
Graph(
let={
"upper": Const(91296),
"d1": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_divisible_and_v1 | null | 3 | 0 | [
"B1"
] | 1 | 3.796 | 2026-02-08T16:35:01.173572Z | {
"verified": true,
"answer": 71847,
"timestamp": "2026-02-08T16:35:04.969799Z"
} | aff2d9 | 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": 974
},
"timestamp": "2026-02-17T07:06:21.000Z",
"answer": 71847
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
51b71c_l | comb_factorial_compute_v1_717093673_819 | Let $n_1 = 0$ and $n_2 = 0$. Define
$$
e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}
$$
and
$$
w = \sum_{k_1 = \sum_{k_2=0}^{5} (-1)^{k_2} \binom{5}{k_2}}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}.
$$
Let $n = 7 \cdot e \cdot w$. Compute $n!$. | 1 | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_factorial_compute_v1 | null | 2 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.003 | 2026-02-08T15:42:09.008436Z | {
"verified": false,
"answer": 5040,
"timestamp": "2026-02-08T15:42:09.011151Z"
} | eea92b | 51b71c | legacy_text | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 560
},
"timestamp": "2026-02-24T18:25:15.374Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | |
5ffa1f | comb_catalan_compute_v1_1520064083_9181 | Let $n$ be the number of integers $t$ such that $20 \leq t \leq 32$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b + 15$. Let $Q$ be the remainder when $70178$ times the $n$th Catalan number is divided by $80625$. Compute $Q$. | 63,908 | graphs = [
Graph(
let={
"_n": Const(80625),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T10:35:14.723516Z | {
"verified": true,
"answer": 63908,
"timestamp": "2026-02-08T10:35:14.725035Z"
} | 40af02 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2944
},
"timestamp": "2026-02-24T12:07:43.094Z",
"answer": 63908
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
04ac9b | nt_min_with_divisor_count_v1_458359167_2896 | Let $ n $ be a positive integer such that $ 1 \leq n \leq 45369 $ and the number of positive divisors of $ n $ is exactly 10. Determine the value of the smallest such $ n $. | 48 | graphs = [
Graph(
let={
"upper": Const(45369),
"div_count": Const(10),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("re... | NT | null | EXTREMUM | sympy | K3 | [
"K3"
] | 54c41e | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"K3"
] | 1 | 2.226 | 2026-02-08T06:49:33.756027Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T06:49:35.981681Z"
} | dd3fcc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 841
},
"timestamp": "2026-02-15T17:47:44.917Z",
"answer": 45328
},
{
"id": 11... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
458592 | comb_bell_compute_v1_1431428450_920 | Let $n$ be the number of integers $t$ such that there exist integers $a$ and $b$ with $1 \le a \le 3$, $1 \le b \le 3$, $5 \le t \le 15$, and $t = 2a + 3b$. Define $r = B_n$, the $n$th Bell number. Compute the remainder when $74732 \cdot r$ is divided by $92583$. | 58,377 | 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... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:47:09.017013Z | {
"verified": true,
"answer": 58377,
"timestamp": "2026-02-08T13:47:09.019738Z"
} | 74662e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T19:06:42.904Z",
"answer": 39964
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
cceb52 | geo_count_lattice_rect_v1_784195855_5004 | Let $a = 64$ and $b = 101$. Define $R$ as the rectangle with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Let $L$ be the number of lattice points (points with integer coordinates) inside or on the boundary of $R$. Find the remainder when $87991 \cdot L$ is divided by $89154$. | 45,708 | graphs = [
Graph(
let={
"a": Const(64),
"b": Const(101),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(87991), Ref("result")), modulus=Const(89154)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.002 | 2026-02-08T07:32:54.532917Z | {
"verified": true,
"answer": 45708,
"timestamp": "2026-02-08T07:32:54.534788Z"
} | 79141d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T08:19:45.541Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
84fa7f_l | modular_product_range_v1_1248542787_159 | Let $n = 90$. Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq 200244$ and $444$ divides $k$. Let $P$ be the product of all integers from $n$ to $|S|$, inclusive. Compute the remainder when $P$ is divided by $11827$. | 1 | ALG | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | modular_product_range_v1 | null | 5 | 0 | [
"C2"
] | 1 | 0.004 | 2026-02-08T02:58:39.053524Z | {
"verified": false,
"answer": 5620,
"timestamp": "2026-02-08T02:58:39.057516Z"
} | ccb2d2 | 84fa7f | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T21:17:58.845Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 4.62,
"mid": 6.54,
"hi": 9.53
} | |
9855b7 | comb_sum_binomial_mod_v1_1353956133_425 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 10$. Define $m = \max_{(x,y) \in T} xy$. Compute the remainder when $$\sum_{k=m}^{62} \binom{89}{k}$$ is divided by $11927$. Let this remainder be $r$. Find the remainder when $35457 \cdot r$ is divided by $57184$. | 29,673 | graphs = [
Graph(
let={
"_n": Const(10),
"sum": Summation(var="k", start=MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_sum_binomial_mod_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.009 | 2026-02-08T11:26:42.741558Z | {
"verified": true,
"answer": 29673,
"timestamp": "2026-02-08T11:26:42.750795Z"
} | 033a03 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T13:48:19.061Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
0c84c9 | antilemma_sum_equals_v1_2051736721_6180 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 46$, $1 \leq i \leq 44$, and $1 \leq j \leq 45$.
Compute the remainder when $44121 \cdot x$ is divided by $51517$. | 35,195 | graphs = [
Graph(
let={
"_n": Const(46),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(44)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.057 | 2026-02-08T18:58:33.372425Z | {
"verified": true,
"answer": 35195,
"timestamp": "2026-02-08T18:58:33.429320Z"
} | 90c13f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1331
},
"timestamp": "2026-02-18T21:01:56.314Z",
"answer": 35195
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
084523 | antilemma_k3_v1_153355830_927 | Let $n = 95209$. Compute the sum of $\varphi(d)$ over all positive divisors $d$ of $n$, where $\varphi$ denotes Euler's totient function. | 95,209 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=95209), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:15:25.230105Z | {
"verified": true,
"answer": 95209,
"timestamp": "2026-02-08T04:15:25.230536Z"
} | cccfc7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 502
},
"timestamp": "2026-02-10T16:08:22.235Z",
"answer": 95209
},
{
"... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
9b4161 | alg_poly_orbit_hensel_v1_1218484723_50 | Define $N = (2a^3 - 4a) \bmod 5329$, $M = (2N^3 - 4N) \bmod 5329$, $R = (2M^3 - 4M) \bmod 5329$, and $S = (2R^3 - 4R) \bmod 5329$. Find the number of non-negative integers $a$ with $0 \le a \le 10125099$ such that $S = a$, $N \ne a$, $M \ne a$, and $R \ne a$. | 7,600 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(-4), Var("a"))), modulus=Const(5329)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(-4), Ref("p1"))), modulus=Const(5329)),
"p3": Mod(value=Sum(Mul(Cons... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.039 | 2026-02-25T01:44:37.866225Z | {
"verified": true,
"answer": 7600,
"timestamp": "2026-02-25T01:44:37.905454Z"
} | 6eb556 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T08:26:19.895Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.77,
"mid": 6.8,
"hi": 9.83
} | ||
27450e | nt_count_digit_sum_v1_48377204_1970 | Let $A$ be the number of integers $t$ such that $9 \leq t \leq 10013$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 633$, $1 \leq b \leq 2791$, and $t = 7a + 2b$. Let $B$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 581$ and $\binom{C}{j}$ is odd, where $C$ is the number of intege... | 15,655 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": 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=633)), Geq(left=... | ALG | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/V8"
] | 654a7e | nt_count_digit_sum_v1 | null | 6 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.411 | 2026-02-08T16:32:01.716503Z | {
"verified": true,
"answer": 15655,
"timestamp": "2026-02-08T16:32:02.127500Z"
} | 508f6a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 5056
},
"timestamp": "2026-02-17T06:24:13.697Z",
"answer": 15655
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
979448 | comb_count_derangements_v1_153355830_2366 | Let $n$ be the smallest divisor of $77077$ that is at least $2$. Compute $71289 - !n$, where $!n$ denotes the number of derangements of $n$ objects. | 69,435 | 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(77077))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Sub(Const(71289), Ref("result"))... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T07:05:01.025241Z | {
"verified": true,
"answer": 69435,
"timestamp": "2026-02-08T07:05:01.026165Z"
} | c94358 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 903
},
"timestamp": "2026-02-13T07:43:44.338Z",
"answer": 69435
},
{
... | 1 | [
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
02a8ba | nt_count_divisible_and_v1_677425708_1213 | Let $d_1 = 4$ and $d_2 = \sum_{k=1}^{3} k$. Let $S$ be the set of all positive integers $n$ such that $n \leq 44064$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute the number of elements in $S$. | 3,672 | graphs = [
Graph(
let={
"upper": Const(44064),
"d1": Const(4),
"d2": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(M... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 1.521 | 2026-02-08T04:02:12.285084Z | {
"verified": true,
"answer": 3672,
"timestamp": "2026-02-08T04:02:13.806150Z"
} | aa83d6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 669
},
"timestamp": "2026-02-09T17:05:47.897Z",
"answer": 3672
},
{
"id... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status":... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
4cf969_l | comb_count_permutations_fixed_v1_124444284_3001 | Let $m = 41327$. Let $d_0$ be the smallest positive divisor of $m$ that is at least the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $n = d_0$ and let $k = 6$. Compute the value of
$$
\binom{n}{k} \cdot !(n - k),
$$
where $!... | 0 | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T05:08:26.010531Z | {
"verified": false,
"answer": 20328,
"timestamp": "2026-02-08T05:08:26.013782Z"
} | 5ad126 | 4cf969 | legacy_text | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1751
},
"timestamp": "2026-02-11T22:53:09.553Z",
"answer": 20328
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"stat... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | |
f0020b | diophantine_fbi2_min_v1_458359167_3279 | Let $n = 12$ and $k = 26$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $P$ be the set of all values of $xy$ as $(x, y)$ ranges over this set. Let $u$ be the maximum value in $P$. Now consider the set of all integers $d$ such that $2 \leq d \leq u$, $d$ divides $k$, and... | 2 | graphs = [
Graph(
let={
"_n": Const(12),
"k": Const(26),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), exp... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | 5b950e | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.011 | 2026-02-08T08:15:25.446183Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T08:15:25.456722Z"
} | 739f64 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 345
},
"timestamp": "2026-02-15T19:45:50.408Z",
"answer": 13
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
e4cb75 | nt_min_crt_v1_971394319_486 | Let $m = 9$, $k = 11$, and $a = 7$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $P$ be the set of all values $xy$ for such pairs. Define $b$ to be the maximum value in $P$. Determine the value of the smallest positive integer $n$ such that $1 \leq n \leq 99$, $n \equiv... | 97 | graphs = [
Graph(
let={
"m": Const(9),
"k": Const(11),
"a": Const(7),
"b": 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"... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"B1"
] | 5b950e | nt_min_crt_v1 | null | 5 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.243 | 2026-02-08T13:07:06.997192Z | {
"verified": true,
"answer": 97,
"timestamp": "2026-02-08T13:07:07.240207Z"
} | 1fbca6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 622
},
"timestamp": "2026-02-15T09:46:07.736Z",
"answer": 97
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
642b1d | comb_count_surjections_v1_1742523217_4380 | Let $n$ be the number of elements in the Cartesian product $\{1, 2\} \times \{1, 2, 3\}$. Let $k = 6$. Let $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $m = |r| + 2$. The Fibonacci entry point modulo $m$ is defined as the smallest positive integer $t$ such that the $t$th F... | 342 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(3)))),
"k": Const(6),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
... | COMB | NT | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T07:14:02.757539Z | {
"verified": true,
"answer": 342,
"timestamp": "2026-02-08T07:14:02.759870Z"
} | d96207 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 4398
},
"timestamp": "2026-02-24T07:47:45.243Z",
"answer": 342
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
d48620 | comb_count_partitions_v1_971394319_11 | Let $S$ be the set of all integers $t$ such that $17 \leq t \leq 65$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 5$, and $t = 2a + 7b + 8$. Let $n$ be the number of elements in $S$. Compute the number of integer partitions of $n$. | 63,261 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T12:48:02.888415Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T12:48:02.892244Z"
} | 230731 | 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": 4084
},
"timestamp": "2026-02-24T16:24:05.670Z",
"answer": 63261
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
22aeda | alg_poly4_min_v1_601307018_2446 | Let $A = \left|\{ v : 41 \leq v \leq 21689,\ \text{there exist integers } a, b \text{ with } 1 \leq a, b \leq 23 \text{ such that } 41a^2 + 2b^2 - 2ab = v \}\right|$. Find the minimum value of $69248 \cdot a^4$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq A$ and $1 \leq b \leq 402$. | 69,248 | graphs = [
Graph(
let={
"_n": Const(402),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(41)), Leq(Var("v... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_poly4_min_v1 | null | 6 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.268 | 2026-03-10T03:11:04.343581Z | {
"verified": true,
"answer": 69248,
"timestamp": "2026-03-10T03:11:04.611323Z"
} | 9fa117 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 889
},
"timestamp": "2026-03-29T05:21:48.441Z",
"answer": 69248
},
{
"i... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
c98680 | nt_count_with_divisor_count_v1_1874849503_1274 | Let $N$ be the smallest divisor of $31603$ that is greater than or equal to $2$. Determine the number of positive integers $n$ such that $1 \leq n \leq 14400$ and the number of positive divisors of $n$ is exactly $N$. Let $Q$ be the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|\... | 4 | graphs = [
Graph(
let={
"upper": Const(14400),
"div_count": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(31603))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n... | NT | null | COUNT | sympy | LTE_DIFF | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"LTE_DIFF",
"MIN_PRIME_FACTOR"
] | 2 | 5.844 | 2026-02-08T13:44:02.831665Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T13:44:08.676136Z"
} | c97ee9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1496
},
"timestamp": "2026-02-10T03:01:59.885Z",
"answer": 4
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
a88603 | nt_count_coprime_v1_1742523217_999 | Let $k = 10$. Determine the number of positive integers $n$ such that $1 \leq n \leq 27720$ and $\gcd(n, k) = \sum_{d \mid \gcd(12,25)} \mu(d)$, where $\mu$ denotes the M\"obius function. Compute this number. | 11,088 | graphs = [
Graph(
let={
"upper": Const(27720),
"k": Const(10),
"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")), SumOverDivisors(n=GCD(a=Const(value=12), b=Const(value=... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_coprime_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 2.127 | 2026-02-08T03:22:55.200437Z | {
"verified": true,
"answer": 11088,
"timestamp": "2026-02-08T03:22:57.327394Z"
} | 05b7d0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1230
},
"timestamp": "2026-02-10T01:47:42.066Z",
"answer": 11088
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
dba581 | nt_min_coprime_above_v1_1526740231_137 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 68$. Let $P$ be the set of all products $xy$ for $(x, y) \in S$. Let $\text{start}$ be the maximum value in $P$. Let $\text{result}$ be the smallest integer $n$ such that $\text{start} < n \leq 1508$ and $\gcd(n, 342) = 1$. Determi... | 1,157 | graphs = [
Graph(
let={
"_n": Const(68),
"start": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | 5b950e | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.03 | 2026-02-08T11:22:02.851696Z | {
"verified": true,
"answer": 1157,
"timestamp": "2026-02-08T11:22:02.882186Z"
} | a2a57a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 642
},
"timestamp": "2026-02-14T12:47:12.293Z",
"answer": 1157
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d0303e | geo_count_lattice_rect_v1_124444284_2424 | Let $a = 25$ and $b = 77$. Let $R$ be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute $\sum_{n=1}^{|R|} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 15,767 | graphs = [
Graph(
let={
"a": Const(25),
"b": Const(77),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Summation(var="n", start=Const(1), end=Abs(arg=Ref(name='result')), expr=NumDivisors(n=Var("n"))),
},
goal=Ref("Q"),
... | GEOM | NT | COUNT | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO"
] | bf46af | geo_count_lattice_rect_v1 | null | 4 | 0 | [
"IDENTITY_POW_ZERO"
] | 1 | 0.001 | 2026-02-08T04:39:16.759802Z | {
"verified": true,
"answer": 15767,
"timestamp": "2026-02-08T04:39:16.761111Z"
} | 6ebe53 | 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": 8246
},
"timestamp": "2026-02-24T01:29:29.289Z",
"answer": 15767
},
{
"... | 1 | [
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
}
] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
a9ba71 | nt_num_divisors_compute_v1_1520064083_3251 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 1607$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 243$, $1 \leq b \leq 196$, and $t = 5a + 2b$. Compute the number of positive divisors of $n$. | 2 | 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=243)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:32:01.942170Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T05:32:01.943612Z"
} | 16b834 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 5315
},
"timestamp": "2026-02-12T10:23:29.059Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
ba372f | nt_gcd_compute_v1_124444284_1281 | Let $n_0=17$. Let $n_1=1$ and let $h$ be the number of distinct prime factors of $n_1$.
Let $N=24017$. For each ordered pair $(x,y)$ of positive integers such that $xy=289$, consider the sum $x+y$. Let $M$ be the minimum of all such values of $x+y$ as $(x,y)$ ranges over these ordered pairs.
Let $T$ be the set of all... | 89,240 | graphs = [
Graph(
let={
"_n": Const(17),
"n1": Const(1),
"h": SmallOmega(n=Ref(name='n1')),
"n": Const(24017),
"f": Pow(MoebiusMu(n=Ref(name='n')), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Min... | NT | null | COMPUTE | sympy | B3 | [
"B3/C2/MOBIUS_SQUAREFREE",
"OMEGA_ZERO"
] | 3945ac | nt_gcd_compute_v1 | null | 6 | 2 | [
"B3",
"C2",
"MOBIUS_SQUAREFREE",
"OMEGA_ZERO"
] | 4 | 0.003 | 2026-02-08T03:48:25.793802Z | {
"verified": true,
"answer": 89240,
"timestamp": "2026-02-08T03:48:25.796473Z"
} | 073774 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 321,
"completion_tokens": 864
},
"timestamp": "2026-02-10T05:32:27.495Z",
"answer": 89240
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok_la... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
4d97ef | nt_count_divisible_v1_1874849503_159 | Let $n$ be a positive integer such that $1 \leq n \leq 56169$. Define $S$ to be the set of all such integers $n$ satisfying
$$
n \equiv \sum_{k=0}^{4} (-1)^k \binom{4}{k} \pmod{2}.
$$
Let $c = 35391$. Compute the remainder when $c$ multiplied by the number of elements in $S$ is divided by $65192$. | 3,612 | graphs = [
Graph(
let={
"upper": Const(56169),
"divisor": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Summation(var="k", start=Const(0),... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 1.828 | 2026-02-08T12:50:29.750497Z | {
"verified": true,
"answer": 3612,
"timestamp": "2026-02-08T12:50:31.578309Z"
} | c2a289 | 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": 2070
},
"timestamp": "2026-02-24T16:34:28.344Z",
"answer": 3612
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
54b059 | comb_count_derangements_v1_1431428450_614 | Let $m$ be the sum of all nonnegative integers $j \le 30$ for which $\binom{30}{j}$ is odd. Let $n$ be the number of positive integers $k \le m$ such that $20$ divides the $k$-th Fibonacci number. Compute the subfactorial of $n$, denoted $!n$, which is the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_m": Const(20),
"_n": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(30)), Eq(Mod(value=Binom(n=Const(30), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"n": Coun... | NT | COMB | COUNT | sympy | V8 | [
"V8/COUNT_FIB_DIVISIBLE"
] | 427a73 | comb_count_derangements_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"V8"
] | 2 | 0.003 | 2026-02-08T13:33:47.476865Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T13:33:47.479659Z"
} | d5ddc3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 4059
},
"timestamp": "2026-02-15T18:07:29.273Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
64c386 | antilemma_count_primes_v1_124444284_666 | Let $S$ be the set of all pairs $(p, q)$ of positive integers such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $S$. Determine the number of prime numbers $n$ such that $N \leq n \leq 1439$. | 228 | graphs = [
Graph(
let={
"_n": Const(1439),
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"COPRIME_PAIRS/COUNT_PRIMES",
"COUNT_PRIMES"
] | e28c42 | antilemma_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"COUNT_PRIMES",
"MAX_PRIME_BELOW"
] | 3 | 0.007 | 2026-02-08T03:26:36.303514Z | {
"verified": true,
"answer": 228,
"timestamp": "2026-02-08T03:26:36.310542Z"
} | cf76c8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 6543
},
"timestamp": "2026-02-09T04:41:13.368Z",
"answer": 228
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
350763 | nt_max_prime_below_v1_1918700295_2621 | Let $T$ be the set of all positive integers $t$ such that $10 \leq t \leq 243$ and there exist positive integers $a \leq 12$ and $b \leq 53$ satisfying $t = 7a + 3b$. Let $k$ be the number of positive integers in $T$ that are divisible by $111$. Let $S$ be the set of all prime numbers $n$ such that $k \leq n \leq 63504... | 63,499 | graphs = [
Graph(
let={
"upper": Const(63504),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/C2"
] | 03e7fc | nt_max_prime_below_v1 | null | 7 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 3.424 | 2026-02-08T08:08:09.633381Z | {
"verified": true,
"answer": 63499,
"timestamp": "2026-02-08T08:08:13.057050Z"
} | 40c43e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 3530
},
"timestamp": "2026-02-13T14:59:20.422Z",
"answer": 63499
},
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
12c059 | alg_sum_powers_v1_1218484723_2790 | Find the remainder when $\sum_{k=1}^{380} k^2$ is divided by $\min\{ x + y \mid x > 0, y > 0,\ xy = 9765625 \}$. | 430 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(1), end=Const(380), expr=Pow(Var("k"), Ref("_n"))), modulus=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsP... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sum_powers_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-25T04:30:48.905951Z | {
"verified": true,
"answer": 430,
"timestamp": "2026-02-25T04:30:48.909986Z"
} | 4feac1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 943
},
"timestamp": "2026-03-29T06:36:46.068Z",
"answer": 430
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
c7d43d | sequence_lucas_compute_v1_1915831931_1375 | Let $a = \sum_{k=1}^{b} k$, where $b = \sum_{k=1}^{3} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor$. Compute the remainder when $24693$ times the $a$-th Lucas number is divided by $83765$. | 21,393 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(83765),
"n": Summation(var="k", start=Const(1), end=Summation(var="k1", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(3), Var("k1"))))), expr=Var("k")),
"result": Lucas(arg=Re... | NT | null | COMPUTE | sympy | K2 | [
"K2/SUM_ARITHMETIC"
] | 5a4674 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.003 | 2026-02-08T16:03:26.665165Z | {
"verified": true,
"answer": 21393,
"timestamp": "2026-02-08T16:03:26.668605Z"
} | f1f498 | 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": 1886
},
"timestamp": "2026-02-16T19:38:14.032Z",
"answer": 21393
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6447d4 | alg_sum_ap_v1_1419126231_677 | Let $M$ be the minimum value of $4a^2 - 20ab + 29b^2$ over positive integers $a, b$ with $1 \leq a, b \leq 14$. Let $T$ be the number of integers $t$ in $[35, 3411]$ that can be written as $t = 14a + 4b + 17$ for some integers $a, b$ with $1 \leq a \leq 117$, $1 \leq b \leq 439$. Find the remainder when $\sum_{k=0}^{15... | 1,380 | graphs = [
Graph(
let={
"_m": Const(29),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(14)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(14)))), expr=Sum(Mul(Const(-20), Var("a"),... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN/LIN_FORM"
] | 8ce6bc | alg_sum_ap_v1 | null | 6 | 0 | [
"LIN_FORM",
"QF_PSD_MIN"
] | 2 | 0.02 | 2026-02-25T10:09:18.344996Z | {
"verified": true,
"answer": 1380,
"timestamp": "2026-02-25T10:09:18.364888Z"
} | ed9d64 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 6674
},
"timestamp": "2026-03-30T09:36:44.620Z",
"answer": 1380
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
a32192 | alg_qf_psd_count_leq_v1_1218484723_6019 | Let
\[
A = \left|\left\{ v : 29 \le v \le 5684,\ \exists\ a, b \in \mathbb Z\text{ with }1 \le a \le 14,\ 1 \le b \le 14,\ 20a^{2} + 17b^{2} - 8ab = v \right\}\right|
\]
and
\[
B = \left|\left\{ (a_1, b_1) : 1 \le a_1 \le 30,\ 1 \le b_1 \le 30,\ 12a_1^{2} b_1^{2} + 2b_1^{4} + 2a_1^{4} + 8a_1^{3} b_1 + 8a_1 b_1^{3} = 91... | 17,955 | graphs = [
Graph(
let={
"_m": Const(8),
"_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(29)... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT",
"POLY4_COUNT"
] | 4583af | alg_qf_psd_count_leq_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 1.199 | 2026-02-25T07:37:24.206692Z | {
"verified": true,
"answer": 17955,
"timestamp": "2026-02-25T07:37:25.406005Z"
} | 087a67 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 382,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T23:53:04.288Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
e5ce1e | diophantine_fbi2_count_v1_1874849503_1564 | Let $k$ be the largest positive divisor of $1609020$ that is at most $1260$. Determine the number of positive integers $d$ such that $3 \leq d \leq 57$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 56$. | 6 | graphs = [
Graph(
let={
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(1260)), Divides(divisor=Var("d"), dividend=Const(1609020))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3))... | NT | null | COUNT | sympy | LIN_FORM | [
"MAX_DIVISOR"
] | 51757e | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 1.585 | 2026-02-08T13:59:07.379845Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T13:59:08.964922Z"
} | 09720f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2592
},
"timestamp": "2026-02-11T08:07:35.740Z",
"answer": 6
},
{
"id"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status"... | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
b4bf49 | nt_sum_gcd_range_mod_v1_153355830_639 | Let $N = 1681$ and $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 57600$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $10937$. | 6,584 | graphs = [
Graph(
let={
"_n": Const(57600),
"N": Const(1681),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ex... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.081 | 2026-02-08T04:06:03.968483Z | {
"verified": true,
"answer": 6584,
"timestamp": "2026-02-08T04:06:04.049022Z"
} | e79de1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 7695
},
"timestamp": "2026-02-10T15:16:14.718Z",
"answer": 6584
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2d296b | comb_binomial_compute_v1_717093673_941 | Let $n = 12$. Define $k$ to be the sum $$\sum_{k_1=1}^{3} k_1.$$ Let $\binom{n}{k}$ denote the binomial coefficient. Compute the remainder when $28935 \cdot \binom{n}{k}$ is divided by $93919$. | 62,944 | graphs = [
Graph(
let={
"n": Const(12),
"k": Summation(var="k1", start=Const(1), end=Const(3), expr=Var("k1")),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(28935),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(93919)),
... | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_binomial_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T15:45:45.504366Z | {
"verified": true,
"answer": 62944,
"timestamp": "2026-02-08T15:45:45.505884Z"
} | 67fe11 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 965
},
"timestamp": "2026-02-24T18:26:32.491Z",
"answer": 62944
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
1c4b61 | nt_count_divisors_in_range_v1_809748730_98 | Let $n = 45360$, $a = 3$, and $b = 1682$. Define $S$ to be the set of all positive integers $d$ such that $d$ divides $n$, $d \geq a$, and $d \leq b$. Let $r$ be the number of elements in $S$. Let $T$ be the set of all ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 2$, $1 \leq b \leq 7$, and $t = 7... | 1,104 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(45360),
"a": Const(3),
"b": Const(1682),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 812dee | nt_count_divisors_in_range_v1 | mod_exp | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.019 | 2026-02-08T11:19:17.427638Z | {
"verified": true,
"answer": 1104,
"timestamp": "2026-02-08T11:19:17.446469Z"
} | 22b36d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 2749
},
"timestamp": "2026-02-14T11:44:18.407Z",
"answer": 1104
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b00623 | modular_modexp_compute_v1_655260480_5621 | Let $n = 2222$. Compute the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Let $e$ be this number. Find the value of $3^e \bmod 19044$, that is, the remainder when $3^e$ is divided by $19044$. | 11,547 | graphs = [
Graph(
let={
"_n": Const(2222),
"a": Const(3),
"e": 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(... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_modexp_compute_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T18:35:04.028704Z | {
"verified": true,
"answer": 11547,
"timestamp": "2026-02-08T18:35:04.030522Z"
} | 734a3e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 3400
},
"timestamp": "2026-02-18T17:56:33.994Z",
"answer": 11547
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8409c9 | algebra_quadratic_discriminant_v1_349078426_1954 | Let $a = -10$, $b = -8$, and $c = 3$. Define $\Delta = b^2 - 4ac$. Let $N$ be the number of positive integers $n \leq 16929$ such that the sum of the digits of $n$ is even. Compute the value of $N - \Delta$. | 8,280 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-10),
"b": Const(-8),
"c": Const(3),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Sub(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(V... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | f8a865 | algebra_quadratic_discriminant_v1 | negation_mod | 3 | 0 | [
"L3B"
] | 1 | 0.003 | 2026-02-08T14:02:02.045781Z | {
"verified": true,
"answer": 8280,
"timestamp": "2026-02-08T14:02:02.048620Z"
} | 662573 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 2730
},
"timestamp": "2026-02-15T23:14:20.756Z",
"answer": 8280
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
e3c5ff | algebra_poly_eval_v1_349078426_932 | Let $k = 10$ and $N = 1258$. Define $S$ to be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 8934121$. Let $s_{\text{min}}$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the value of
$$
\frac{490k^5 - 168k^4 - 1126k^3 + Nk^2 - 836k + 126}{s_{\text{min}}}.
$$ | 7,747 | graphs = [
Graph(
let={
"_n": Const(1258),
"k": Const(10),
"result": Div(Sum(Mul(Const(490), Pow(Ref("k"), Const(5))), Mul(Const(-168), Pow(Ref("k"), Const(4))), Mul(Const(-1126), Pow(Ref("k"), Const(3))), Mul(Ref("_n"), Pow(Ref("k"), Const(2))), Mul(Const(-836), Ref("k")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T13:20:32.819896Z | {
"verified": true,
"answer": 7747,
"timestamp": "2026-02-08T13:20:32.830204Z"
} | 7e8632 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1632
},
"timestamp": "2026-02-15T13:25:35.230Z",
"answer": 7747
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
251bd7 | antilemma_sum_factor_cartesian_v1_458359167_1490 | Let $x$ be the sum of $ij$ over all ordered pairs $(i,j)$ with $1 \leq i \leq 23$ and $1 \leq j \leq 6$. Let $A$ be the set of positive integers $n \leq 23$ such that the sum of the decimal digits of $n$ is even. Define $m = |A|$. Compute the remainder when the Bell number $B_{|x| \bmod m}$ is divided by $76019$. | 39,956 | graphs = [
Graph(
let={
"_n": Const(23),
"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(23)), right=IntegerRange(start=Const(1), end=Const(6)))), expr=Mu... | NT | COMB | COMPUTE | sympy | L3B | [
"L3B",
"SUM_FACTOR_CARTESIAN"
] | 2702c5 | antilemma_sum_factor_cartesian_v1 | bell_mod | 6 | 0 | [
"L3B",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T04:38:02.687644Z | {
"verified": true,
"answer": 39956,
"timestamp": "2026-02-08T04:38:02.688974Z"
} | a73742 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 729
},
"timestamp": "2026-02-18T13:04:13.801Z",
"answer": null
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
446c75 | antilemma_k2_v1_655260480_3456 | Let $\phi(n)$ denote Euler's totient function. Define
$$
x = \sum_{k=1}^{282} \phi(k) \left\lfloor \frac{282}{k} \right\rfloor.
$$
Find the remainder when $18997x$ is divided by $74146$. | 42,733 | graphs = [
Graph(
let={
"_n": Const(282),
"x": Summation(var="k", start=Div(Const(71), Const(71)), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(282), Var("k"))))),
"Q": Mod(value=Mul(Const(18997), Ref("x")), modulus=Const(74146)),
},
goal=... | NT | COMB | COMPUTE | sympy | K13 | [
"IDENTITY_DIV_SELF",
"K2"
] | 39e678 | antilemma_k2_v1 | null | 4 | 0 | [
"IDENTITY_DIV_SELF",
"K13",
"K2"
] | 3 | 0.004 | 2026-02-08T17:23:22.672355Z | {
"verified": true,
"answer": 42733,
"timestamp": "2026-02-08T17:23:22.676595Z"
} | 90d765 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 1367
},
"timestamp": "2026-02-18T00:57:15.808Z",
"answer": 42733
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5021ee | alg_poly_preperiod_count_v1_1218484723_2958 | For a non-negative integer $a$, define the sequence $N, M, R, S, T$ by:
\[
\begin{aligned}
N &= (a^2 + a - 17) \bmod 41, \\
M &= (N^2 + N - 17) \bmod 41, \\
R &= (M^2 + M - 17) \bmod 41, \\
S &= (R^2 + R - 17) \bmod 41, \\
T &= (S^2 + S - 17) \bmod 41.
\end{aligned}
\]
Find the number of integers $a$ with $0 \leq a \le... | 13,944 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-17)), modulus=Const(41)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-17)), modulus=Const(41)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-17)), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.03 | 2026-02-25T04:42:03.000270Z | {
"verified": true,
"answer": 13944,
"timestamp": "2026-02-25T04:42:03.030300Z"
} | 003dd1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 15387
},
"timestamp": "2026-03-29T07:32:11.451Z",
"answer": 0
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
c8b5a6_n | comb_count_partitions_v1_601307018_972 | A baker uses two types of ingredients to make energy bars: type A (contributes 3 units of energy per piece) and type B (contributes 7 units per piece). Each bar must use between 1 and 13 pieces of type A and between 1 and 3 pieces of type B, contributing a total energy level $t$. Only bars with total energy $t$ between... | 31,185 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-03-10T01:33:48.008273Z | null | 6730e8 | c8b5a6 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 2522
},
"timestamp": "2026-03-29T14:44:09.916Z",
"answer": 31185
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
04c7c9_n | alg_poly3_min_v1_601307018_9878 | A factory produces three components $a$, $b$, and $c$, each requiring integer settings from 1 to 30. The total energy cost of a production run is given by the expression $$275a^3 + 375a^2b + 225a^2c + 50b^3 -75ab^{\left|\{ k : 1 \le k \le 16,\, 8 \mid k \}\right|} + 150abc + 45ac^2 + 30bc^2.$$ The exponent $\left|\{ k ... | 1,075 | graphs = [
Graph(
let={
"_n": Const(275),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Geq(Var("c"), Const(1... | ALG | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | alg_poly3_min_v1 | null | 6 | null | [
"C2"
] | 1 | 0.098 | 2026-03-10T10:16:16.677545Z | null | a5fc58 | 04c7c9 | narrative | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 664
},
"timestamp": "2026-04-23T14:24:55.997Z",
"answer": 1075
}
] | 2 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} |
703b00 | nt_count_divisible_and_v1_677425708_144 | Let $N = 67260$, $d_1 = 10$, and $d_2 = 12$. Consider the set of all positive integers $n$ such that $1 \le n \le N$, $n$ is divisible by $d_1$, and the remainder when $n$ is divided by $d_2$ equals $\sum_{k=0}^{7} (-1)^k \binom{7}{k}$. Compute the number of such integers $n$. Determine the value of this number. | 1,121 | graphs = [
Graph(
let={
"upper": Const(67260),
"d1": Const(10),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 2.676 | 2026-02-08T03:06:35.035078Z | {
"verified": true,
"answer": 1121,
"timestamp": "2026-02-08T03:06:37.711187Z"
} | 6273cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 637
},
"timestamp": "2026-02-08T20:20:02.005Z",
"answer": 1121
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -5.96,
"mid": -3.96,
"hi": -1.95
} | ||
a7353b | antilemma_sum_equals_v1_124444284_1042 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 36$, $1 \le i \le 35$, and $1 \le j \le 35$. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14002$. Let $t$ be an integer satisfying $7 \le t \le 349$, and let $S$ be the set of a... | 6,778 | graphs = [
Graph(
let={
"_m": Const(14002),
"_n": Const(59573),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(36)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=I... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COMB1",
"COUNT_SUM_EQUALS"
] | 77e8ba | antilemma_sum_equals_v1 | two_moduli | 7 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.027 | 2026-02-08T03:40:02.217948Z | {
"verified": true,
"answer": 6778,
"timestamp": "2026-02-08T03:40:02.244662Z"
} | 482565 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 312,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T22:43:05.318Z",
"answer": 6778
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LI... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
59a89b | nt_min_coprime_above_v1_397696148_61 | Let $A$ be the set of all integers $n$ such that $1 \leq n \leq 308$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $m$ be the number of elements in $A$. Find the smallest integer $n$ such that $51076 < n \leq 51130$ and $\gcd(n, m) = 1$. | 51,077 | graphs = [
Graph(
let={
"_n": Const(308),
"start": Const(51076),
"upper": Const(51130),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.04 | 2026-02-08T11:16:54.834874Z | {
"verified": true,
"answer": 51077,
"timestamp": "2026-02-08T11:16:54.875336Z"
} | 7bad20 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1053
},
"timestamp": "2026-02-14T11:00:28.932Z",
"answer": 51077
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
1b64e6 | antilemma_k3_v1_153355830_1353 | Let $ n = 95185 $. Define
$$
x = \sum_{d \mid n} \phi(d),
$$
where the sum is over all positive divisors $ d $ of $ n $, and $ \phi(d) $ is Euler's totient function.
Let $ Q = (2022 - x) \bmod 67564 $.
Compute $ Q $. | 41,965 | graphs = [
Graph(
let={
"_n": Const(95185),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(2022),
"Q": Mod(value=Sub(Ref("_c"), Ref("x")), modulus=Const(67564)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T06:20:22.228296Z | {
"verified": true,
"answer": 41965,
"timestamp": "2026-02-08T06:20:22.229224Z"
} | 9df52e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 634
},
"timestamp": "2026-02-12T23:03:11.628Z",
"answer": 41965
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
5b3bb3 | nt_sum_gcd_range_mod_v1_124444284_7281 | Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 90$. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$. Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = n$. Let ... | 4,820 | graphs = [
Graph(
let={
"_m": 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(90)))), expr=Mul(Var("x"), Var("y")))),
"_n": MinOverSet(se... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3/B1"
] | 644515 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.097 | 2026-02-08T08:58:53.343937Z | {
"verified": true,
"answer": 4820,
"timestamp": "2026-02-08T08:58:53.441336Z"
} | 63a7a4 | 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": 2471
},
"timestamp": "2026-02-13T23:43:37.886Z",
"answer": 4820
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5cf888 | nt_count_digit_sum_v1_349078426_783 | Let $U$ be the total number of ordered pairs $(a, b)$ such that $1 \leq a \leq 99$ and $1 \leq b \leq 101$. Compute the number of positive integers $n \leq U$ such that the sum of the decimal digits of $n$ is 15. | 592 | graphs = [
Graph(
let={
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(99)), right=IntegerRange(start=Const(1), end=Const(101)))),
"target_sum": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_count_digit_sum_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 5.484 | 2026-02-08T13:17:39.573855Z | {
"verified": true,
"answer": 592,
"timestamp": "2026-02-08T13:17:45.057555Z"
} | 3f48e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1269
},
"timestamp": "2026-02-15T12:23:38.089Z",
"answer": 592
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5c274e | nt_max_prime_below_v1_1470522791_883 | Let $s$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of prime numbers $n$ such that $s \leq n \leq 60000$. Let $r$ be the largest element of $S$. Find the remainder when $53904 \cdot r$ is divided by $... | 60,015 | graphs = [
Graph(
let={
"_n": Const(78329),
"upper": Const(60000),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.491 | 2026-02-08T13:18:03.935481Z | {
"verified": true,
"answer": 60015,
"timestamp": "2026-02-08T13:18:07.426415Z"
} | e6c340 | 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": 3503
},
"timestamp": "2026-02-15T13:08:03.424Z",
"answer": 60015
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c0cf81 | alg_poly_preperiod_count_v1_1218484723_1636 | For a non-negative integer $a$, define a sequence by $N = (a^2 + a - 6) \bmod 59$, $M = (N^2 + N - 6) \bmod 59$, $R = (M^2 + M - 6) \bmod 59$, and $S = (R^2 + R - 6) \bmod 59$. Find the number of integers $a$ with $0 \le a \le 42361$ such that $S = M$ and $R \ne M$. | 4,308 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-6)), modulus=Const(59)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-6)), modulus=Const(59)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-6)), mod... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.029 | 2026-02-25T03:20:20.364919Z | {
"verified": true,
"answer": 4308,
"timestamp": "2026-02-25T03:20:20.394097Z"
} | 976100 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T00:41:54.902Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
2d47ce | antilemma_sum_equals_v1_1520064083_648 | Let $m$ be the number of integers $t$ such that $16 \leq t \leq 354$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 24$, $1 \leq b \leq 19$, and $t = 10a + 6b$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the number of ordered pairs ... | 78 | 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=24)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | b14821 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.078 | 2026-02-08T03:30:50.103809Z | {
"verified": true,
"answer": 78,
"timestamp": "2026-02-08T03:30:50.181986Z"
} | f75502 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T22:37:21.453Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
606ec6 | alg_poly_orbit_count_v1_1218484723_4853 | For an integer $a$, define
\begin{align*}
N &\equiv 2a^{3} - 4a^{2} - 4a \pmod{97},\\
M &\equiv 2N^{3} - 4N^{2} - 4N \pmod{97},\\
R &\equiv 2M^{3} - 4M^{2} - 4M \pmod{97},\\
S &\equiv 2R^{3} - 4R^{2} - 4R \pmod{97},\\
T &\equiv 2S^{3} - 4S^{2} - 4S \pmod{97},\\
K &\equiv 2T^{3} - 4T^{2} - 4T \pmod{97}.
\end{align*}
Let... | 6,306 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(-4), Pow(Var("a"), Const(2))), Mul(Const(-4), Var("a"))), modulus=Const(97)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(-4), Pow(Ref("p1"), Const(2))), Mul(Const... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.096 | 2026-02-25T06:29:06.851879Z | {
"verified": true,
"answer": 6306,
"timestamp": "2026-02-25T06:29:06.947485Z"
} | 677a9e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 363,
"completion_tokens": 20193
},
"timestamp": "2026-03-29T18:07:23.896Z",
"answer": 6
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
b69ab0 | alg_telescope_v1_1218484723_3572 | Let $S$ be the set of positive integers $n \le 2599$ such that $\gcd(n, 15) = 1$. Let $M = \left( \sum_{k=0}^{|S|} (4k^3 + 6k^2 + 4k + 1) \right) \bmod 3956$. Compute $|M|$. | 784 | graphs = [
Graph(
let={
"_n": Const(2599),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(15)), Const(1))))), expr=Sum(Mul(Const(4), Pow... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | alg_telescope_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.111 | 2026-02-25T05:12:10.290959Z | {
"verified": true,
"answer": 784,
"timestamp": "2026-02-25T05:12:10.401570Z"
} | 3e42f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 2311
},
"timestamp": "2026-03-29T11:01:00.996Z",
"answer": 784
},
{
"id... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
896852 | nt_sum_divisors_range_v1_1248542787_740 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 12250000$. Let $u$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Now consider all integers $n$ from $\phi(2)$ to $u$, inclusive. For each such $n$, compute the number of its positive divisors, and let the result be the ... | 63,071 | 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(12250000)))), expr=Sum(Var("x"), Var("y")))),
"result": ... | NT | null | SUM | sympy | MOBIUS_COPRIME | [
"ONE_PHI_2",
"B3"
] | 0519c9 | nt_sum_divisors_range_v1 | null | 5 | 0 | [
"B3",
"MOBIUS_COPRIME",
"ONE_PHI_2"
] | 3 | 0.655 | 2026-02-08T03:21:36.215287Z | {
"verified": true,
"answer": 63071,
"timestamp": "2026-02-08T03:21:36.870774Z"
} | 1e7ce3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 3673
},
"timestamp": "2026-02-09T20:35:18.549Z",
"answer": 63071
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
4e1373 | alg_poly4_min_v1_601307018_6020 | Let $Q$ be the minimum value of
$$
19532a^4 + \min\{ x + y : x, y > 0,\, xy = 13307904,\, x \leq y \} \cdot ab^3 + 31008a^2b^2 + \left|\{ k : 1 \leq k \leq 75392,\, 31 \mid k \}\right| \cdot b^4 + 38304a^3b
$$
over all positive integers $a, b$ with $1 \leq a \leq \left|\{ (a1, b1) : 1 \leq a1, b1 \leq 20,\, 10a1^2 - 18... | 98,572 | graphs = [
Graph(
let={
"_d": Const(4),
"_c": Const(3),
"_m": Const(25),
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSe... | NT | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"B3_CLOSEST",
"C2",
"B3"
] | 433d01 | alg_poly4_min_v1 | null | 6 | 0 | [
"B3",
"B3_CLOSEST",
"C2",
"QF_PSD_COUNT_LEQ"
] | 4 | 1.008 | 2026-03-10T06:36:54.806935Z | {
"verified": true,
"answer": 98572,
"timestamp": "2026-03-10T06:36:55.815322Z"
} | bc8150 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 341,
"completion_tokens": 5507
},
"timestamp": "2026-04-19T03:24:22.947Z",
"answer": 98572
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lem... | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
9bcd08 | geo_visible_lattice_v1_2051736721_3009 | Let $n = 81$. Define $R$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $Q = 9801 - R$. Compute $Q$. | 5,762 | graphs = [
Graph(
let={
"n": Const(81),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(9801),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.305 | 2026-02-08T17:03:49.762420Z | {
"verified": true,
"answer": 5762,
"timestamp": "2026-02-08T17:03:50.067567Z"
} | 4c69ed | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 2269
},
"timestamp": "2026-02-17T18:10:07.573Z",
"answer": 5762
},
{... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
4178b1 | diophantine_sum_product_min_v1_1520064083_916 | Let $S = 55$. Let $P$ be the number of positive integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 49$, $1 \leq b \leq 12$, $12 \leq t \leq 329$, and $t = 5a + 7b$. Let $x$ be the smallest positive integer such that $1 \leq x \leq Q$, where $Q$ is the number of positive integers $t$ su... | 61,374 | graphs = [
Graph(
let={
"_n": Const(70116),
"S": Const(55),
"P": 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=... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_sum_product_min_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-08T03:40:09.036672Z | {
"verified": true,
"answer": 61374,
"timestamp": "2026-02-08T03:40:09.043866Z"
} | 823236 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 320,
"completion_tokens": 7486
},
"timestamp": "2026-02-10T14:02:35.514Z",
"answer": 61374
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
be1ef7 | alg_poly3_sum_v1_1218484723_6355 | Compute the sum $$\sum_{\substack{1 \le a,b,c \le 42}} \left( -144abc -128b^3 + D \cdot a c^2 -240b c^2 + 96b^2 c + 90a^2 c + 253a^3 + 432a b^2 -492a^2 b + 57c^3 \right),$$ where $$D = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 25,\ 25b_1^2 -18a_1 b_1 + 10a_1^2 \le 3316 \}\right|,$$ and find the remainder when this sum i... | 44,174 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(42)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(42)), Geq(Var("c"),... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_sum_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 1.104 | 2026-02-25T07:54:20.680035Z | {
"verified": true,
"answer": 44174,
"timestamp": "2026-02-25T07:54:21.784242Z"
} | 93cc92 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 16170
},
"timestamp": "2026-03-30T01:20:36.104Z",
"answer": 45348
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
03567d | algebra_quadratic_discriminant_v1_1915831931_2226 | Let $a = \sum_{k=1}^{2} k$, $b = -2$, and $c = 8$. Let $\Delta = b^2 - 4ac$. Compute the remainder when $62573 \cdot \Delta$ is divided by $89718$. | 74,954 | graphs = [
Graph(
let={
"_n": Const(89718),
"a": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"b": Const(-2),
"c": Const(8),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"_c": Const(6257... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T16:40:42.324876Z | {
"verified": true,
"answer": 74954,
"timestamp": "2026-02-08T16:40:42.326413Z"
} | b4043e | 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": 858
},
"timestamp": "2026-02-17T09:06:28.688Z",
"answer": 74954
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a97a1d | alg_qf_psd_min_v1_601307018_2161 | Let $d_{\text{max}}$ be the largest positive divisor of $87918752$ such that $d_{\text{max}}^2 \le 87918752$. Find the minimum value of the expression
$$
d_{\text{max}} \cdot b \cdot c - 9376a \cdot c + 21096a \cdot b + 20510a^2 + 10548b^2 + 18752c^2
$$
over all ordered triples $(a, b, c)$ of positive integers with $1 ... | 70,906 | graphs = [
Graph(
let={
"_m": Const(21),
"_n": Const(20510),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MaxOverSet(set=SolutionsSet(var=Var("k"), condition=L... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST",
"MAX_VAL"
] | ce8f09 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"B3_CLOSEST",
"MAX_VAL"
] | 2 | 0.054 | 2026-03-10T02:52:01.729901Z | {
"verified": true,
"answer": 70906,
"timestamp": "2026-03-10T02:52:01.784085Z"
} | ab1efa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T04:37:07.440Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"st... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
e63e12 | nt_min_with_divisor_count_v1_168721529_5 | Let $c$ be the number of positive integers $n$ such that $1 \leq n \leq 96$ and $21$ divides $F_n$, where $F_n$ denotes the $n$-th Fibonacci number. Let $m$ be the smallest positive integer $n$ such that $1 \leq n \leq 40804$ and the number of positive divisors of $n$ is equal to $c$. Compute the remainder when $55354 ... | 79,920 | graphs = [
Graph(
let={
"_n": Const(55354),
"upper": Const(40804),
"div_count": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(96)), Divides(divisor=Const(21), dividend=Fibonacci(arg=Var(name='n')))))),
"... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 2.541 | 2026-02-08T12:45:49.935052Z | {
"verified": true,
"answer": 79920,
"timestamp": "2026-02-08T12:45:52.476429Z"
} | c81281 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 2508
},
"timestamp": "2026-02-08T20:52:44.224Z",
"answer": 79920
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.02,
"mid": 1.85,
"hi": 5.2
} | ||
d09fec | antilemma_cartesian_v1_1353956133_337 | Compute the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 21$ and $1 \leq b \leq 28$. | 588 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=Const(28)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T11:25:08.534361Z | {
"verified": true,
"answer": 588,
"timestamp": "2026-02-08T11:25:08.534850Z"
} | 32db65 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 130
},
"timestamp": "2026-02-24T13:41:18.882Z",
"answer": 588
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
cf1eab | sequence_lucas_compute_v1_784195855_5975 | Let $m = 196$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $n$ be the largest prime number that is at least 2 and at most $s$. Compute the $n$-th Lucas number. | 64,079 | graphs = [
Graph(
let={
"_m": Const(196),
"_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")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.001 | 2026-02-08T08:14:56.949582Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T08:14:56.950973Z"
} | 4632e7 | 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": 1013
},
"timestamp": "2026-02-13T15:55:15.585Z",
"answer": 64079
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
87eb36 | comb_count_derangements_v1_48377204_985 | Let $m = 8$. Let $S$ be the set of all positive integers $n_1$ such that $1 \le n_1 \le 205$ and $\gcd(n_1, 14) = 1$. Let $d$ be the number of elements in $S$. Define $n$ to be the largest positive divisor of $d$ that is at most $m$. Compute the remainder when $44121$ times the subfactorial of $n$ is divided by $72859$... | 27,255 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(205)), Eq(GCD(a=Var("n1"), b=Const(14)), Const(1))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(... | NT | COMB | COUNT | sympy | C4 | [
"C4/MAX_DIVISOR"
] | 747897 | comb_count_derangements_v1 | null | 5 | 0 | [
"C4",
"MAX_DIVISOR"
] | 2 | 0.003 | 2026-02-08T15:50:52.526777Z | {
"verified": true,
"answer": 27255,
"timestamp": "2026-02-08T15:50:52.529962Z"
} | 300647 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1788
},
"timestamp": "2026-02-16T14:56:44.171Z",
"answer": 27255
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a3b48f | comb_binomial_compute_v1_677425708_2590 | Let $n = 14$ and $k = 6$. Let $c$ be the number of positive integers $n$ not exceeding 40599 such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $Q$ be the remainder when $\binom{n}{k} \cdot c$ is divided by 91165. Find the value of $Q$. | 40,302 | graphs = [
Graph(
let={
"n": Const(14),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(40599)), Congruent(a=Var(name='n'), b=Floor(arg=Div(lef... | NT | null | COMPUTE | sympy | COMB1 | [
"L3C"
] | 141fd9 | comb_binomial_compute_v1 | affine_mod | 4 | 0 | [
"COMB1",
"L3C"
] | 2 | 0.033 | 2026-02-08T05:08:51.600329Z | {
"verified": true,
"answer": 40302,
"timestamp": "2026-02-08T05:08:51.633307Z"
} | 2ac4f8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2524
},
"timestamp": "2026-02-11T22:58:02.548Z",
"answer": 40302
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
f59588 | modular_count_residue_v1_124444284_410 | Let $r$ be the sum of the first $t$ positive integers, where $t$ is the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 3000$, $\gcd(p, q) = 1$, and $p < q$. Let $\text{result}$ be the number of integers $n$ with $1 \leq n \leq 32768$ such that $n \equiv r \pmod{12}$. Compu... | 2,730 | graphs = [
Graph(
let={
"upper": Const(32768),
"m": Const(12),
"r": Summation(var="k", start=Const(1), end=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=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_ARITHMETIC"
] | 10b314 | modular_count_residue_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 2.004 | 2026-02-08T03:15:50.958173Z | {
"verified": true,
"answer": 2730,
"timestamp": "2026-02-08T03:15:52.962535Z"
} | c44d3d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2449
},
"timestamp": "2026-02-09T17:18:48.850Z",
"answer": 2730
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
eb3da1 | diophantine_product_count_v1_971394319_357 | Let $n = 2$ and $k = 60$. Define $\text{upper} = 35$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq \text{upper}$, $x$ divides $60$, and $\frac{60}{x} \leq 35$. Let $r$ be the number of elements in $S$. Compute $r + 2^{r \bmod 15} \bmod 91924$, where the exponent is reduced modulo $15 = \sum_... | 1,034 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(60),
"upper": Const(35),
"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 | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 129eee | diophantine_product_count_v1 | mod_exp | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.009 | 2026-02-08T13:02:47.622070Z | {
"verified": true,
"answer": 1034,
"timestamp": "2026-02-08T13:02:47.630701Z"
} | ec0d90 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 999
},
"timestamp": "2026-02-15T08:50:17.788Z",
"answer": 1034
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
32ea09 | geo_count_lattice_triangle_v1_1439011603_1959 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(136,6)$, and $(40,128)$, 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:
- $\gcd(|136 - 0|, |6 - 0|)$,
- $\gcd(|40 - 136|, |128 - 6|)$,
- $\gcd(|0 - 40|, |0... | 34,509 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=136), Const(value=128)), Mul(Const(value=40), Sub(left=Const(value=0), right=Const(value=6))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=136)), b=Abs(arg=Const(value=6))), GCD(a=Abs(arg=Sub(left=Const(value=40), right=C... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.005 | 2026-02-08T16:24:24.092280Z | {
"verified": true,
"answer": 34509,
"timestamp": "2026-02-08T16:24:24.097135Z"
} | 47a865 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1233
},
"timestamp": "2026-02-17T03:55:28.597Z",
"answer": 34509
},
... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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