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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5e189d | algebra_vieta_sum_v1_1520064083_67 | Let $S$ be the set of all real numbers $x$ satisfying
$$
-x^2 - 13x - 40 = \sum_{d \mid \gcd(96,32)} \mu(d),
$$
where $\mu$ is the M\"obius function. Let $P$ be the product of all elements of $S$. Compute $(12101 \cdot P) \bmod 96989$. | 96,084 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Const(value=-1), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const(value=-13), Var(name='x')), Const(value=-40)), right=SumOverDivisors(n=GCD(a=Const(value=96), b=Const(value=32))... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"MOBIUS_COPRIME"
] | ac54ac | algebra_vieta_sum_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME",
"SUM_ARITHMETIC"
] | 2 | 0.031 | 2026-02-08T02:58:36.993082Z | {
"verified": true,
"answer": 96084,
"timestamp": "2026-02-08T02:58:37.023812Z"
} | c064b9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 596
},
"timestamp": "2026-02-17T16:59:29.654Z",
"answer": 96084
}
] | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
64884a | comb_count_permutations_fixed_v1_1125832087_2226 | Let $n = \sum_{k=1}^{3} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\varphi$ denotes Euler's totient function. Let $k = 0$. Define the quantity
$$
\binom{n}{k} \cdot !\!(n - k),
$$
where $!\!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the remainder when $21817$ times this quantity... | 15,217 | graphs = [
Graph(
let={
"_n": Const(86064),
"n": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T04:25:28.999386Z | {
"verified": true,
"answer": 15217,
"timestamp": "2026-02-08T04:25:29.000909Z"
} | 3fc229 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 1264
},
"timestamp": "2026-02-10T16:44:52.512Z",
"answer": 15217
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
744298 | diophantine_fbi2_count_v1_1353956133_377 | Let $k$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 25$ and $1 \leq j \leq 46$ such that $\gcd(i, j) = 1$. Let $R$ be the number of divisors $d$ of $k$ such that $4 \leq d \leq 73$ and $2 \leq \frac{k}{d} \leq 71$. Compute $21609 - R$. | 21,596 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(46))))),
"r... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.008 | 2026-02-08T11:25:41.664270Z | {
"verified": true,
"answer": 21596,
"timestamp": "2026-02-08T11:25:41.671911Z"
} | 4981db | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 2066
},
"timestamp": "2026-02-14T13:43:50.637Z",
"answer": 21596
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6793ed | modular_modexp_compute_v1_1978505735_7207 | Let $e$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 17$, $1 \le j \le 62$, and $\gcd(i, j) = 1$. Compute the remainder when $3^e$ is divided by $33124$. | 12,821 | graphs = [
Graph(
let={
"a": Const(3),
"e": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Co... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | modular_modexp_compute_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.002 | 2026-02-08T20:06:51.001975Z | {
"verified": true,
"answer": 12821,
"timestamp": "2026-02-08T20:06:51.004160Z"
} | 2fe1cf | 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": 4201
},
"timestamp": "2026-02-18T23:58:56.563Z",
"answer": 12821
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a870d0_l | nt_count_divisible_v1_971394319_37 | Let $d$ be the number of prime numbers $n$ such that $2 \le n \le 103$. Determine the number of positive integers $n$ such that $1 \le n \le 90000$ and $n$ is divisible by $d$. | 3,600 | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_divisible_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 5.468 | 2026-02-08T12:48:19.262945Z | {
"verified": false,
"answer": 3333,
"timestamp": "2026-02-08T12:48:24.730633Z"
} | 96bab7 | a870d0 | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 540
},
"timestamp": "2026-02-15T05:37:34.424Z",
"answer": 3333
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | |
b64d5d | sequence_count_fib_divisible_v1_1125832087_1148 | Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq 441$ and $13$ divides the $n$-th Fibonacci number. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|r| + 2$. | 35 | graphs = [
Graph(
let={
"upper": Const(441),
"d": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
"Q": Fib... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM/C4"
] | 8073ef | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C4",
"VIETA_SUM"
] | 2 | 0.067 | 2026-02-08T03:33:49.166167Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T03:33:49.233248Z"
} | ab4c64 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 3454
},
"timestamp": "2026-02-10T14:54:50.285Z",
"answer": 35
},
{
"id"... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
280ddf_l | comb_sum_binomial_mod_v1_784195855_5834 | Let $n = 282$. For each integer $k$ from 8 to $n$, inclusive, define $a_k$ to be the number of integers $t$ such that $27 \leq t \leq 978$ and $t = 6a + 21b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 156$ and $1 \leq b \leq 2$. Define
$$
S = \sum_{k=8}^{282} \binom{a_k}{k}.
$$
Compute the remainder when $... | 0 | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_mod_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.014 | 2026-02-08T08:08:43.794950Z | {
"verified": false,
"answer": 10670,
"timestamp": "2026-02-08T08:08:43.809112Z"
} | 9cbc53 | 280ddf | 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": 248,
"completion_tokens": 31605
},
"timestamp": "2026-02-24T08:58:55.620Z",
"answer": 8858
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | |
c2ce10_n | alg_qf_psd_min_v1_1218484723_4864 | An engineer designs a rectangular frame where the cost function depends on side lengths $a$ and $b$ (each between 1 and 172 units) via the expression $5490a^2 + 5490ab + 1525b^2$. What is the lowest possible cost for such a frame? | 12,505 | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL",
"ONE_PHI_1"
] | 5903db | alg_qf_psd_min_v1 | null | 3 | null | [
"ONE_PHI_1",
"POLY_ORBIT_HENSEL"
] | 2 | 0.801 | 2026-02-25T06:30:20.862062Z | null | c32521 | c2ce10 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1164
},
"timestamp": "2026-03-30T22:30:51.628Z",
"answer": 12505
},
{
"... | 2 | [
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
b88990 | nt_num_divisors_compute_v1_124444284_9978 | Let $n$ be the number of positive integers $k \le 6001$ such that $\gcd(k, 20) = 1$.
Let $d$ be the number of positive divisors of $n$.
Compute the remainder when $52730 \cdot d$ is divided by $69321$. | 55,687 | graphs = [
Graph(
let={
"_n": Const(69321),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6001)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"result": NumDivisors(n=Ref("n")),
"Q": Mod(value=Mul... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.003 | 2026-02-08T12:45:26.057703Z | {
"verified": true,
"answer": 55687,
"timestamp": "2026-02-08T12:45:26.061141Z"
} | c18219 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1027
},
"timestamp": "2026-02-15T04:50:56.818Z",
"answer": 55687
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
593c3e | diophantine_product_count_v1_1742523217_4668 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $r$ be the number of positive integers $x$ such that $1 \leq x \leq 298$, $x$ divides $k$, and $\frac{k}{x} \leq 298$. Let $p$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positiv... | 5,188 | graphs = [
Graph(
let={
"_m": Const(124),
"_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)))), ex... | NT | null | COUNT | sympy | B1 | [
"B1",
"B3"
] | f5c732 | diophantine_product_count_v1 | quadratic_mod | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.013 | 2026-02-08T09:01:38.138592Z | {
"verified": true,
"answer": 5188,
"timestamp": "2026-02-08T09:01:38.152004Z"
} | 2165a7 | 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": 2073
},
"timestamp": "2026-02-13T23:18:26.105Z",
"answer": 5188
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3826a4 | geo_visible_lattice_v1_124444284_2462 | Let $n = 100$. Define $\text{result}$ to be the number of visible lattice points $(x, y)$ such that $1 \le x, y \le n$ and $\gcd(x, y) = 1$. Let $Q$ be the remainder when $58999 \cdot \text{result}$ is divided by $85755$. Compute $Q$. | 70,728 | graphs = [
Graph(
let={
"n": Const(100),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(58999), Ref("result")), modulus=Const(85755)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.212 | 2026-02-08T04:42:07.414400Z | {
"verified": true,
"answer": 70728,
"timestamp": "2026-02-08T04:42:07.625930Z"
} | dd5a50 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 11329
},
"timestamp": "2026-02-24T01:27:11.703Z",
"answer": 70728
},
{
... | 1 | [] | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||||
d9a1bf | modular_mod_compute_v1_238844314_572 | Let $a$ be the sum of all real solutions $x$ to the equation $x^2 - 44x + 435 = 0$. Let $r$ be the remainder when $a$ is divided by $28657$. Compute the remainder when $76825 \cdot r$ is divided by $94369$. | 77,385 | graphs = [
Graph(
let={
"_n": Const(94369),
"a": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-44), Var("x")), Const(435)), Const(0)))),
"m": Const(28657),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_mod_compute_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T13:24:38.373812Z | {
"verified": true,
"answer": 77385,
"timestamp": "2026-02-08T13:24:38.375063Z"
} | 28ab6e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 483
},
"timestamp": "2026-02-15T15:14:27.702Z",
"answer": 77385
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f41571 | lin_form_endings_v1_1520064083_2594 | Let $a = 12$, $b = 20$, $A = 22$, and $B = 33$. Define $g = \gcd(a, b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$.
Let $r = a'A + b'B - a'b'$, and define $s = 5260 \cdot r$.
Compute the remainder when $s$ is divided by $81596$. | 75,412 | graphs = [
Graph(
let={
"a_coeff": Const(12),
"b_coeff": Const(20),
"A_val": Const(22),
"B_val": Const(33),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:52:56.913925Z | {
"verified": true,
"answer": 75412,
"timestamp": "2026-02-08T04:52:56.914853Z"
} | 465060 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 858
},
"timestamp": "2026-02-11T22:24:17.876Z",
"answer": 75412
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
a5aec4 | nt_count_divisible_and_v1_1440796553_81 | Determine the number of positive integers $n$ such that $n \leq 33264$, $n$ is divisible by 4, and $n$ is divisible by 6. | 2,772 | graphs = [
Graph(
let={
"upper": Const(33264),
"d1": Const(4),
"d2": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(1))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Cons... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"ONE_PHI_1"
] | 1 | 4.258 | 2026-02-08T11:15:39.892857Z | {
"verified": true,
"answer": 2772,
"timestamp": "2026-02-08T11:15:44.151109Z"
} | a01a40 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 324
},
"timestamp": "2026-02-21T22:06:46.279Z",
"answer": 2772
}
] | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
2b8e1f | sequence_lucas_compute_v1_784195855_2809 | Let $S$ be the set of all nonnegative integers $j$ such that $j \leq 20498$ and $\binom{20498}{j}$ is odd. Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 14$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Define $k_{\text{sum}} = \sum_{k=0}^{... | 28,583 | graphs = [
Graph(
let={
"_m": Const(56680),
"_n": Const(3),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Summation(var="k", start=Const(0), end=Const(10), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(10), k=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING/V8"
] | cd53f8 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM",
"V8"
] | 3 | 0.011 | 2026-02-08T06:03:08.046077Z | {
"verified": true,
"answer": 28583,
"timestamp": "2026-02-08T06:03:08.057202Z"
} | 8aa6fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 306,
"completion_tokens": 3469
},
"timestamp": "2026-02-24T05:15:19.233Z",
"answer": 28583
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
e4c576 | antilemma_sum_equals_v1_1820931509_44 | Let $C$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 48$. Let $M$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 23$, $1 \leq j \leq 24$, and $i + j = C$. Let $N$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 21$, $1 \leq j \leq 22$, an... | 21 | graphs = [
Graph(
let={
"_c": Const(48),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | a57484 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.034 | 2026-02-08T11:19:07.301078Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T11:19:07.335411Z"
} | bd92ff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 744
},
"timestamp": "2026-02-24T13:28:34.452Z",
"answer": 21
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
26c04d | nt_min_coprime_above_v1_784195855_1332 | Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 401956$. Let $s$ be the minimum value of $x + y$ over all pairs in $A$. Let $B$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 13689$. Let $m$ be the minimum value of $x + y$ over all pairs in $B$. Deter... | 86,925 | graphs = [
Graph(
let={
"_n": Const(13689),
"start": Const(1024),
"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(40... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.047 | 2026-02-08T04:58:08.423325Z | {
"verified": true,
"answer": 86925,
"timestamp": "2026-02-08T04:58:08.470410Z"
} | 2280ce | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 3070
},
"timestamp": "2026-02-11T22:34:45.124Z",
"answer": 86925
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6593b7 | comb_sum_binomial_row_v1_1431428450_1210 | Let $n_1 = 0$ and $n_2 = 0$. Define
$$
c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}
\quad\text{and}\quad
u = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 11 \nu$, and let $r = (2c)^n$. Compute the sum of the number of positive divisors of all integers from $0!$ to $|r|$, inclusive. | 15,937 | graphs = [
Graph(
let={
"n2": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"u": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | NT | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 8794cb | comb_sum_binomial_row_v1 | null | 2 | 2 | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 2 | 0.003 | 2026-02-08T13:58:09.286560Z | {
"verified": true,
"answer": 15937,
"timestamp": "2026-02-08T13:58:09.289288Z"
} | fea713 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 2603
},
"timestamp": "2026-02-15T22:16:49.391Z",
"answer": 15937
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
949cf1 | comb_count_partitions_v1_1125832087_1706 | Let $n$ be the number of positive integers less than or equal to $115$ that are relatively prime to $12$. Compute the number of integer partitions of $n$. | 31,185 | graphs = [
Graph(
let={
"_n": Const(12),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(115)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("... | NT | COMB | COUNT | sympy | C4 | [
"C4"
] | 08d162 | comb_count_partitions_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.001 | 2026-02-08T03:53:19.541063Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T03:53:19.542427Z"
} | 99e422 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 1424
},
"timestamp": "2026-02-10T16:07:13.041Z",
"answer": 31185
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
d48789 | nt_count_with_divisor_count_v1_898971024_1602 | Let $t$ be a positive integer such that $27 \leq t \leq 23805$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3614$, $1 \leq b \leq 101$, and $t = 6a + 21b$. Let $\text{upper}$ be the number of such values of $t$. Let $\text{div\_count} = 2$. Compute the remainder when $18572$ times the number of pos... | 3,171 | graphs = [
Graph(
let={
"_n": Const(97219),
"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=3614)), Geq(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.344 | 2026-02-08T16:12:21.885060Z | {
"verified": true,
"answer": 3171,
"timestamp": "2026-02-08T16:12:22.228750Z"
} | 8e7dde | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 2932
},
"timestamp": "2026-02-16T22:35:04.505Z",
"answer": 3171
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
688c32 | v7_endings_v1_677425708_373 | Let $ k $ be an integer such that $ 0 \leq k \leq 996 $. For each such $ k $, define $ v_5\left(\binom{996}{k}\right) $ to be the largest integer $ m $ such that $ 5^m $ divides $ \binom{996}{k} $. Let $ M $ be the maximum value of $ v_5\left(\binom{996}{k}\right) $ over all such $ k $. Compute the remainder when $ 552... | 22,116 | graphs = [
Graph(
let={
"_inner_result": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(996)))), expr=MaxKDivides(target=Binom(n=Const(996), k=Var("k")), base=Const(5)))),
"_scale_k": Const(5529),
"_scal... | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.002 | 2026-02-08T03:14:47.902774Z | {
"verified": true,
"answer": 22116,
"timestamp": "2026-02-08T03:14:47.904486Z"
} | 9a2812 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 2365
},
"timestamp": "2026-02-08T20:29:42.912Z",
"answer": 22116
},
{
"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
fd0f57 | nt_sum_gcd_range_mod_v1_1978505735_7883 | Let $N = \sum_{k=1}^{49} \phi(k) \left\lfloor \frac{49}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $k = 84$ and $M = 10037$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $M$. | 7,549 | graphs = [
Graph(
let={
"_n": Const(49),
"N": Summation(var="k1", start=Const(1), end=Const(49), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Ref("_n"), Var("k1"))))),
"k": Const(84),
"M": Const(10037),
"sum": Summation(var="n", start=Const(1), end=Re... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.055 | 2026-02-08T20:34:08.929448Z | {
"verified": true,
"answer": 7549,
"timestamp": "2026-02-08T20:34:08.984629Z"
} | e052a3 | 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": 2496
},
"timestamp": "2026-02-19T00:41:25.639Z",
"answer": 7549
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a7fb0b | diophantine_product_count_v1_1439011603_340 | Let $m = 81$. Let $s$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 176400$. Let $k$ be the sum of $\phi(d)$ over all positive divisors $d$ of $s$. Compute $81$ minus the number of positive integers $x \leq 183$ such that $x$ divides $k$ and $\frac{k}{x} \leq 183$. | 57 | graphs = [
Graph(
let={
"_m": Const(81),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | B1 | [
"B3/K3"
] | 4a4ef2 | diophantine_product_count_v1 | null | 7 | 0 | [
"B1",
"B3",
"K3"
] | 3 | 14.469 | 2026-02-08T15:25:06.747591Z | {
"verified": true,
"answer": 57,
"timestamp": "2026-02-08T15:25:21.216273Z"
} | 88da5f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1481
},
"timestamp": "2026-02-16T06:26:58.762Z",
"answer": 57
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5104aa | antilemma_cartesian_v1_717093673_2376 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 12$ and $1 \leq b \leq 12$. Compute the remainder when $86960 \cdot x$ is divided by $63573$. Find the value of this remainder. | 61,932 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(12)))),
"Q": Mod(value=Mul(Const(86960), Ref("x")), modulus=Const(63573)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T16:47:33.876818Z | {
"verified": true,
"answer": 61932,
"timestamp": "2026-02-08T16:47:33.877682Z"
} | 474f3b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 788
},
"timestamp": "2026-02-17T12:24:49.881Z",
"answer": 61932
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
35d1f7 | antilemma_cartesian_v1_1978505735_7441 | Let $x$ be the number of elements in the Cartesian product of the sets $\{1, 2, \dots, 10\}$ and $\{1, 2, \dots, 12\}$. Compute the value of
$$
x + \phi\left(|x| + \binom{19}{0}\right) + \tau\left(|x| + 0!\right),
$$
where $\phi$ denotes Euler's totient function and $\tau(n)$ denotes the number of positive divisors of ... | 233 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(12)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Binom(n=Const(19), k=Const(0)))), NumDivisors(n=Sum(Abs(arg=... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0",
"ONE_BINOM_0"
] | 122c03 | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_0",
"ONE_FACTORIAL_0"
] | 3 | 0.001 | 2026-02-08T20:16:01.297215Z | {
"verified": true,
"answer": 233,
"timestamp": "2026-02-08T20:16:01.298463Z"
} | f9002c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 542
},
"timestamp": "2026-02-19T00:14:10.400Z",
"answer": 233
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "ONE_FACTOR... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
82ad26 | nt_max_prime_below_v1_784195855_2857 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $m \leq n \leq 21904$. Determine the value of the largest element in $T$... | 21,893 | graphs = [
Graph(
let={
"upper": Const(21904),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.514 | 2026-02-08T06:05:03.950340Z | {
"verified": true,
"answer": 21893,
"timestamp": "2026-02-08T06:05:04.463894Z"
} | 7fd1c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 2587
},
"timestamp": "2026-02-12T18:57:01.190Z",
"answer": 21893
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
401374 | nt_count_primes_v1_898971024_1904 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $pq = 72$. Let $m$ be the number of elements in $S$. Determine the number of prime numbers $n$ such that $m \leq n \leq 32400$. | 3,476 | graphs = [
Graph(
let={
"upper": Const(32400),
"result": 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'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.781 | 2026-02-08T16:24:53.878219Z | {
"verified": true,
"answer": 3476,
"timestamp": "2026-02-08T16:24:54.658723Z"
} | 280bfd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2245
},
"timestamp": "2026-02-17T02:50:31.812Z",
"answer": 3476
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1ee2db | comb_count_permutations_fixed_v1_1520064083_9010 | Let $N = 88341$. Let $t = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $c = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Let $n$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 6$, $1 \leq j \leq 7$, and $i + j = 7$. Define $\mathcal{D}$ to be the number of derangements of $n - t$ elements. Compute the remainder when $N... | 8,955 | graphs = [
Graph(
let={
"_n": Const(88341),
"n2": Const(0),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | b9499e | comb_count_permutations_fixed_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T10:28:31.821444Z | {
"verified": true,
"answer": 8955,
"timestamp": "2026-02-08T10:28:31.833683Z"
} | 018b92 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 1158
},
"timestamp": "2026-02-24T12:04:29.144Z",
"answer": 8955
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
12cdd0 | v1_endings_v1_124444284_774 | Let $n = 27043$ and $p = 7$. Let $v_p(n!)$ denote the largest integer $k$ such that $p^k$ divides $n!$. Let $\ell = \lfloor \log_p n \rfloor$. Compute $v_p(n!) - \ell$. | 4,499 | graphs = [
Graph(
let={
"n_val": Const(27043),
"p_val": Const(7),
"n_fact": Factorial(Ref("n_val")),
"vp_fact": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
"log_p_n": Floor(Log(left=Ref(name='n_val'), right=Ref(name='p_val'))),
... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 4 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T03:30:18.751103Z | {
"verified": true,
"answer": 4499,
"timestamp": "2026-02-08T03:30:18.751639Z"
} | 35374e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 762
},
"timestamp": "2026-02-09T21:48:51.985Z",
"answer": 4499
},
{
"id... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
}... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
bc8c96 | modular_inverse_v1_168721529_1982 | Let $a = 174$ and let $m$ be the largest prime number satisfying $2 \leq n \leq 311$. Determine the smallest positive integer $x$ such that $1 \leq x \leq 310$ and $ax \equiv 1 \pmod{m}$. Compute this value of $x$. | 227 | graphs = [
Graph(
let={
"a": Const(174),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(311)), IsPrime(Var("n"))))),
"upper": Const(310),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=A... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_inverse_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.114 | 2026-02-08T14:02:30.010611Z | {
"verified": true,
"answer": 227,
"timestamp": "2026-02-08T14:02:30.124788Z"
} | 7ccb29 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1413
},
"timestamp": "2026-02-10T00:32:05.107Z",
"answer": 227
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
90f315 | comb_factorial_compute_v1_1116507919_366 | Let $N=58$. Let
$$h=\sum_{k=0}^0(-1)^k\binom{0}{k}.$$
Consider all integers $t$ such that there exist integers $a$ and $b$ with $1\le a\le 4$, $1\le b\le 7$, $5\le t\le 26$, and
$$t=3a+2b.$$
Let $K$ be the number of such integers $t$.
Let
$$s=\sum_{k=\binom{K}{0}-1}^0(-1)^k\binom{0}{k},$$
and let $n=8s$.
Let $R$ be ... | 30,581 | graphs = [
Graph(
let={
"_n": Const(58),
"n2": Const(0),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"s": Summation(var="k", start=Sub(Binom(n=CountOver... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING",
"LIN_FORM/ZERO_BINOM_0/BINOMIAL_ALTERNATING"
] | f5f949 | comb_factorial_compute_v1 | negation_mod | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"LIN_FORM",
"ZERO_BINOM_0"
] | 4 | 0.004 | 2026-02-08T02:32:18.924188Z | {
"verified": true,
"answer": 30581,
"timestamp": "2026-02-08T02:32:18.928127Z"
} | eb7d9c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 334,
"completion_tokens": 5344
},
"timestamp": "2026-02-08T19:26:40.454Z",
"answer": 30581
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_F... | {
"lo": -1.79,
"mid": 0.18,
"hi": 1.94
} | ||
7e07f0 | nt_count_coprime_v1_1353956133_470 | Let $k$ be the largest prime number satisfying $2 \leq n \leq 11$. Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 52441$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 47,674 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(52441),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 5.368 | 2026-02-08T11:27:58.902393Z | {
"verified": true,
"answer": 47674,
"timestamp": "2026-02-08T11:28:04.270606Z"
} | 855d17 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 824
},
"timestamp": "2026-02-14T14:46:32.036Z",
"answer": 47674
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5da6bc | nt_num_divisors_compute_v1_655260480_5308 | Let $S$ be the set of all positive integers $t$ such that $27 \leq t \leq 1917$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 288$, and $t = 21a + 6b$. Let $n$ be the number of positive integers $j$ such that $1 \leq j \leq 25$ and $j^2 \leq |S|$. Compute the number of positive di... | 61,998 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(25)), Leq(Pow(Var("j"), Const(2)), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C3"
] | 89f9f8 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T18:25:18.235317Z | {
"verified": true,
"answer": 61998,
"timestamp": "2026-02-08T18:25:18.240687Z"
} | 84a974 | 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": 6387
},
"timestamp": "2026-02-18T16:53:01.903Z",
"answer": 61998
},
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4bd4e2 | nt_min_coprime_above_v1_809748730_458 | Let $S$ be the set of all integers $t$ such that $16 \le t \le 744$ and there exist positive integers $a$ and $b$ with $1 \le a \le 21$, $1 \le b \le 89$, and $t = 10a + 6b$. Let $m$ be the number of elements in $S$. Determine the smallest integer $n$ such that $3000 < n \le 3367$ and $\gcd(n, m) = 1$. Compute this val... | 3,001 | graphs = [
Graph(
let={
"start": Const(3000),
"upper": Const(3367),
"modulus": 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(nam... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.06 | 2026-02-08T11:32:06.076013Z | {
"verified": true,
"answer": 3001,
"timestamp": "2026-02-08T11:32:06.135882Z"
} | bdd6d6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2166
},
"timestamp": "2026-02-14T15:34:16.583Z",
"answer": 3001
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
0694be | nt_min_coprime_above_v1_458359167_5207 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. For each integer $n$ from 1 to 5, compute the sum of the decimal digits of $n$, and let $R$ be the number of these $n$ for wh... | 32,401 | graphs = [
Graph(
let={
"start": Const(32400),
"upper": Const(32843),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(5)), Eq(Mod(value=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/L3B/MIN_PRIME_FACTOR"
] | 5c3b45 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"L3B",
"MIN_PRIME_FACTOR"
] | 3 | 0.064 | 2026-02-08T12:20:46.615442Z | {
"verified": true,
"answer": 32401,
"timestamp": "2026-02-08T12:20:46.679897Z"
} | de6895 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 2927
},
"timestamp": "2026-02-15T00:36:48.496Z",
"answer": 32401
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"stat... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
d17ec2 | comb_count_partitions_v1_1218484723_6868 | Let $n$ be the number of integers $a$ with $0 \le a \le 1368$ such that
$$\bigl(a^{3} + 5a^{2} + 4a + 3 \bmod 1369\bigr)^{3} + 5\bigl(a^{3} + 5a^{2} + 4a + 3 \bmod 1369\bigr)^{2} + 4\bigl(a^{3} + 5a^{2} + 4a + 3 \bmod 1369\bigr) + 3 \bmod 1369 = a,$$
and
$$a^{3} + 5a^{2} + 4a + 3 \bmod 1369 \ne a.$$
Let $Q = p(n)$. Com... | 26,015 | graphs = [
Graph(
let={
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(1368)), Eq(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Var("a"), Ref("_n")), Mul(Const(5), Pow(Var("a"), Const(2))), Mul(Const(4), Var("a")), Co... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_partitions_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.002 | 2026-02-25T08:19:50.228808Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-25T08:19:50.230608Z"
} | 76111c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 22357
},
"timestamp": "2026-03-30T02:57:17.386Z",
"answer": 26015
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
dcb87b | comb_count_permutations_fixed_v1_1978505735_7542 | Let $n = 5$. Define $k$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the subfactorial of $m$. Let $Q$ be the remainder when this value is multiplie... | 70,053 | graphs = [
Graph(
let={
"n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=12)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T20:18:16.406005Z | {
"verified": true,
"answer": 70053,
"timestamp": "2026-02-08T20:18:16.407402Z"
} | c58777 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1285
},
"timestamp": "2026-02-19T00:20:01.733Z",
"answer": 70053
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5e4e8e | nt_count_divisible_and_v1_1978505735_3194 | Let $d_1$ be the number of integers $t$ such that $5 \leq t \leq 14$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $d_2 = 12$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 96960$, $n$ is divisible by $d_1$, and $n$ is divisible... | 75,776 | graphs = [
Graph(
let={
"upper": Const(96960),
"d1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 8.959 | 2026-02-08T17:27:04.267076Z | {
"verified": true,
"answer": 75776,
"timestamp": "2026-02-08T17:27:13.226423Z"
} | b05150 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1332
},
"timestamp": "2026-02-18T02:14:02.848Z",
"answer": 75776
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2372a2 | nt_count_divisible_and_v1_1915831931_878 | Let $d_1 = 6$. Let $d_2$ be the sum of all real solutions $x$ to the equation $x^2 - 9x - 5236 = 0$. Determine the number of positive integers $n$ such that $1 \leq n \leq 71280$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 3,960 | graphs = [
Graph(
let={
"upper": Const(71280),
"d1": Const(6),
"d2": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-9), Var("x")), Const(-5236)), Const(0)))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"),... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_divisible_and_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 2.977 | 2026-02-08T15:44:21.357528Z | {
"verified": true,
"answer": 3960,
"timestamp": "2026-02-08T15:44:24.334754Z"
} | ded379 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 460
},
"timestamp": "2026-02-16T12:19:11.167Z",
"answer": 3960
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3aea88 | v1_endings_v1_677425708_1206 | Let $n = 51264$ and let $n!$ denote the factorial of $n$. Determine the largest integer $x$ such that $2^x$ divides $n!$. Compute $x$. | 51,260 | graphs = [
Graph(
let={
"n_val": Const(51264),
"p_val": Const(2),
"n_fact": Factorial(Ref("n_val")),
"x": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 5 | null | [
"V1"
] | 1 | 0 | 2026-02-08T04:02:10.666692Z | {
"verified": true,
"answer": 51260,
"timestamp": "2026-02-08T04:02:10.666956Z"
} | e9a99a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1308
},
"timestamp": "2026-02-09T17:02:17.028Z",
"answer": 51260
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"sta... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
115209 | nt_min_with_divisor_count_v1_865884756_3474 | Let $ d = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor $. Determine the value of the smallest positive integer $ n $ such that $ n \leq 10201 $ and the number of positive divisors of $ n $ is equal to $ d $. | 4 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(10201),
"div_count": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"K2"
] | 6897ab | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"K2",
"MOBIUS_COPRIME"
] | 2 | 12.089 | 2026-02-08T17:28:11.131199Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T17:28:23.220255Z"
} | f184ee | 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": 537
},
"timestamp": "2026-02-18T02:25:05.999Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9ca841 | algebra_quadratic_discriminant_v1_784195855_5898 | Let $a = 2$, $b = 4$, and $c = 2$. Define $S$ as the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Define $s$ as the minimum value of $x + y$ over... | 31,329 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(4),
"c": Const(2),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.003 | 2026-02-08T08:10:34.050699Z | {
"verified": true,
"answer": 31329,
"timestamp": "2026-02-08T08:10:34.053746Z"
} | f5fca3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1059
},
"timestamp": "2026-02-13T15:24:18.894Z",
"answer": 31329
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
c835b9 | algebra_quadratic_discriminant_v1_601307018_894 | Let $D = 2^{2} - 41 \cdot 5$ and let $N = 2 \cdot [D > 0] + [D = 0]$. Let $Q = B_{|N| \bmod 11}$, where $B_n$ denotes the $n$-th Bell number. Compute $Q$. | 1 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(2),
"c": Const(5),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Const(... | COMB | COMB | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"HALFPLANE_COUNT/POLY_ORBIT_HENSEL"
] | 4fe815 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"HALFPLANE_COUNT",
"POLY_ORBIT_HENSEL"
] | 3 | 0.27 | 2026-03-10T01:30:13.463137Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-03-10T01:30:13.732989Z"
} | 668752 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 272
},
"timestamp": "2026-03-29T00:29:40.014Z",
"answer": 1
},
{
"id": ... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "HALFPLANE_COUNT",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8... | {
"lo": -10,
"mid": -6.42,
"hi": -2.84
} | ||
a87759 | modular_count_residue_v1_548369836_48 | Let $m$ be the smallest divisor of $1031153$ that is at least $2$. Let $s$ be the sum of $\mu(d)$ over all positive divisors $d$ of $\gcd(7, 143)$, where $\mu$ is the Möbius function. Determine the number of integers $n$ such that $s \leq n \leq 46368$ and $n \equiv 3 \pmod{m}$. | 1,599 | graphs = [
Graph(
let={
"_n": Const(143),
"upper": Const(46368),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1031153))))),
"r": Const(3),
"result": CountOverSet(set=... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_COPRIME"
] | 60ba20 | modular_count_residue_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 2 | 3.711 | 2026-02-08T02:44:36.527354Z | {
"verified": true,
"answer": 1599,
"timestamp": "2026-02-08T02:44:40.238452Z"
} | 99f422 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1897
},
"timestamp": "2026-02-08T19:44:58.221Z",
"answer": 1599
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"... | {
"lo": -4.84,
"mid": -1.65,
"hi": 1.92
} | ||
456cb5 | nt_count_coprime_v1_1431428450_5 | Let $k$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 14$. Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 32768$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 28,087 | graphs = [
Graph(
let={
"upper": Const(32768),
"k": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(14)))), expr=Mul(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_coprime_v1 | null | 3 | 0 | [
"B1"
] | 1 | 3.462 | 2026-02-08T13:07:02.987017Z | {
"verified": true,
"answer": 28087,
"timestamp": "2026-02-08T13:07:06.448943Z"
} | f382db | 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": 666
},
"timestamp": "2026-02-15T10:59:17.992Z",
"answer": 28087
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9d8f40 | algebra_quadratic_discriminant_v1_1439011603_2507 | Let $a = -1$, $b = -5$, and $n = 4$. Let $c$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 625$. Compute $b^2 - nac$. | 225 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-1),
"b": Const(-5),
"c": 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("... | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3",
"BINOMIAL_ALTERNATING"
] | 2 | 0.02 | 2026-02-08T16:50:20.819647Z | {
"verified": true,
"answer": 225,
"timestamp": "2026-02-08T16:50:20.839240Z"
} | a85d60 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 605
},
"timestamp": "2026-02-17T13:30:15.754Z",
"answer": 225
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
05e54e | algebra_poly_eval_v1_1742523217_2882 | Let $t = 5$ and $n = 3$. Define
$$
\text{result} = 6t^4 - t^n + d_{\min} \cdot t^2 + 7t - 3,
$$
where $d_{\min}$ is the smallest integer $d \geq 2$ that divides 75. Let $Q$ be the remainder when $20325 \cdot \text{result}$ is divided by 64394. Find the value of $Q$. | 61,162 | graphs = [
Graph(
let={
"_n": Const(3),
"t": Const(5),
"result": Sum(Mul(Const(6), Pow(Ref("t"), Const(4))), Mul(Const(-1), Pow(Ref("t"), Ref("_n"))), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=C... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.005 | 2026-02-08T05:25:53.243803Z | {
"verified": true,
"answer": 61162,
"timestamp": "2026-02-08T05:25:53.248594Z"
} | 3dc298 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1044
},
"timestamp": "2026-02-12T08:27:20.636Z",
"answer": 61162
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a847b9 | geo_count_lattice_triangle_v1_1248542787_896 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(100,80)$, and $(21,196)$, multiplied by $2$. Let $B$ be the number of lattice points on the boundary of this triangle, computed as the sum of the greatest common divisors of the differences in coordinates along each side. Compute $\frac{A + 2 - B}{2}$. Fi... | 8,947 | graphs = [
Graph(
let={
"_n": Const(21),
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=196)), Mul(Ref(name='_n'), Sub(left=Const(value=0), right=Const(value=80))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(value=80))), GCD(a=Abs(arg=Sub... | ALG | NT | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T03:28:35.771843Z | {
"verified": true,
"answer": 8947,
"timestamp": "2026-02-08T03:28:35.781766Z"
} | 60390b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2159
},
"timestamp": "2026-02-09T09:43:53.307Z",
"answer": 8947
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 0.96,
"hi": 5.17
} | ||
e35c33 | antilemma_k2_v1_153355830_2460 | Let $\phi(n)$ denote Euler's totient function. Define $x = \sum_{k=1}^{d} \phi(k) \left\lfloor \frac{52}{k} \right\rfloor$, where $d = \sum_{d' \mid 52} \phi(d')$. Compute the remainder when $84620 \cdot x$ is divided by $68289$. | 37,037 | graphs = [
Graph(
let={
"_n": Const(52),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=52), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Mod(value=Mul(Const(84620), Ref("x")), ... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T07:08:40.129298Z | {
"verified": true,
"answer": 37037,
"timestamp": "2026-02-08T07:08:40.130043Z"
} | 40b1ef | 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": 1374
},
"timestamp": "2026-02-13T08:19:10.572Z",
"answer": 37037
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
87e7fb | antilemma_sum_equals_v1_1520064083_4752 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 33$, $1 \le i \le 31$, and $1 \le j \le 32$. Compute the value of $$
x + \varphi(|x| + 1) + \tau(|x| + 1),
$$ where $\varphi(k)$ denotes Euler's totient function and $\tau(k)$ denotes the number of positive divisors of $k$. | 53 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(33)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(31)), right=IntegerRange(start=Const(1), end=Const(32))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.119 | 2026-02-08T06:25:14.308053Z | {
"verified": true,
"answer": 53,
"timestamp": "2026-02-08T06:25:14.427149Z"
} | 0a5342 | 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": 844
},
"timestamp": "2026-02-24T06:06:33.626Z",
"answer": 53
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
938ec9 | comb_binomial_compute_v1_2051736721_3993 | Let $t$ be an integer satisfying $21 \leq t \leq 72$. Define $n$ to be the number of integers $t$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 2$, such that $t = 6a + 15b$.
Let $k$ be the largest positive integer at most 6 that divides 66.
Compute the remainder when $7020... | 42,513 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(50077),
"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=... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR",
"LIN_FORM"
] | 35b5d8 | comb_binomial_compute_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 0.004 | 2026-02-08T17:40:16.570774Z | {
"verified": true,
"answer": 42513,
"timestamp": "2026-02-08T17:40:16.574534Z"
} | cd5ee1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1209
},
"timestamp": "2026-02-18T05:49:26.097Z",
"answer": 42513
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
558c38 | comb_count_surjections_v1_1742523217_428 | Let $k$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 3$, $1 \leq j \leq 3$, and $i + j = 5$. Compute the value of $k! \cdot S(7,k)$, where $S(n,k)$ denotes the Stirling number of the second kind. Find the value of this expression. | 126 | graphs = [
Graph(
let={
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(5)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T03:01:53.143146Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T03:01:53.155411Z"
} | b1ce89 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 682
},
"timestamp": "2026-02-09T17:44:49.733Z",
"answer": 126
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
2dc130 | modular_mod_compute_v1_1439011603_238 | Let $t$ be an integer. Consider all values of $t$ such that $8 \leq t \leq 44$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 4$, and $t = 3a + 5b$. Let $N$ be the number of such integers $t$. Let $r$ be the remainder when $-50176$ is divided by $24025$. Compute the remainder when ... | 62,860 | graphs = [
Graph(
let={
"_n": Const(63579),
"a": Const(-50176),
"m": Const(24025),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": Mod(value=Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | modular_mod_compute_v1 | affine_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T15:22:13.083702Z | {
"verified": true,
"answer": 62860,
"timestamp": "2026-02-08T15:22:13.086142Z"
} | b86282 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 1874
},
"timestamp": "2026-02-16T05:17:04.137Z",
"answer": 62860
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b02b2f | comb_binomial_compute_v1_601307018_9753 | For an integer $a$ with $0 \le a \le 360$, define sequences $R, S, T, K$ recursively by:
\[
R = (3a^4 - 4a^3 - a^2 + 4a - 5) \bmod 361,
\]
\[
S = (3R^4 - 4R^3 - R^2 + 4R - 5) \bmod d, \quad \text{where } d = \min\{ |x - y| : x,y > 0,\, xy = 267176 \},
\]
\[
T = (3S^4 - 4S^3 - S^2 + 4S - 5) \bmod 361,
\]
\[
K = (3T^4 - ... | 12,870 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(4),
"n": Const(16),
"k": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(360)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p... | COMB | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"B3_DIFF/POLY_ORBIT_HENSEL"
] | 91f215 | comb_binomial_compute_v1 | null | 7 | 0 | [
"B3_DIFF",
"POLY_ORBIT_HENSEL",
"POLY_ORBIT_LEGENDRE"
] | 3 | 0.024 | 2026-03-10T10:11:28.181241Z | {
"verified": true,
"answer": 12870,
"timestamp": "2026-03-10T10:11:28.204848Z"
} | b607b4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 362,
"completion_tokens": 11835
},
"timestamp": "2026-04-19T11:59:32.665Z",
"answer": 12870
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"le... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
7c35e2 | modular_mod_compute_v1_601307018_2360 | Let $D$ be the set of positive divisors $d$ of $1806$ such that $d^2 \le 1806$. Let $N = \max D$. Let $a$ be the largest prime number $n$ with $2 \le n \le N$. Let $m = \min\{ |x - y| : x, y \in \mathbb{Z}^+,\, xy = 109734677 \}$. Define $M = a \bmod m$. Compute $65536 - M$. | 65,495 | graphs = [
Graph(
let={
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(1806)), Leq(Mul(Var("d"), Var("d")), Const(1806)))... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/MAX_PRIME_BELOW",
"B3_DIFF"
] | 79451a | modular_mod_compute_v1 | null | 5 | 0 | [
"B3_CLOSEST",
"B3_DIFF",
"MAX_PRIME_BELOW"
] | 3 | 0.01 | 2026-03-10T03:02:16.732921Z | {
"verified": true,
"answer": 65495,
"timestamp": "2026-03-10T03:02:16.742639Z"
} | 3845a0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:08:11.609Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
... | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
a55788 | alg_qf_psd_min_v1_1218484723_4380 | Let
$$H = \min\{2b_2^{2} + 25a_2^{2} + 2a_2b_2 : 1 \le a_2 \le 5,\ 1 \le b_2 \le 5\},$$
$$I = \min\{H a_1^{2} + 34b_1^{2} - 50a_1b_1 : 1 \le a_1 \le 14,\ 1 \le b_1 \le 14\}.$$
Consider all ordered triples $(a,b,c)$ of positive integers such that $1 \le a \le 13$, $1 \le c \le 13$, and $1 \le b \le I$. Let $Q$ be the mi... | 36,708 | graphs = [
Graph(
let={
"_m": Const(25),
"_n": Const(57960),
"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(13)), Geq(Var("b"), Const(1)), Leq(Var("b"), Mi... | ALG | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"QF_PSD_MIN/QF_PSD_MIN"
] | d79671 | alg_qf_psd_min_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"QF_PSD_MIN"
] | 2 | 1.317 | 2026-02-25T05:59:57.558521Z | {
"verified": true,
"answer": 36708,
"timestamp": "2026-02-25T05:59:58.875585Z"
} | 05480c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 340,
"completion_tokens": 18467
},
"timestamp": "2026-03-29T15:23:27.449Z",
"answer": 36708
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
164f57 | alg_poly3_count_v1_601307018_1023 | Let $B = \sum a1^2 + b1^2 + c^2$, where the sum is taken over all ordered triples $(a1, b1, c)$ of positive integers satisfying $a1^2 + b1^2 + c^2 = a1b1 + b1c + ca1$, $3a1 + 6b1 + 7c = 192$, $a1 \ge 1$, $b1 \ge 1$, $c \ge 1$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 432$ and $1 ... | 432 | graphs = [
Graph(
let={
"_n": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(432)), Geq(Var("b"), Const(1)), Leq(Var("b"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elem... | ALG | null | COUNT | sympy | POLY3_COUNT | [
"SUM_SQUARES_IDENTITY"
] | 9879b8 | alg_poly3_count_v1 | null | 8 | 0 | [
"POLY3_COUNT",
"SUM_SQUARES_IDENTITY"
] | 2 | 9.589 | 2026-03-10T01:36:46.029274Z | {
"verified": true,
"answer": 432,
"timestamp": "2026-03-10T01:36:55.618126Z"
} | d2d52f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 1858
},
"timestamp": "2026-04-18T15:11:05.240Z",
"answer": 432
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok"
}
] | {
"lo": -3.63,
"mid": -0.6,
"hi": 2.71
} | ||
2f9a1f | comb_count_derangements_v1_1116507919_217 | Let $m$ be the number of positive integers $n \leq 4$ such that $2$ divides $n$ and $\gcd(n, 21) = 1$. Let $T$ be the set of all positive integers $t \leq 7586$ such that $t \geq 18$ and there exist positive integers $a \leq 782$, $b \leq 133$ satisfying $t = 8a + 10b$. Let $n$ be the smallest divisor of $|T|$ that is ... | 68,814 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4)), Divides(divisor=Const(2), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"_n": Const(74024),
"n": MinOverSet(set=S... | NT | COMB | COUNT | sympy | C5 | [
"C5/LIN_FORM/MIN_PRIME_FACTOR"
] | 05b64f | comb_count_derangements_v1 | null | 7 | 0 | [
"C5",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.003 | 2026-02-08T02:28:55.792144Z | {
"verified": true,
"answer": 68814,
"timestamp": "2026-02-08T02:28:55.795101Z"
} | 928040 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T13:51:57.619Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lem... | {
"lo": 3.93,
"mid": 5.44,
"hi": 7.1
} | ||
fae1e6 | alg_poly_preperiod_count_v1_601307018_1904 | Let $f(x) = 2x^3 + 4x^2 + 5x + 3$. For a non-negative integer $a$, define the sequence $N = f(a) \bmod 37$, $M = f(N) \bmod 37$, $R = f(M) \bmod 37$, and $S = f(R) \bmod 37$. Find the number of integers $a$ with $0 \le a \le 48506$ such that $S = M$ and $R \neq M$. | 22,287 | 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(5), Var("a")), Const(3)), modulus=Const(37)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(4), Pow(Ref("p1"), Const(2))), Mu... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.054 | 2026-03-10T02:40:06.941032Z | {
"verified": true,
"answer": 22287,
"timestamp": "2026-03-10T02:40:06.994781Z"
} | 1fbeff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 27649
},
"timestamp": "2026-03-29T03:47:50.178Z",
"answer": 22287
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
9c93e6 | nt_count_divisors_in_range_v1_1431428450_785 | Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 176400$.
Let $m$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 174$. Let $b$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(... | 5,376 | graphs = [
Graph(
let={
"_n": Const(87115),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.009 | 2026-02-08T13:41:47.397423Z | {
"verified": true,
"answer": 5376,
"timestamp": "2026-02-08T13:41:47.405977Z"
} | aad320 | 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": 1452
},
"timestamp": "2026-02-15T19:56:44.944Z",
"answer": 5376
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1ac82f | comb_count_permutations_fixed_v1_784195855_5885 | Let $n$ be the smallest integer $d$ such that $d \ge 2$ and $d$ divides $77077$. Let $k = 3$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the subfactorial of $m$, the number of derangements of $m$ elements.
Compute the value of $r$. | 315 | 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))))),
"k": Const(3),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T08:10:14.969750Z | {
"verified": true,
"answer": 315,
"timestamp": "2026-02-08T08:10:14.972040Z"
} | 624fb5 | 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": 877
},
"timestamp": "2026-02-13T15:25:21.161Z",
"answer": 315
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
f54a66 | modular_sum_quadratic_residues_v1_124444284_1799 | Let $p$ be the largest prime number less than or equal to $195$. Let $c$ be the number of unordered pairs of coprime positive integers $(p, q)$ such that $p < q$ and $pq = 6750$. Compute the remainder when $62863 \cdot \frac{p(p-1)}{c}$ is divided by $72588$. | 61,896 | graphs = [
Graph(
let={
"_n": Const(72588),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(195)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), CountOverSet(set=SolutionsSet(var=Var("... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T04:09:23.041602Z | {
"verified": true,
"answer": 61896,
"timestamp": "2026-02-08T04:09:23.044680Z"
} | 3bc987 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2608
},
"timestamp": "2026-02-10T15:33:29.018Z",
"answer": 61896
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2583d2 | diophantine_product_count_v1_1915831931_3262 | Let $m = 5$ and $n = 15$. Define
$$
k = \sum_{k_1=1}^{\sum_{k_2=1}^{m} \phi(k_2) \left\lfloor \frac{5}{k_2} \right\rfloor} \phi(k_1) \left\lfloor \frac{n}{k_1} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $r$ be the number of positive integers $x$ such that $1 \le x \le 33$, $x$ divides $k$, and... | 22 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(15),
"k": Summation(var="k1", start=Const(1), end=Summation(var="k2", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k2")), Floor(Div(Const(5), Var("k2"))))), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Ref("_n"),... | NT | null | COUNT | sympy | VIETA_SUM | [
"K2/K2"
] | ddede2 | diophantine_product_count_v1 | null | 7 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.209 | 2026-02-08T17:31:30.879730Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T17:31:31.088351Z"
} | 9f07a8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1880
},
"timestamp": "2026-02-18T02:57:46.717Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
92de47 | modular_sum_quadratic_residues_v1_168721529_2040 | Let $p$ be the largest prime number not exceeding $231$. Compute $\frac{p(p-1)}{4}$. | 13,053 | graphs = [
Graph(
let={
"_n": Const(231),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T14:03:36.420313Z | {
"verified": true,
"answer": 13053,
"timestamp": "2026-02-08T14:03:36.421571Z"
} | 23ad78 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 197
},
"timestamp": "2026-02-10T01:13:26.178Z",
"answer": 13053
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status":... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
80e03f | geo_count_lattice_rect_v1_1440796553_1094 | Let $a = 222$ and $b = 72$. Let $\text{result}$ be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries.
Let $Q$ be the remainder when $44121 \cdot \text{result}$ is divided by $97726$.
Compute $Q$. | 57,385 | graphs = [
Graph(
let={
"a": Const(222),
"b": Const(72),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(97726)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T12:11:14.462066Z | {
"verified": true,
"answer": 57385,
"timestamp": "2026-02-08T12:11:14.463239Z"
} | 9fa136 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T15:25:14.459Z",
"answer": 80125
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
44f154 | sequence_count_fib_divisible_v1_677425708_993 | Let $ f(x) = x^2 - 324x + 9860 $. Let $ S $ be the set of all real solutions to $ f(x) = 0 $, and let $ s $ be the sum of all elements in $ S $. Let $ u $ be the number of positive integers $ k \leq 257580 $ such that $ s $ divides $ k $. Let $ r $ be the number of positive integers $ n \leq u $ such that $ 13 $ divide... | 157 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(257580)), Divides(divisor=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-324), Var(... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"VIETA_SUM/C2"
] | 0c1c77 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"C2",
"ONE_PHI_1",
"VIETA_SUM"
] | 3 | 0.069 | 2026-02-08T03:56:42.576472Z | {
"verified": true,
"answer": 157,
"timestamp": "2026-02-08T03:56:42.645481Z"
} | 6cf4e2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 2051
},
"timestamp": "2026-02-10T14:54:34.655Z",
"answer": 157
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
22bebe | sequence_lucas_compute_v1_677425708_448 | Let $n$ be the largest prime number such that $2 \leq n \leq 27$. Compute the $n$th Lucas number. | 64,079 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(27)), IsPrime(Var("n"))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T03:33:02.535490Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T03:33:02.536323Z"
} | c93a75 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 776
},
"timestamp": "2026-02-08T20:35:19.298Z",
"answer": 64079
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
2a3759 | sequence_fibonacci_compute_v1_1520064083_5875 | Let $n$ be the largest integer such that $2^n \leq 61305209$. Define $F_n$ to be the $n$th Fibonacci number, where $F_0 = 0$, $F_1 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 2$. Compute the remainder when $1 - F_n$ is divided by $56927$. | 38,830 | graphs = [
Graph(
let={
"_n": Const(56927),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(2), Var("k")), Const(61305209)))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Sub(Const(1), Ref("result")), modulus=Ref("_n")),
... | NT | null | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T07:42:00.759919Z | {
"verified": true,
"answer": 38830,
"timestamp": "2026-02-08T07:42:00.760698Z"
} | 64a4d6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 931
},
"timestamp": "2026-02-13T11:39:33.566Z",
"answer": 38830
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lem... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
c1b369 | comb_catalan_compute_v1_1218484723_1701 | Let $C_n$ denote the $n$-th Catalan number, defined by $C_n = \frac{1}{n+1}\binom{2n}{n}$. Let $N = C_{10}$. Find the remainder when $44121N$ is divided by $82505$. | 78,911 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(82505)),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | HALFPLANE_COUNT | [
"HALFPLANE_COUNT"
] | 0861dc | comb_catalan_compute_v1 | null | 2 | 0 | [
"HALFPLANE_COUNT"
] | 1 | 0.01 | 2026-02-25T03:23:53.712962Z | {
"verified": true,
"answer": 78911,
"timestamp": "2026-02-25T03:23:53.722725Z"
} | 01a5da | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1376
},
"timestamp": "2026-03-29T00:52:46.923Z",
"answer": 78911
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "HALFPLANE_COUNT",
"status": "ok"
},
{
"lemma": "V8_SUM... | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
43f16c_n | algebra_poly_eval_v1_1218484723_561 | An architect designs a rectangular garden with area $10316944$ square units and wishes to minimize the perimeter. The cost of fencing depends on a polynomial evaluated at $z = 19$: $120z^5 - 278z^4 + 29z^3 + 320z^2 - 233z + 42$. The total project cost is this value divided by the minimum possible sum of the garden's le... | 40,662 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 4 | null | [
"B3"
] | 1 | 0.005 | 2026-02-25T02:13:06.349017Z | null | db978d | 43f16c | narrative | 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": 1705
},
"timestamp": "2026-03-30T15:34:36.315Z",
"answer": 40662
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
a0118e | modular_modexp_compute_v1_1978505735_1713 | Let $m = 2$. Define $s$ to be the sum of all even integers $n$ such that $1 \le n \le m$. Let $a$ be the smallest divisor of $224939$ that is at least $s$. Compute the value of $a^{4181} \bmod 70000$. | 60,811 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Eq(Mod(value=Var("n"), modulus=Const(2)), Const(0))))),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Ge... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/MIN_PRIME_FACTOR"
] | 57d6d0 | modular_modexp_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 2 | 0.004 | 2026-02-08T16:21:49.035681Z | {
"verified": true,
"answer": 60811,
"timestamp": "2026-02-08T16:21:49.039575Z"
} | e8670a | 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": 3018
},
"timestamp": "2026-02-17T02:21:22.286Z",
"answer": 60811
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9becad_l | nt_sum_totient_over_divisors_v1_1116507919_94 | Let $n = 84852$. Define $\varphi(d)$ to be Euler's totient function. Compute
$$
\sum_{d \mid n} \varphi(d).
$$
Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 14002$ and the sum of the decimal digits of $n$ is even. Let $c$ be the number of elements in $A$. Let $P$ be the set of all prime numbe... | 59,244 | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"L3B"
] | 6bca7f | nt_sum_totient_over_divisors_v1 | two_moduli | 5 | 0 | [
"L3B",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T02:25:31.456965Z | {
"verified": false,
"answer": 59457,
"timestamp": "2026-02-08T02:25:31.461828Z"
} | 7c7576 | 9becad | 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": 321,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:26:25.149Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
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},
{
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},
{
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{
"lemma": "V7",
"status": "no"
},
{
... | {
"lo": 5.23,
"mid": 7.03,
"hi": 9.99
} | |
4fd5fe_n | alg_telescope_v1_1218484723_6865 | A robot moves across a linear track, increasing its position by $(k+1)^2 - k^2$ units in step $k$, for $k = 0$ to $78$. The total distance it travels is the sum of these increments. Meanwhile, a sensor network can register signals at frequencies $t = 3a + 7b + 18$, where $a$ ranges from $1$ to $1213$ and $b$ from $1$ t... | 6,241 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_telescope_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-25T08:19:24.427696Z | null | f78625 | 4fd5fe | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
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},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T01:54:13.405Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
565523_n | alg_poly3_min_v1_601307018_2246 | A music producer samples beats at intervals divisible by $99$ within the first $198$ milliseconds and sums their timestamps to get $M$. She then identifies the latest millisecond $P \le M$ that is a prime number. A sound engineer tunes a parameter $(a, b)$, where $a$ ranges from $1$ to $293$ and $b$ from $1$ to $P$, mi... | 15,127 | ALG | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/MAX_PRIME_BELOW"
] | caf344 | alg_poly3_min_v1 | null | 4 | null | [
"MAX_PRIME_BELOW",
"SUM_DIVISIBLE"
] | 2 | 0.133 | 2026-03-10T02:54:27.622050Z | null | f87d26 | 565523 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 7203
},
"timestamp": "2026-03-29T15:57:53.188Z",
"answer": 25127
},
{
... | 1 | [
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
07c042 | antilemma_sum_equals_v1_151522320_2164 | Let $n$ be the number of ordered pairs $(i,j)$ where $i$ is an integer from 1 to 6 and $j$ is an integer from 1 to 17. Determine the number of ordered pairs $(i,j)$ of positive integers with $1 \le i \le 100$ and $1 \le j \le 101$ such that $i + j = n$. Compute this value. | 100 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(17)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.047 | 2026-02-08T04:39:35.528758Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T04:39:35.575651Z"
} | 07211d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 870
},
"timestamp": "2026-02-24T01:23:51.460Z",
"answer": 100
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
6400c8 | comb_catalan_compute_v1_784195855_4703 | Let $n$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 2$ and $1 \leq b \leq 5$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.184 | 2026-02-08T07:17:15.632380Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T07:17:15.816475Z"
} | aa151b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 439
},
"timestamp": "2026-02-24T07:50:57.499Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
958381 | nt_sum_divisors_mod_v1_784195855_2567 | Let $n = 720$ and $M = 10{,}009$. Define $\sigma$ to be the sum of all positive divisors of $n$. Let $r$ be the remainder when $\sigma$ is divided by $M$. Compute the number of positive integers $n'$ such that $1 \leq n' \leq 53{,}900$ and $n' \equiv \left\lfloor \frac{n'}{2} \right\rfloor \pmod{11}$. Subtract $r$ from... | 2,482 | graphs = [
Graph(
let={
"n": Const(720),
"M": Const(10009),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": Sub(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | fba717 | nt_sum_divisors_mod_v1 | negation_mod | 5 | 0 | [
"L3C"
] | 1 | 0.005 | 2026-02-08T05:52:38.968515Z | {
"verified": true,
"answer": 2482,
"timestamp": "2026-02-08T05:52:38.973254Z"
} | 24ab02 | 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": 1200
},
"timestamp": "2026-02-12T16:05:16.061Z",
"answer": 2482
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e61d94 | antilemma_k3_v1_1918700295_4163 | Let $n = 93572$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Compute the remainder when $x^2 + 13x + 29$ is divided by $50643$. | 1,304 | graphs = [
Graph(
let={
"_n": Const(93572),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(29),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Const(13), Ref("x")), Ref("_c")), modulus=Const(50643)),
},
... | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T09:11:08.938589Z | {
"verified": true,
"answer": 1304,
"timestamp": "2026-02-08T09:11:08.939059Z"
} | 13c3fb | 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": 1859
},
"timestamp": "2026-02-14T01:45:27.201Z",
"answer": 1304
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1197da | comb_binomial_compute_v1_458359167_4797 | Let $n$ be the number of positive integers $j$ with $1 \leq j \leq 12$ such that $j^5 \leq 248832$. Let $k$ be the smallest divisor of $13013$ that is at least $2$. Compute $28224 - \binom{n}{k}$. | 27,432 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": Const(13013),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_m")), Leq(Pow(Var("j"), Const(5)), Const(248832))), domain='positive_integers')),
"k": MinO... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"C3"
] | 6c0ca7 | comb_binomial_compute_v1 | null | 4 | 0 | [
"C3",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T12:02:41.629277Z | {
"verified": true,
"answer": 27432,
"timestamp": "2026-02-08T12:02:41.631025Z"
} | 559d50 | 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": 1009
},
"timestamp": "2026-02-14T22:11:34.953Z",
"answer": 27432
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
300d11 | antilemma_sum_equals_v1_2051736721_4128 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 99$ and $1 \leq i, j \leq 99$. Compute the value of $$
Q = x + \left(2^{(x \bmod 16)} \bmod 98864\right).$$ | 102 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(99)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(99)), right=IntegerRange(start=Const(1), end=Const(99))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.027 | 2026-02-08T17:45:06.269550Z | {
"verified": true,
"answer": 102,
"timestamp": "2026-02-08T17:45:06.296079Z"
} | 7e8cf9 | 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": 700
},
"timestamp": "2026-02-24T22:58:55.833Z",
"answer": 102
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
d8843e | diophantine_product_count_v1_1918700295_4224 | Let $k = 840$ and $u = 317$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Let $r$ be the number of elements in $S$. Determine the value of the smallest positive integer $m$ such that the $m$-th Fibonacci number is divisible by $|r| + 2$. | 60 | graphs = [
Graph(
let={
"k": Const(840),
"upper": Const(317),
"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"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"K2"
] | 6897ab | diophantine_product_count_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"K2"
] | 2 | 0.316 | 2026-02-08T09:14:14.715599Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T09:14:15.031225Z"
} | c10d2a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1998
},
"timestamp": "2026-02-14T01:52:35.574Z",
"answer": 60
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ea4842 | sequence_count_fib_divisible_v1_238844314_106 | Let $n$ be a positive integer such that $1 \leq n \leq s$, where $s$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers satisfying $xy = 94864$. Let $d = 16$. Define $r$ to be the number of such $n$ for which $d$ divides the $n$th Fibonacci number. Compute the remainder when $12316 \cd... | 42,546 | graphs = [
Graph(
let={
"_n": Const(12316),
"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(94864)))), expr=Sum(Var("x"), Var("y... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.074 | 2026-02-08T13:07:30.152544Z | {
"verified": true,
"answer": 42546,
"timestamp": "2026-02-08T13:07:30.226186Z"
} | e62e57 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 2386
},
"timestamp": "2026-02-15T10:07:53.712Z",
"answer": 42546
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2be312 | modular_product_range_v1_601307018_316 | Let $T$ be the set of integers $t$ such that $t = 15a + 21b$ for some integers $a, b$ with $1 \le a \le 42$, $1 \le b \le 6$, and $36 \le t \le 756$. Let $M = \prod_{i=128}^{|T|} i$. Find the remainder when $M$ is divided by $11369$. | 8,951 | graphs = [
Graph(
let={
"_n": Const(128),
"prod": MathProduct(expr=Var("i"), var="i", start=Ref("_n"), end=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)), ... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_product_range_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-03-10T00:51:07.919031Z | {
"verified": true,
"answer": 8951,
"timestamp": "2026-03-10T00:51:07.923434Z"
} | 9c8885 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T22:48:51.104Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": 5.21,
"mid": 7.83,
"hi": 10
} | ||
4d6902 | comb_binomial_compute_v1_865884756_4208 | Let $n = 12$ and let $k$ be the largest prime number satisfying $2 \leq k \leq 8$. Compute $\binom{n}{k}$. | 792 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(12),
"k": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(8)), IsPrime(Var("n1"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=R... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T17:46:51.072293Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T17:46:51.074329Z"
} | 564dfb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 562
},
"timestamp": "2026-02-16T11:38:44.105Z",
"answer": 792
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
f8bbde | diophantine_product_count_v1_784195855_5307 | Let $k$ be the number of integers $t$ such that $8 \leq t \leq 1275$ and $t = 5a + 3b$ for some integers $a$ and $b$ with $1 \leq a \leq 54$ and $1 \leq b \leq 335$. Let $\text{upper}$ be the number of integers $t$ such that $31 \leq t \leq 1282$ and $t = 9a + 12b + 10$ for some integers $a$ and $b$ with $1 \leq a \leq... | 30 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=54)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 6 | 0 | [
"LIN_FORM",
"MOBIUS_COPRIME"
] | 2 | 0.122 | 2026-02-08T07:49:23.711918Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T07:49:23.833590Z"
} | 7bef20 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 6800
},
"timestamp": "2026-02-13T12:33:50.497Z",
"answer": 30
},
{
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ce4ffd | comb_binomial_compute_v1_655260480_4366 | Let $n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $\binom{n}{6}$ and subtract this value from $50625$. Find the result. | 45,620 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Summation(var="k1", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Ref("_n"), Var("k1"))))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(50625),
... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T17:54:17.924576Z | {
"verified": true,
"answer": 45620,
"timestamp": "2026-02-08T17:54:17.927828Z"
} | 860e82 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 892
},
"timestamp": "2026-02-18T09:39:08.394Z",
"answer": 45620
},
{... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b3467c | nt_count_intersection_v1_655260480_422 | Let $N$ be the number of integers $t$ with $11 \leq t \leq 10028$ for which there exist positive integers $a \leq 1478$ and $b \leq 588$ such that $t = 4a + 7b$. Let $a = 11$ and $b = 12$. Let $r$ be the number of positive integers $n \leq N$ such that $11$ divides $n$ and $\gcd(n, 12) = 1$. Compute the remainder when ... | 18,861 | 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=1478)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 12.469 | 2026-02-08T15:22:22.169282Z | {
"verified": true,
"answer": 18861,
"timestamp": "2026-02-08T15:22:34.637934Z"
} | 483956 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 5321
},
"timestamp": "2026-02-16T04:51:51.567Z",
"answer": 18861
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0374d9 | comb_sum_binomial_row_v1_124444284_7391 | Let $n_2 = 1$ and define $t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $u = 10 + t$ and $n_1 = u + 1$. Define $f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 12$ and $r = 2^n$. Compute $r \bmod (11 + f)$, and let $m$ be the resulting value. Determine the $m$-th Bell number. | 15 | graphs = [
Graph(
let={
"n2": Const(1),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Sum(Const(10), Ref("t")),
"n1": Sum(Ref("u"), Const(1)),
"f": Summation(var="k"... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T09:06:08.344170Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T09:06:08.345052Z"
} | 4e8113 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 623
},
"timestamp": "2026-02-24T10:30:42.962Z",
"answer": 15
},
{
"id":... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
adf764 | antilemma_coprime_grid_v1_1248542787_767 | Let $x$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 40$ and $1 \leq j \leq 177$ such that $\gcd(i,j) = \phi(1)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $52750x$ is divided by $55951$. | 18,719 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=Const(1))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(40)), right=IntegerRange(start=Const(1), end=Const(177))))),
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 3d404c | antilemma_coprime_grid_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 2 | 0.001 | 2026-02-08T03:24:50.464180Z | {
"verified": true,
"answer": 18719,
"timestamp": "2026-02-08T03:24:50.464960Z"
} | a8c537 | 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": 4263
},
"timestamp": "2026-02-09T20:50:21.321Z",
"answer": 18719
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
0bad8e | nt_num_divisors_compute_v1_1439011603_2730 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 50$. Let $c = 32914$. Find the remainder when $c \cdot \tau(n)$ is divided by $77907$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 8,756 | graphs = [
Graph(
let={
"_n": Const(50),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.008 | 2026-02-08T16:55:39.193726Z | {
"verified": true,
"answer": 8756,
"timestamp": "2026-02-08T16:55:39.202136Z"
} | e37724 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 790
},
"timestamp": "2026-02-16T08:41:07.852Z",
"answer": 8756
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
b9e8ea | comb_catalan_compute_v1_124444284_2639 | Let $t$ be a positive integer such that $34 \leq t \leq 60$. Suppose there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$ and $1 \leq b \leq 2$ such that $t = 4a + 10b + 20$. Let $n$ be the number of such integers $t$. Define $\text{result} = C_n$, the $n$-th Catalan number. Let $N = 87656$. Compute the rem... | 15,908 | graphs = [
Graph(
let={
"_n": Const(87656),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:52:02.043476Z | {
"verified": true,
"answer": 15908,
"timestamp": "2026-02-08T04:52:02.045252Z"
} | de0191 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 3229
},
"timestamp": "2026-02-24T02:08:50.806Z",
"answer": 15908
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_F... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
068d79 | comb_count_partitions_v1_1520064083_4578 | Let $m=76$. Let $N$ be the number of ordered pairs $(x_1,x_2)$ of positive integers such that $x_1$ and $x_2$ are odd and $x_1+x_2=76$.
Let $r$ be the number of integers $t$ for which there exist integers $a$ and $b$ with $1\le a\le 3$, $1\le b\le 2$, $5\le t\le 12$, and
$$t=2a+3b.$$
Define
$$u=\sum_{k=0}^{r}(-1)^k\b... | 26,015 | graphs = [
Graph(
let={
"_m": Const(76),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/LIN_FORM/BINOMIAL_ALTERNATING"
] | 3dc877 | comb_count_partitions_v1 | null | 8 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"LIN_FORM"
] | 3 | 0.003 | 2026-02-08T06:19:54.749612Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T06:19:54.752366Z"
} | d32606 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 327,
"completion_tokens": 1397
},
"timestamp": "2026-02-24T05:58:22.487Z",
"answer": 26015
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"l... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
9639d0 | modular_inverse_v1_1526740231_18 | Let $m$ be the largest prime number $n$ such that $2 \leq n \leq t$, where $t$ is the number of positive integers $k$ satisfying $1 \leq k \leq 183138$ and $233 \mid k$. Let $a = 283$. Let $\text{result}$ be the smallest positive integer $x$ such that $1 \leq x \leq 772$ and
$$
a \cdot x \equiv 1 \pmod{m}.
$$
Find the ... | 295 | graphs = [
Graph(
let={
"_n": Const(233),
"a": Const(283),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(183138)), ... | NT | null | EXTREMUM | sympy | C2 | [
"C2/MAX_PRIME_BELOW"
] | 38c8ef | modular_inverse_v1 | null | 6 | 0 | [
"C2",
"MAX_PRIME_BELOW"
] | 2 | 0.039 | 2026-02-08T11:18:32.470451Z | {
"verified": true,
"answer": 295,
"timestamp": "2026-02-08T11:18:32.509816Z"
} | 6c50a1 | 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": 2480
},
"timestamp": "2026-02-14T11:49:42.073Z",
"answer": 295
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
78642e | diophantine_fbi2_min_v1_1431428450_741 | Let $k = 48$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 841$. Let $d$ be the smallest positive integer such that $3 \le d \le s_{\text{min}}$, $d$ divides $k$, and $\frac{k}{d} \ge \sum_{i=1}^3 \phi(i) \left\lfloor \frac{3}{i} \right\rfloor... | 93,855 | graphs = [
Graph(
let={
"k": Const(48),
"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(841)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"K2",
"B3"
] | f1ea07 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B3",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.035 | 2026-02-08T13:39:34.000058Z | {
"verified": true,
"answer": 93855,
"timestamp": "2026-02-08T13:39:34.035225Z"
} | af4af3 | 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": 985
},
"timestamp": "2026-02-15T19:05:24.019Z",
"answer": 93855
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ff5517 | nt_min_coprime_above_v1_48377204_471 | Let $N = 50652$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq N$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $U$ be the number of elements in $S$. Let $M = 170$. Find the smallest positive integer $n_1$ such that $n_1 > 7056$, $n_1 \leq U$, and $\gcd(n_1, M) = 1$. | 7,057 | graphs = [
Graph(
let={
"_n": Const(50652),
"start": Const(7056),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), m... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.062 | 2026-02-08T15:30:50.613206Z | {
"verified": true,
"answer": 7057,
"timestamp": "2026-02-08T15:30:50.674788Z"
} | 8d8ccf | 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": 1723
},
"timestamp": "2026-02-16T07:31:04.692Z",
"answer": 7057
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1e8024 | antilemma_k3_v1_1874849503_1263 | Let $n = 80795$. Compute the remainder when $65989 \cdot \sum_{d \mid n} \phi(d)$ is divided by $67852$, where the sum is taken over all positive divisors $d$ of $n$ and $\phi$ denotes Euler's totient function. | 42,503 | graphs = [
Graph(
let={
"_n": Const(80795),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(65989), Ref("x")), modulus=Const(67852)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:43:48.791994Z | {
"verified": true,
"answer": 42503,
"timestamp": "2026-02-08T13:43:48.792790Z"
} | 25721a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1641
},
"timestamp": "2026-02-10T02:56:43.997Z",
"answer": 42503
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
e5a8cf | nt_count_intersection_v1_1742523217_3736 | Let $n = 6$ and $N = 100000$. Define $a$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Define $b$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 121$. Compute the number of positive integers $n \leq 10... | 5,051 | graphs = [
Graph(
let={
"_n": Const(6),
"N": Const(100000),
"a": 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... | NT | null | COUNT | sympy | B1 | [
"B1",
"B3"
] | 655d51 | nt_count_intersection_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 3.334 | 2026-02-08T06:04:49.648518Z | {
"verified": true,
"answer": 5051,
"timestamp": "2026-02-08T06:04:52.982678Z"
} | ed7448 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 2819
},
"timestamp": "2026-02-12T18:44:13.294Z",
"answer": 0
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemm... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
54d950 | antilemma_k2_v1_124444284_790 | Let $n = 349$. Compute $$\sum_{k=1}^{\sum_{d \mid n} \phi(d)} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.$$. Compute the value of this expression. | 61,075 | graphs = [
Graph(
let={
"_n": Const(349),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=349), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.004 | 2026-02-08T03:30:54.743843Z | {
"verified": true,
"answer": 61075,
"timestamp": "2026-02-08T03:30:54.747665Z"
} | d28ba1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 3204
},
"timestamp": "2026-02-09T05:58:33.035Z",
"answer": 61075
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2e0830 | geo_count_lattice_triangle_v1_1918700295_3899 | Let the points $A = (0, 0)$, $B = (111, 90)$, and $C = (222, 233)$ define a triangle. The area of the triangle is half the absolute value of $111 \cdot 233 - 222 \cdot 90$. Let $b$ be the number of lattice points on the boundary of triangle $ABC$, computed as the sum of the greatest common divisors of the absolute diff... | 2,940 | graphs = [
Graph(
let={
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=233)), Mul(Const(value=222), Sub(left=Const(value=0), right=Const(value=90))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const(value=90))), GCD(a=Abs(arg=Su... | ALG | NT | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.008 | 2026-02-08T09:01:57.551226Z | {
"verified": true,
"answer": 2940,
"timestamp": "2026-02-08T09:01:57.558895Z"
} | 2a87c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1551
},
"timestamp": "2026-02-13T23:25:12.572Z",
"answer": 2940
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9957ad | nt_count_with_divisor_count_v1_124444284_1228 | Let $ d $ be the number of integers $ n $ from 1 to 13, inclusive, such that the sum of the digits of $ n $ is odd. Let $ r $ be the number of positive integers $ n $ from 1 to 61009, inclusive, that have exactly $ d $ positive divisors. Compute $ r + \phi(r+1) + \tau(r+1) $, where $ \phi $ denotes Euler's totient func... | 8 | graphs = [
Graph(
let={
"upper": Const(61009),
"div_count": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(13)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"result": CountOverSet(set=SolutionsS... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"L3B"
] | 1 | 2.604 | 2026-02-08T03:44:41.296438Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T03:44:43.900579Z"
} | 65efea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 2341
},
"timestamp": "2026-02-10T04:39:58.968Z",
"answer": 8
},
{
"id":... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} |
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