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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
b026d6 | alg_linear_system_2x2_v1_1218484723_2090 | Let $N$ be the number of elements in the Cartesian product $\{1, 2, \ldots, 5\} \times \{1, 2, \ldots, 167\}$. Let $\det = (-16)(-5) - (-18)(-17)$, $R = (-1563758)(-5) - (-1762646)(-17)$, and $S = (-16)(-1762646) - (-18)(-1563758)$. Define $T = \frac{R}{\det} + \frac{S}{\det}$. Find the remainder when $N \cdot T$ is di... | 57,983 | graphs = [
Graph(
let={
"_n": Const(63871),
"num_x": Sub(Mul(Const(-1563758), Const(-5)), Mul(Const(-1762646), Const(-17))),
"num_y": Sub(Mul(Const(-16), Const(-1762646)), Mul(Const(-18), Const(-1563758))),
"det": Sub(Mul(Const(-16), Const(-5)), Mul(Const(-18)... | ALG | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 27a9f8 | alg_linear_system_2x2_v1 | affine_mod | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-25T03:47:54.836219Z | {
"verified": true,
"answer": 57983,
"timestamp": "2026-02-25T03:47:54.838047Z"
} | 93e737 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 1899
},
"timestamp": "2026-03-29T02:54:43.744Z",
"answer": 57983
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
c58ba4 | comb_factorial_compute_v1_655260480_1268 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 8336$ such that $\binom{8336}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(8336),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(8336)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T16:00:47.077936Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T16:00:47.079223Z"
} | a5bf25 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1005
},
"timestamp": "2026-02-24T19:36:53.881Z",
"answer": 40320
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
46250c | algebra_vieta_sum_v1_124444284_9001 | Let $p$ be a positive integer. Define $k$ to be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 926100$, $\gcd(p, q) = 1$, and $p < q$. Consider the cubic equation $x^3 + kx^2 - 35x - 150 = 0$. Let $R$ be the set of all positive real solutions to this equation. Compute the product of all eleme... | 150 | graphs = [
Graph(
let={
"_n": Const(2),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=3)), Mul(CountOverSet(set=SolutionsSet(var=Var(name='p'), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_vieta_sum_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.012 | 2026-02-08T12:07:51.486506Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T12:07:51.498526Z"
} | f45243 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1178
},
"timestamp": "2026-02-14T22:35:17.057Z",
"answer": 5
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7ca89d | comb_count_derangements_v1_784195855_5687 | Let $ n $ be the number of nonnegative integers $ j $ such that $ 0 \leq j \leq 45056 $ and $ \binom{45056}{j} $ is odd. Compute the subfactorial of $ n $, denoted $ !n $, which is the number of derangements of $ n $ elements. Determine the value of $ !n $. | 14,833 | graphs = [
Graph(
let={
"_n": Const(45056),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(45056), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T08:02:45.608535Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T08:02:45.609212Z"
} | 0496a5 | 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": 1205
},
"timestamp": "2026-02-24T08:43:57.794Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
9efada | comb_binomial_compute_v1_784195855_1413 | Let $p$ be a positive integer. Suppose there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of such integers $p$. Let $k$ be the number of prime numbers $n$ such that $m \leq n \leq 11$. Compute $\binom{13}{k}$, then multiply the result by $44121$. Find the remai... | 44,017 | graphs = [
Graph(
let={
"_m": Const(56570),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=12)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COUNT_PRIMES"
] | c35fa2 | comb_binomial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"COUNT_PRIMES"
] | 2 | 0.002 | 2026-02-08T05:00:36.833595Z | {
"verified": true,
"answer": 44017,
"timestamp": "2026-02-08T05:00:36.835571Z"
} | 715cb4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1477
},
"timestamp": "2026-02-11T22:40:51.790Z",
"answer": 44017
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
de0d9d | antilemma_k3_v1_349078426_876 | Let $x = \sum_{d \mid 97933} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $19171 \cdot x$ is divided by $97272$. | 26,671 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=97933), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(19171),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(97272)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:19:13.840851Z | {
"verified": true,
"answer": 26671,
"timestamp": "2026-02-08T13:19:13.841740Z"
} | 8ee871 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 2793
},
"timestamp": "2026-02-15T13:22:00.019Z",
"answer": 26671
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d126f7 | nt_sum_gcd_range_mod_v1_784195855_5252 | Let $N$ be the largest positive divisor of $100059993$ that is less than or equal to $9999$. Define $k = 480$ and $M = 11483$. Let $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Define $\text{result} = \text{sum} \bmod M$. Finally, let $Q = 25200 - \text{result}$. Find the value of $Q$. | 23,865 | graphs = [
Graph(
let={
"N": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(9999)), Divides(divisor=Var("d"), dividend=Const(100059993))))),
"k": Const(480),
"M": Const(11483),
"sum": Summation(var="n", sta... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.897 | 2026-02-08T07:47:45.409240Z | {
"verified": true,
"answer": 23865,
"timestamp": "2026-02-08T07:47:46.306335Z"
} | b464cf | 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": 3384
},
"timestamp": "2026-02-13T12:31:51.495Z",
"answer": 23865
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
bc88c8 | comb_sum_binomial_row_v1_1742523217_5180 | Let $m$ be the number of ordered pairs $(p, q)$ of positive integers such that $p \cdot q = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of integers $t$ with $10 \le t \le 32$ for which there exist integers $a$ and $b$ such that $1 \le a \le 2$, $1 \le b \le 5$, and $t = 6a + 4b$. Compute $m^n$. | 1,024 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM"
] | a1eac8 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T10:50:56.069618Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T10:50:56.071913Z"
} | 03cd21 | 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": 1208
},
"timestamp": "2026-02-14T09:02:30.062Z",
"answer": 1024
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ba82dd | algebra_poly_eval_v1_601307018_335 | Let $y$ be the number of positive integers $t$ such that $t = 6a + 4b$ for some integers $a, b$ with $1 \le a \le 3$, $1 \le b \le 3$, and $10 \le t \le 30$. Let $S$ be the number of integers $t1$ such that $t1 = 2a + 3b$ for some integers $a, b$ with $1 \le a \le 4$, $1 \le b \le 2$, and $5 \le t1 \le 14$. Define $R =... | 6,000 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(3),
"y": 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=Cons... | NT | NT | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"LIN_FORM"
] | 7209d0 | algebra_poly_eval_v1 | null | 5 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.015 | 2026-03-10T00:52:13.895910Z | {
"verified": true,
"answer": 6000,
"timestamp": "2026-03-10T00:52:13.910916Z"
} | 1b3e34 | CC BY 4.0 | null | null | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"statu... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
3ca9f7 | nt_sum_divisors_mod_v1_458359167_2853 | Let $n = 1260$ and $M = 10691$. Let $\sigma$ be the sum of the positive divisors of $n$. Let $r$ be the remainder when $\sigma$ is divided by $M$. Let $c$ be the smallest divisor of $4028033$ that is at least 2. Compute the remainder when $\left(r \bmod 293\right) + c \cdot \left(r \bmod 337\right)$ is divided by $9180... | 6,575 | graphs = [
Graph(
let={
"_n": Const(91809),
"n": Const(1260),
"M": Const(10691),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"_c": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Va... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | nt_sum_divisors_mod_v1 | two_moduli | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T06:48:13.153253Z | {
"verified": true,
"answer": 6575,
"timestamp": "2026-02-08T06:48:13.154773Z"
} | 67c9bb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1830
},
"timestamp": "2026-02-13T04:48:37.315Z",
"answer": 6575
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
226cdc | alg_poly_orbit_hensel_v1_1218484723_4631 | Let $N = (a^3 - 4a^2 - 5a + 3) \bmod 5041$ and $M = (N^3 - 4N^2 - 5N + 3) \bmod 5041$. Find the number of non-negative integers $a$ with $0 \le a \le 8272280$ such that $M = a$ and $N \ne a$. | 3,282 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-4), Pow(Var("a"), Const(2))), Mul(Const(-5), Var("a")), Const(3)), modulus=Const(5041)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-4), Pow(Ref("p1"), Const(2))), Mul(Const(-5), Ref("p1")), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.022 | 2026-02-25T06:18:36.034819Z | {
"verified": true,
"answer": 3282,
"timestamp": "2026-02-25T06:18:36.056385Z"
} | e01600 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T16:39:35.656Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
80336a | comb_binomial_compute_v1_1520064083_10262 | Let $n$ be the smallest integer $d \geq 2$ such that $d$ divides $79781$. Let $k$ be the smallest integer $d \geq 2$ such that $d$ divides $3773$. Compute the value of $\binom{n}{k}$. | 1,716 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(79781))))),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T11:18:46.677091Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T11:18:46.678650Z"
} | 7d9e73 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 1258
},
"timestamp": "2026-02-14T12:01:22.545Z",
"answer": 1716
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f9e8b5 | geo_count_lattice_triangle_v1_124444284_8720 | Let $n = 144$. Define $A$ to be twice the area of the polygon with vertices at $(0,0)$, $(120,0)$, $(120,144)$, and $(0,169)$, which is given by
$$
A = \left| 120 \cdot \left| \left\{ t \in \mathbb{Z} \mid 7 \leq t \leq 179 \text{ and } \exists a,b \in \mathbb{Z}^+ \text{ such that } 1 \leq a \leq 47,\ 1 \leq b \leq 17... | 70,155 | graphs = [
Graph(
let={
"_n": Const(144),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), CountOverSet(set=SolutionsSet(var=Var(name='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(na... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T11:52:44.605526Z | {
"verified": true,
"answer": 70155,
"timestamp": "2026-02-08T11:52:44.611012Z"
} | 4050a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 304,
"completion_tokens": 5550
},
"timestamp": "2026-02-14T20:18:02.280Z",
"answer": 70155
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0176ab | antilemma_cartesian_v1_898971024_969 | Let $m=5$. Consider all ordered pairs $(x_1,x_2)$ of positive integers such that both $x_1$ and $x_2$ are odd and $x_1+x_2=6$. Let $n_0$ be the number of such ordered pairs.
Let $x$ be the number of ordered pairs $(u,v)$ of integers such that $1\le u\le 44$ and $1\le v\le 48$.
Consider all ordered triples $(x_{11},x_... | 16,511 | graphs = [
Graph(
let={
"_m": Const(5),
"_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")), Co... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COMB1/ONE_BINOM_N",
"COUNT_CARTESIAN"
] | cc9bf9 | antilemma_cartesian_v1 | sum_divisor_count | 6 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"ONE_BINOM_N"
] | 3 | 0.004 | 2026-02-08T15:48:58.221285Z | {
"verified": true,
"answer": 16511,
"timestamp": "2026-02-08T15:48:58.224965Z"
} | 02ae65 | 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": 3044
},
"timestamp": "2026-02-24T18:55:28.377Z",
"answer": 16511
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ON... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
039115 | sequence_count_fib_divisible_v1_1742523217_2269 | Let $u = 181$ and $d = 10$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $d$ divides the $n$th Fibonacci number. Find the remainder when the absolute value of this count is divided by 97577. | 12 | graphs = [
Graph(
let={
"upper": Const(181),
"d": Const(10),
"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": Mod... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.04 | 2026-02-08T04:39:47.202441Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T04:39:47.242504Z"
} | c4a4a5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 731
},
"timestamp": "2026-02-11T21:43:15.799Z",
"answer": 12
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b02ff9 | sequence_lucas_compute_v1_601307018_2513 | Let $M$ be the number of distinct positive integers $t$ in the range $[22, 156]$ that can be expressed as $t = 14a + 8b$ for integers $a, b$ with $1 \leq a \leq 6$ and $1 \leq b \leq 9$. Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 30$ such that
$$
-100ab + 50a^2 + M ... | 64,079 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Var(n... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3_DIFF/QF_PSD_ORBIT"
] | 6e0b24 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"B3_DIFF",
"LIN_FORM",
"QF_PSD_ORBIT"
] | 3 | 0.009 | 2026-03-10T03:13:30.276896Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-03-10T03:13:30.285851Z"
} | 049995 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:36:15.919Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
c49d1d | alg_qf_psd_min_v1_601307018_4809 | Find the minimum value of $33066a^2 - 33066bc + 14529b^2 + 33066c^2 - 10020ab + 25050ac$ over all ordered triples $(a, b, c)$ of positive integers with $1 \leq a \leq 17$, $1 \leq b \leq 17$, and $1 \leq c \leq \min\left\{ 408a_1^2b_1^2 - 160a_1^3b_1 + 32a_1^4 - 520a_1b_1^3 + 257b_1^4 : a_1, b_1 \in \mathbb{Z}^+,\, 1 \... | 62,625 | graphs = [
Graph(
let={
"_n": Const(25050),
"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(17)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(17)), Geq(Var("c"), Const... | ALG | null | COMPUTE | sympy | POLY4_MIN | [
"POLY4_MIN"
] | 82de3b | alg_qf_psd_min_v1 | null | 8 | 0 | [
"POLY4_MIN"
] | 1 | 0.03 | 2026-03-10T05:30:06.672276Z | {
"verified": true,
"answer": 62625,
"timestamp": "2026-03-10T05:30:06.702677Z"
} | 95fb35 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 3159
},
"timestamp": "2026-04-19T00:21:26.077Z",
"answer": 62625
},
{
... | 1 | [
{
"lemma": "POLY4_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
8eb257_n | alg_sum_ap_v1_1419126231_1323 | A botanist studies plant growth patterns where the health score of a plant is given by $20b^2 + M a^2 - 12ab$, with $a$ and $b$ representing sunlight and water units (each from 1 to 40). The constant $M$ is the smallest prime factor of 75809. A plant is considered healthy if its score is at most 51476. Let $C$ be the n... | 8,094 | ALG | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/QF_PSD_COUNT_LEQ"
] | bbcc84 | alg_sum_ap_v1 | null | 5 | null | [
"MIN_PRIME_FACTOR",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.027 | 2026-02-25T10:44:58.356460Z | null | d51276 | 8eb257 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T04:36:47.658Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
b8a435 | alg_poly4_count_v1_601307018_8506 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 294$ such that
$$
32a b^3 + 2b^4 + 512a^3 b + 192a^2 b^2 + \left( \min_{\substack{1 \le a_1 \le 20 \\ 1 \le b_1 \le 20}} (63a_1^3 + 195a_1^2 b_1 + 189a_1 b_1^2 + 65b_1^3) \right) a^4 = 40302242.
$$ | 16 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(294)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(294)), Eq(Sum(Mul(Const(32), Var("a"), Pow(Var("b")... | ALG | null | COUNT | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | alg_poly4_count_v1 | null | 7 | 0 | [
"POLY3_MIN"
] | 1 | 1.006 | 2026-03-10T08:59:03.445161Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-03-10T08:59:04.451006Z"
} | f55cad | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 3273
},
"timestamp": "2026-04-19T09:10:23.115Z",
"answer": 16
},
{
"id... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
26f43e | antilemma_k3_v1_1915831931_718 | Let $d = 76272$. Let $m = \sum_{d \mid 1521} \phi(d)$, where $\phi$ is Euler's totient function. Let $n = 86499$. Define $x = \sum_{d_1 \mid n} \phi(d_1)$ and $c = \sum_{d_2 \mid m} \phi(d_2)$. Let $Q$ be the remainder when $c - x$ is divided by $d$. Find the value of $Q$. | 67,566 | graphs = [
Graph(
let={
"_d": Const(76272),
"_m": SumOverDivisors(n=Const(value=1521), var='d', expr=EulerPhi(n=Var(name='d'))),
"_n": Const(86499),
"x": SumOverDivisors(n=Ref(name='_n'), var='d1', expr=EulerPhi(n=Var(name='d1'))),
"_c": SumOverDiv... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3",
"K3"
] | 229767 | antilemma_k3_v1 | negation_mod | 3 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T15:38:49.583156Z | {
"verified": true,
"answer": 67566,
"timestamp": "2026-02-08T15:38:49.585227Z"
} | 1b446f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 601
},
"timestamp": "2026-02-16T10:19:10.707Z",
"answer": 67566
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2c67b3 | lte_diff_endings_v1_1874849503_41 | Let $a = 31$, $b = 3$, $p = 2$, and $T = 17$. Let $v_p(a - b)$ denote the largest integer $k$ such that $p^k$ divides $a - b$. Define $x = p^{T - v_p(a - b)}$. Compute the value of $x$. | 32,768 | graphs = [
Graph(
let={
"a_val": Const(31),
"b_val": Const(3),
"p_val": Const(2),
"T_val": Const(17),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val")),
"exp": Sub(Ref("T_... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 3 | null | [
"LTE_DIFF"
] | 1 | 0 | 2026-02-08T12:46:19.790040Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T12:46:19.790502Z"
} | d3e7b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 175
},
"timestamp": "2026-02-09T13:31:17.131Z",
"answer": 32768
},
{
"i... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
7dc01d | nt_sum_divisors_mod_v1_717093673_809 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 705600$. Define $n$ to be the minimum value of $x + y$ over all such pairs in $S$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute $10080 - (\sigma(n) \bmod 10993)$. | 4,128 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(705600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10993... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T15:42:02.053237Z | {
"verified": true,
"answer": 4128,
"timestamp": "2026-02-08T15:42:02.057299Z"
} | f535e8 | 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": 2966
},
"timestamp": "2026-02-16T11:44:54.391Z",
"answer": 4128
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0e68c2 | algebra_quadratic_discriminant_v1_655260480_1520 | Let $a = -2$, $b = -2$, and $m = 4$, $n = 2$. Let $P$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 144$. Let $M$ be the maximum value of $x_1 y_1$ over all such pairs. Let $c$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy =... | 2 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"a": Const(-2),
"b": Const(-2),
"c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"B1/B3"
] | 80b49d | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B1",
"B3",
"COPRIME_PAIRS"
] | 3 | 0.045 | 2026-02-08T16:12:28.324408Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:12:28.369802Z"
} | 055860 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 706
},
"timestamp": "2026-02-16T07:10:41.339Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma"... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
bed83d | alg_linear_system_2x2_v1_601307018_6825 | Let $\det = -7 \cdot (-14) - 3 \cdot (-10)$, $M = -102240 \cdot (-14) - 51808 \cdot (-10)$, and $R = -7 \cdot 51808 - \left|\{ (x_1, x_2, x_3) : x_i > 0,\ x_i\ \text{odd},\ x_1 + x_2 + x_3 = 5 \}\right| \cdot (-102240)$. Let $S = \frac{M}{\det} + \frac{R}{\det}$ and $Q = B_{|S| \bmod 11}$, where $B_n$ denotes the $n$-t... | 21,147 | graphs = [
Graph(
let={
"_n": Const(51808),
"num_x": Sub(Mul(Const(-102240), Const(-14)), Mul(Ref("_n"), Const(-10))),
"num_y": Sub(Mul(Const(-7), Const(51808)), Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPosit... | COMB | COMB | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | alg_linear_system_2x2_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-03-10T07:27:55.470667Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-03-10T07:27:55.473579Z"
} | e17144 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 1351
},
"timestamp": "2026-04-19T05:22:38.892Z",
"answer": 21147
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
9e0b94 | lin_form_endings_v1_397696148_1468 | Let $g = \gcd(10, 4)$, $a = \left\lfloor \frac{10}{g} \right\rfloor$, and $b = \left\lfloor \frac{4}{g} \right\rfloor$. Define $s = a \cdot 48 + b \cdot 48 - a \cdot b$. Let $M = 98603$ and compute the remainder when $14227 \cdot s$ is divided by $M$. | 3,661 | graphs = [
Graph(
let={
"a_coeff": Const(10),
"b_coeff": Const(4),
"A_val": Const(48),
"B_val": Const(48),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:34:08.297128Z | {
"verified": true,
"answer": 3661,
"timestamp": "2026-02-08T12:34:08.297830Z"
} | a378e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 630
},
"timestamp": "2026-02-15T01:54:57.870Z",
"answer": 3661
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cea878 | comb_count_surjections_v1_601307018_4309 | Let $k = \sum_{k1=\binom{17}{0} - 1}^{2} 2^{k1}$. Let $M = k! \cdot S(7, k)$, where $S(7, k)$ denotes the Stirling number of the second kind. Find the remainder when $12577 \cdot M$ is divided by $85143$. | 41,688 | graphs = [
Graph(
let={
"n": Const(7),
"k": Summation(var="k1", start=Sub(Binom(n=Const(17), k=Const(0)), Const(1)), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": Const(1257... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_0"
] | 71c45c | comb_count_surjections_v1 | null | 4 | 0 | [
"SUM_GEOM",
"ZERO_BINOM_0"
] | 2 | 0.006 | 2026-03-10T04:53:32.351467Z | {
"verified": true,
"answer": 41688,
"timestamp": "2026-03-10T04:53:32.357527Z"
} | ec8219 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1259
},
"timestamp": "2026-03-29T11:48:53.571Z",
"answer": 41688
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
d9eed6 | comb_count_permutations_fixed_v1_1520064083_6938 | Let $n = 8$ and $k = 3$. Define the quantity $$ \binom{n}{k} \cdot !(n - k), $$ where $!m$ denotes the number of derangements of $m$ elements. Let $d_0$ be the smallest divisor of $31603$ that is at least $2$. Compute the Bell number $B_r$, where $r$ is the absolute value of the above quantity modulo $d_0$. | 1 | graphs = [
Graph(
let={
"_n": Const(31603),
"n": Const(8),
"k": Const(3),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOver... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | comb_count_permutations_fixed_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T08:25:42.411495Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T08:25:42.413372Z"
} | 014ed6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1173
},
"timestamp": "2026-02-13T18:14:05.437Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
effe52 | nt_num_divisors_compute_v1_784195855_3686 | Let $n$ be the largest prime number less than or equal to 35 that is at least 2. Compute the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(35)), IsPrime(Var("n"))))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T06:34:56.719622Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T06:34:56.721393Z"
} | 61b619 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 255
},
"timestamp": "2026-02-15T17:36:14.948Z",
"answer": 2
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
789e68 | diophantine_fbi2_count_v1_1456120455_91 | Let $k = 1260$ and $n_{\min} = 6$. Define $\text{result}$ as the number of positive integers $d$ such that $5 \leq d \leq 161$, $d$ divides $k$, and $\frac{k}{d}$ is an integer satisfying $6 \leq \frac{k}{d} \leq 162$. Define $c$ as the number of positive integers $n \leq 55112$ such that $21$ divides the $n$-th Fibona... | 7,747 | graphs = [
Graph(
let={
"_n": Const(6),
"k": Const(1260),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(161)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Ref("_n")), Leq(Div... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | a43f88 | diophantine_fbi2_count_v1 | quadratic_mod | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.018 | 2026-02-08T02:53:35.919866Z | {
"verified": true,
"answer": 7747,
"timestamp": "2026-02-08T02:53:35.938288Z"
} | 4c488f | 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": 32768
},
"timestamp": "2026-02-23T17:52:07.169Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": 0.2,
"mid": 2.67,
"hi": 4.72
} | ||
cb7ed4 | nt_count_gcd_equals_v1_458359167_5190 | Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 1034289$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq s$ and the $n$-th Fibonacci number is divisible by 4. Let $u = 32768$ and $d = 1$. Compute ... | 21,653 | graphs = [
Graph(
let={
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1034289)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 2.969 | 2026-02-08T12:20:25.822287Z | {
"verified": true,
"answer": 21653,
"timestamp": "2026-02-08T12:20:28.791370Z"
} | e22834 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1908
},
"timestamp": "2026-02-15T00:03:04.438Z",
"answer": 21653
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ecd2c6 | nt_num_divisors_compute_v1_655260480_4578 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 2226131188222441500$. Compute the number of positive divisors of $n$. | 11 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=2226131188222441500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=C... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.006 | 2026-02-08T18:00:10.226505Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T18:00:10.232982Z"
} | a605de | 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": 2551
},
"timestamp": "2026-02-18T11:44:19.526Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
41e7d1 | geo_count_lattice_triangle_v1_1520064083_6438 | Consider a triangle with vertices at $(0,0)$, $(441,169)$, and $(289,120)$. Let $A$ be twice the area of this triangle, and let $B$ be the number of lattice points on the boundary of the triangle, including the vertices.
Define
$$
I = \frac{A + 2 - B}{2}.
$$
Compute
$$
\sum_{n=1}^{|I|} \tau(n),
$$
where $\tau(n)$ is ... | 15,843 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=441), Const(value=120)), Mul(Const(value=289), Sub(left=Const(value=0), right=Const(value=169))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=441)), b=Abs(arg=Const(value=169))), GCD(a=Abs(arg=Sub(left=Const(value=289), r... | NT | null | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 6 | 0 | null | null | 0.004 | 2026-02-08T08:04:25.418288Z | {
"verified": true,
"answer": 15843,
"timestamp": "2026-02-08T08:04:25.422295Z"
} | 416736 | 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": 3877
},
"timestamp": "2026-02-13T15:07:27.501Z",
"answer": 15843
},
... | 1 | [] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||||
994e37 | diophantine_product_count_v1_1520064083_6514 | Let $S$ be the set of all integers $t$ for which there exist integers $a$ and $b$ with $1\le a\le 3$ and $1\le b\le 4$ such that
$$10\le t\le 34\quad\text{and}\quad t=6a+4b.$$
Let $m$ be the number of elements of $S$.
Let $c=14$. Let $U$ be the number of integers $n$ with $1\le n\le 21600$ such that $c$ divides the $... | 9,165 | graphs = [
Graph(
let={
"_c": Const(14),
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_FIB_DIVISIBLE",
"COUNT_FIB_DIVISIBLE/B3"
] | 2aa12e | diophantine_product_count_v1 | bell_mod | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 3 | 0.009 | 2026-02-08T08:08:16.571798Z | {
"verified": true,
"answer": 9165,
"timestamp": "2026-02-08T08:08:16.580785Z"
} | 7b45f2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 314,
"completion_tokens": 2915
},
"timestamp": "2026-02-13T15:12:03.301Z",
"answer": 9165
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"l... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b6d476 | nt_count_divisible_v1_124444284_352 | Let $u = 84681$. Consider the set of all positive integers $n$ such that $n \leq u$ and $n$ is divisible by $12$. Compute the number of such integers $n$. | 7,056 | graphs = [
Graph(
let={
"upper": Const(84681),
"divisor": Const(12),
"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("divisor")), Const(0))))),
... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_divisible_v1 | null | 3 | 0 | [
"ONE_PHI_1"
] | 1 | 5.319 | 2026-02-08T03:13:30.327056Z | {
"verified": true,
"answer": 7056,
"timestamp": "2026-02-08T03:13:35.646458Z"
} | 81ac1d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 209
},
"timestamp": "2026-02-09T16:26:40.661Z",
"answer": 7056
},
{
"id... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
631c7f | sequence_count_fib_divisible_v1_971394319_1728 | Let $n = 5$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1030225$. Let $M$ be the minimum value of $x + y$ over all such pairs. Let $U$ be the number of positive integers $k \le M$ such that $n$ divides the $k$-th Fibonacci number.
Let $T$ be the set of all positive integers $... | 42,420 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositi... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.037 | 2026-02-08T13:52:42.798741Z | {
"verified": true,
"answer": 42420,
"timestamp": "2026-02-08T13:52:42.835810Z"
} | d16e3f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1627
},
"timestamp": "2026-02-15T21:37:24.886Z",
"answer": 42420
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
27941c | geo_count_lattice_rect_v1_124444284_7686 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 88$ and $0 \leq y \leq 106$. | 9,523 | graphs = [
Graph(
let={
"a": Const(88),
"b": Const(106),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0 | 2026-02-08T09:17:01.943445Z | {
"verified": true,
"answer": 9523,
"timestamp": "2026-02-08T09:17:01.943869Z"
} | ec80e1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 257
},
"timestamp": "2026-02-24T11:02:27.701Z",
"answer": 9523
},
{
"id... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
253963 | diophantine_sum_product_min_v1_124444284_8274 | Let $m = 2$ and let $k$ be the largest positive integer such that $2^k \leq 821726451$. Let $S = 11$ and $P = 18$. Consider the set of all positive integers $n$ such that $1 \leq n \leq k$ and $\gcd(n, 6) = 1$. Let $t$ be the number of elements in this set.
Now consider the set of all positive integers $x$ such that $... | 2 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_m"), Var("k")), Const(821726451)))),
"S": Const(11),
"P": Const(18),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(G... | NT | null | EXTREMUM | sympy | B3 | [
"MAX_VAL/C4"
] | 33188f | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"B3",
"C4",
"MAX_VAL"
] | 3 | 0.026 | 2026-02-08T09:37:25.977276Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T09:37:26.003391Z"
} | 0c85a1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 672
},
"timestamp": "2026-02-15T20:47:08.797Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
62e1e5 | modular_sum_quadratic_residues_v1_238844314_850 | Let $n = 30967$. Let $p$ be the smallest divisor of $n$ that is at least $2$. Compute $\frac{p(p-1)}{4}$. | 7,439 | graphs = [
Graph(
let={
"_n": Const(30967),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T13:39:04.709273Z | {
"verified": true,
"answer": 7439,
"timestamp": "2026-02-08T13:39:04.711037Z"
} | 6d6c23 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 1731
},
"timestamp": "2026-02-15T18:40:52.581Z",
"answer": 7439
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e05cb3 | algebra_poly_eval_v1_971394319_449 | Let $A$ be the number of positive integers $n$ with $1 \leq n \leq 35$ such that the sum of the digits of $n$ is odd. Let $B$ be the number of integers $t$ with $27 \leq t \leq 312$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 8$, $1 \leq b \leq 24$, and $t = 21a + 6b$. Compute the value... | 1,065 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(51),
"n": Const(21),
"result": Div(Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(35)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Cons... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"L3B"
] | f85b0e | algebra_poly_eval_v1 | null | 5 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.007 | 2026-02-08T13:06:24.494211Z | {
"verified": true,
"answer": 1065,
"timestamp": "2026-02-08T13:06:24.501332Z"
} | c411d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 7345
},
"timestamp": "2026-02-15T09:46:01.552Z",
"answer": 1065
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dd863b | alg_sym_quad_system_v1_1218484723_3713 | Compute the remainder when
$$\sum_{(a, b, c),\ a^{2} + b^{2} + c^{2} = ab + bc + ca,\ 2a + 7b + 4c = 4537,\ a, b, c \ge 1} a^{5} + b^{5} + c^{5}$$
is divided by
$$\left|\left\{k : 1 \le k \le 73917,\ \left|\{j : 1 \le j \le 43,\ j^{2} \le \max\{xy : (x, y),\ x > 0,\ y > 0,\ x + y = 86\}\}\right| \mid k\right\}\right|.$... | 948 | graphs = [
Graph(
let={
"_c": Const(5),
"_m": Const(4537),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)),... | NT | null | COMPUTE | sympy | B1 | [
"B1/C3/C2"
] | c87e87 | alg_sym_quad_system_v1 | null | 8 | 0 | [
"B1",
"C2",
"C3"
] | 3 | 0.031 | 2026-02-25T05:20:04.519334Z | {
"verified": true,
"answer": 948,
"timestamp": "2026-02-25T05:20:04.550671Z"
} | b05084 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 1772
},
"timestamp": "2026-03-29T11:51:46.358Z",
"answer": 948
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
cb832c | algebra_poly_eval_v1_784195855_10453 | Let $t = 5$. Define $S$ as the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $e$ be the number of elements in $S$. Compute the value of
$$
\frac{6t^5 - 5t^4 - 48t^3 + 15t^e + 31t + 15}{15}.
$$Then let $Q$ be the remainder wh... | 31,904 | graphs = [
Graph(
let={
"_n": Const(512),
"t": Const(5),
"result": Div(Sum(Mul(Const(6), Pow(Ref("t"), Const(5))), Mul(Const(-5), Pow(Ref("t"), Const(4))), Mul(Const(-48), Pow(Ref("t"), Const(3))), Mul(Const(15), Pow(Ref("t"), CountOverSet(set=SolutionsSet(var=Var("p"), c... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T18:07:45.105172Z | {
"verified": true,
"answer": 31904,
"timestamp": "2026-02-08T18:07:45.108101Z"
} | cfff44 | 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": 1657
},
"timestamp": "2026-02-18T13:42:58.301Z",
"answer": 31904
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ef5ca3 | sequence_count_fib_divisible_v1_1874849503_178 | Let $d = 9$ and let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 237$ and $d$ divides the $n$-th Fibonacci number. Let $B$ be the number of integers $t$ such that $9 \leq t \leq 950$ and there exist positive integers $a \leq 391$ and $b \leq 24$ satisfying $t = 2a + 7b$. Compute $A \cdot B$. | 17,784 | graphs = [
Graph(
let={
"upper": Const(237),
"d": Const(9),
"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')))))),
"_c": Cou... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | sequence_count_fib_divisible_v1 | affine_mod | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.013 | 2026-02-08T12:52:16.262729Z | {
"verified": true,
"answer": 17784,
"timestamp": "2026-02-08T12:52:16.275828Z"
} | 3b39e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 5646
},
"timestamp": "2026-02-09T14:29:43.845Z",
"answer": 17784
},
{
"... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
ebd782 | nt_count_coprime_v1_784195855_1738 | Let $k$ be the number of positive integers $n$ with $1 \leq n \leq 307$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Determine the number of positive integers $n$ with $1 \leq n \leq 11299$ such that $\gcd(n, k) = 1$. | 7,533 | graphs = [
Graph(
let={
"upper": Const(11299),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(307)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_count_coprime_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 3.369 | 2026-02-08T05:16:17.060044Z | {
"verified": true,
"answer": 7533,
"timestamp": "2026-02-08T05:16:20.429077Z"
} | 3dd29c | 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": 1190
},
"timestamp": "2026-02-12T06:11:21.776Z",
"answer": 7533
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9a0f6e | sequence_fibonacci_compute_v1_1470522791_1193 | Let $n$ be the largest prime number at most 26. Find the value of the $n$-th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_n": Const(26),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T13:29:42.761495Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T13:29:42.762882Z"
} | a8b4f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 73,
"completion_tokens": 446
},
"timestamp": "2026-02-15T16:56:33.098Z",
"answer": 28657
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
711105 | nt_count_divisible_v1_151522320_1453 | Let $A$ be the number of positive integers $n$ such that $n \leq 86436$ and $n$ is divisible by $9$. Let $c$ be the number of nonnegative integers $j \leq 24360$ such that $\binom{24360}{j}$ is odd. Compute the remainder when $c - A$ is divided by $91972$. | 82,624 | graphs = [
Graph(
let={
"_n": Const(24360),
"upper": Const(86436),
"divisor": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Co... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 04a712 | nt_count_divisible_v1 | negation_mod | 5 | 0 | [
"V8"
] | 1 | 3 | 2026-02-08T04:01:46.814757Z | {
"verified": true,
"answer": 82624,
"timestamp": "2026-02-08T04:01:49.814301Z"
} | 5c18bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1227
},
"timestamp": "2026-02-23T23:12:13.878Z",
"answer": 82624
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
427076 | nt_count_divisible_and_v1_1915831931_4025 | Let $A$ be the number of positive integers $n$ at most $169920$ that are divisible by both $12$ and $18$. Compute the sum $\sum_{i=0}^{d-1} a_i (i+1)^2$, where $d$ is the number of digits in $A$ and $a_i$ is the $i$-th decimal digit of $A$ (with $a_0$ the units digit). To this result, add the number of nonnegative inte... | 4,231 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(169920),
"d1": Const(12),
"d2": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modul... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86b5fc | nt_count_divisible_and_v1 | digits_weighted_mod | 6 | 0 | [
"V8"
] | 1 | 6.077 | 2026-02-08T18:03:48.240368Z | {
"verified": true,
"answer": 4231,
"timestamp": "2026-02-08T18:03:54.317294Z"
} | c51d8a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 3935
},
"timestamp": "2026-02-18T13:08:56.183Z",
"answer": 4231
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
c9b0b1 | antilemma_sum_equals_v1_238844314_189 | Let $m$ be the number of ordered pairs of integers $(i, j)$ such that $1 \leq i \leq 12$ and $1 \leq j \leq 15$. Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = m$. Let $x$ be the number of ordered pairs of positive integers $(i, j)$ such that $1 \leq i \leq 88$, $1 \... | 3,867 | graphs = [
Graph(
let={
"_m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(15)))),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 9b4db5 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 4 | 0.045 | 2026-02-08T13:09:46.360595Z | {
"verified": true,
"answer": 3867,
"timestamp": "2026-02-08T13:09:46.405100Z"
} | 923fbb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 793
},
"timestamp": "2026-02-24T17:20:08.218Z",
"answer": 3867
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
8e20eb | nt_min_coprime_above_v1_784195855_3063 | Let $p = 23$ and $n_1 = p^2$. Define $e$ to be the number of distinct prime factors of $n_1$. Let $n = 71$ and $h = \lambda(n) + e$, where $\lambda(n)$ is the Liouville function evaluated at $n$. Let $\mathcal{S}$ be the set of all integers $n$ such that $55225 < n \leq 55701$ and $\gcd(n, 466 + h) = 1$. Determine the ... | 55,227 | graphs = [
Graph(
let={
"p": Const(23),
"n1": Pow(Ref("p"), Const(2)),
"e": SmallOmega(n=Ref(name='n1')),
"n": Const(71),
"h": Sum(LiouvilleLambda(n=Ref(name='n')), Ref("e")),
"start": Const(55225),
"upper": Const(55701),
... | NT | null | EXTREMUM | sympy | LIOUVILLE_MINUS_ONE | [
"LIOUVILLE_MINUS_ONE",
"OMEGA_ONE"
] | 1d1751 | nt_min_coprime_above_v1 | null | 5 | 2 | [
"LIOUVILLE_MINUS_ONE",
"OMEGA_ONE"
] | 2 | 0.081 | 2026-02-08T06:12:42.730819Z | {
"verified": true,
"answer": 55227,
"timestamp": "2026-02-08T06:12:42.812155Z"
} | 46abeb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 374
},
"timestamp": "2026-02-19T02:10:42.499Z",
"answer": 55227
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "OMEGA_ONE",
"status": "ok"
},
{
"lemma": "POLY_PADIC_V... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
643ded | nt_count_divisible_and_v1_1874849503_740 | Let $n$ be a positive integer. Define $A$ as the set of all integers $n$ such that $1 \leq n \leq 15359$ and $\gcd(n, 20) = 1$. Let $u$ be the number of elements in $A$. Define $B$ as the set of all positive integers $n$ such that $1 \leq n \leq u$, $n$ is divisible by 6, and $n$ is divisible by 8. Let $r$ be the numbe... | 3,677 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(15359)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"d1": Const(6),
"d2": Const(8),
"res... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.262 | 2026-02-08T13:16:27.410087Z | {
"verified": true,
"answer": 3677,
"timestamp": "2026-02-08T13:16:27.671980Z"
} | 9a9f48 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 1354
},
"timestamp": "2026-02-09T20:28:05.753Z",
"answer": 3677
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
269ff4 | modular_count_residue_v1_1431428450_1261 | Let $m$ be the largest prime number less than or equal to $8$. Let $R$ be the number of positive integers $n$ less than or equal to $38809$ such that $n \equiv 6 \pmod{m}$. Compute $41616 - R$. | 36,072 | graphs = [
Graph(
let={
"_n": Const(8),
"upper": Const(38809),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"r": Const(6),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.504 | 2026-02-08T13:59:02.542281Z | {
"verified": true,
"answer": 36072,
"timestamp": "2026-02-08T13:59:04.046356Z"
} | 628a0c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 401
},
"timestamp": "2026-02-16T05:09:58.254Z",
"answer": 36072
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
5d67d3 | alg_sum_powers_v1_1218484723_5652 | Let $m = \min\{ x + y : x, y > 0,\ xy = 703921 \}$. Find the remainder when $\sum_{k=1}^{m} k^3$ is divided by $4437$. | 3,313 | graphs = [
Graph(
let={
"_n": Const(4437),
"result": Mod(value=Summation(var="k", start=Const(1), end=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(... | ALG | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"B3"
] | 0cd20d | alg_sum_powers_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 9.209 | 2026-02-25T07:11:00.636949Z | {
"verified": true,
"answer": 3313,
"timestamp": "2026-02-25T07:11:09.846197Z"
} | e2905a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1618
},
"timestamp": "2026-03-29T22:08:16.729Z",
"answer": 3313
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
bb9919 | nt_num_divisors_compute_v1_655260480_393 | Let $ n = 94864 $. Compute the number of positive divisors of $ n $. | 45 | graphs = [
Graph(
let={
"n": Const(94864),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T15:22:07.033823Z | {
"verified": true,
"answer": 45,
"timestamp": "2026-02-08T15:22:07.042861Z"
} | 608ab5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 572
},
"timestamp": "2026-02-16T04:43:56.646Z",
"answer": 45
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d24e34 | alg_qf_psd_sum_v1_1218484723_6833 | Find the remainder when $$\sum_{\substack{1 \le a \le 60 \\ 1 \le b \le 60 \\ 1 \le c \le C}} \left( 21a^2 - 16bc + 13c^2 + 10ac - 16ab + 14b^2 \right)$$ is divided by $95579$, where $C = \left| \left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 40,\ 16a_1^2 - 32a_1b_1 + 16b_1^2 = D \right\} \right|$ and $D = \left| \left\{ (a_2,... | 253 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(60)), Geq(Var("b"), Const(1)), Leq(Var("b"... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_COUNT"
] | 831c70 | alg_qf_psd_sum_v1 | null | 6 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.808 | 2026-02-25T08:18:23.133592Z | {
"verified": true,
"answer": 253,
"timestamp": "2026-02-25T08:18:23.941127Z"
} | f88b7c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 337,
"completion_tokens": 5171
},
"timestamp": "2026-03-30T02:45:22.085Z",
"answer": 253
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
ad6ffb | comb_factorial_compute_v1_1248542787_938 | Let $n$ be the number of nonnegative integers $j \leq 3104$ for which the binomial coefficient $\binom{3104}{j}$ is odd. Compute the value of $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(3104)), Eq(Mod(value=Binom(n=Const(3104), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"res... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T03:29:48.871408Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T03:29:48.874591Z"
} | 7e324f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 961
},
"timestamp": "2026-02-09T10:14:04.227Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.46,
"hi": 3.54
} | ||
9ea44b | modular_min_linear_v1_798873815_194 | Let $ a = 33847 $, $ b = 22567 $, and $ m = 59899 $. Determine the value of $ x $, where $ x $ is the smallest integer satisfying $ 1 \leq x \leq m $ and $ ax \equiv b \pmod{m} $. | 48,947 | graphs = [
Graph(
let={
"a": Const(33847),
"b": Const(22567),
"m": Const(59899),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), EulerPhi(n=Const(2))), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | modular_min_linear_v1 | null | 5 | 0 | [
"ONE_PHI_2"
] | 1 | 2.268 | 2026-02-08T02:31:02.899894Z | {
"verified": true,
"answer": 48947,
"timestamp": "2026-02-08T02:31:05.167635Z"
} | 13db9c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 3277
},
"timestamp": "2026-02-09T14:13:08.283Z",
"answer": 48947
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -1.81,
"mid": 2.18,
"hi": 5.82
} | ||
310a53 | nt_count_intersection_v1_784195855_2534 | Let $m = 18$. Define $N$ to be the number of ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Let $a$ be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 6$, $1 \leq j \leq 6$, and $i + j = 8$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that ... | 1,333 | graphs = [
Graph(
let={
"_m": Const(18),
"_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("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B1 | [
"B1/COUNT_SUM_EQUALS/B3"
] | c6b1d1 | nt_count_intersection_v1 | null | 6 | 0 | [
"B1",
"B3",
"COUNT_SUM_EQUALS"
] | 3 | 1.061 | 2026-02-08T05:50:47.252459Z | {
"verified": true,
"answer": 1333,
"timestamp": "2026-02-08T05:50:48.313554Z"
} | 3fc6de | 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": 2122
},
"timestamp": "2026-02-12T14:48:58.795Z",
"answer": 1333
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f18c73 | antilemma_k3_v1_124444284_8356 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $61243$, where $\phi$ denotes Euler's totient function. Let $Q$ be the remainder when $54221 \cdot x$ is divided by $99391$. Compute $Q$. | 3,393 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=61243), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(54221), Ref("x")), modulus=Const(99391)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T09:39:12.733547Z | {
"verified": true,
"answer": 3393,
"timestamp": "2026-02-08T09:39:12.734441Z"
} | 30d240 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 1106
},
"timestamp": "2026-02-14T05:33:59.636Z",
"answer": 3393
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
22da6d | nt_count_divisible_and_v1_717093673_3818 | Let $u = 138300$ and $d_1 = 10$. Define $d_2 = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$. Let $r$ be the number of positive integers $n \leq u$ such that $n$ is divisible by both $d_1$ and $d_2$. Compute the value of
$$
r + \phi(|r| + 1) + \tau(|r| + 1),
$$
where $\tau(x)$ denotes the number of po... | 7,530 | graphs = [
Graph(
let={
"upper": Const(138300),
"d1": Const(10),
"d2": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 5 | 0 | [
"K2"
] | 1 | 4.507 | 2026-02-08T17:52:40.130961Z | {
"verified": true,
"answer": 7530,
"timestamp": "2026-02-08T17:52:44.637803Z"
} | 5f97fb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1561
},
"timestamp": "2026-02-18T09:02:16.731Z",
"answer": 7530
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e3c637 | comb_count_derangements_v1_124444284_8558 | Let $u_1 = 4$, and let $n_2 = u_1 + 1$. Define $h = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = h + 1$, and define $f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 8 + f$. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"u1": Const(4),
"n2": Sum(Ref("u1"), Const(1)),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Ref("h"),
"n1": Sum(Ref("u"), Const(1)),
... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_derangements_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T09:47:04.776693Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T09:47:04.777538Z"
} | 00e303 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1733
},
"timestamp": "2026-02-24T11:42:34.507Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
46b9da | nt_count_gcd_equals_v1_124444284_652 | Let $k$ be the number of integers $t$ such that $9 \leq t \leq 191$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 19$, $1 \leq b \leq 23$, and
$$
t = 4a + 5b.
$$
Let $d = 57$. Compute the number of positive integers $n$ such that $1 \leq n \leq 21025$ and $\gcd(n, k) = d$. | 246 | graphs = [
Graph(
let={
"upper": Const(21025),
"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=19)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.751 | 2026-02-08T03:25:57.623250Z | {
"verified": true,
"answer": 246,
"timestamp": "2026-02-08T03:25:59.374348Z"
} | 7f6d53 | 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": 2491
},
"timestamp": "2026-02-09T04:27:59.326Z",
"answer": 246
},
{
"i... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6186df | alg_qf_psd_count_v1_601307018_1173 | Let $C = \left|\{ (a_1, b_1) \in \mathbb{Z}^+ \times \mathbb{Z}^+ : a_1 \leq 30,\ b_1 \leq 30,\ 41a_1^2 -12a_1b_1 + 20b_1^2 \leq 5536 \}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le C$ and $1 \le b \le 159$ satisfying $50a^2 + 60ab + 18b^2 = 1299272$. | 31 | graphs = [
Graph(
let={
"_n": Const(20),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const... | ALG | null | COUNT | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_count_v1 | null | 6 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 10.976 | 2026-03-10T01:47:00.590629Z | {
"verified": true,
"answer": 31,
"timestamp": "2026-03-10T01:47:11.566438Z"
} | 7c0f11 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 4772
},
"timestamp": "2026-03-29T01:27:07.627Z",
"answer": 31
},
{
"id"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
97f206 | modular_sum_quadratic_residues_v1_1125832087_611 | Let $m = 30976$. Define $n$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $p$ be the largest prime number less than or equal to $n$. Compute $\frac{p(p-1)}{4}$, multiply this by $44121$, and find the remainder when the result is divided by $77153$. | 38,384 | graphs = [
Graph(
let={
"_m": Const(30976),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),... | NT | null | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T03:10:06.884100Z | {
"verified": true,
"answer": 38384,
"timestamp": "2026-02-08T03:10:06.886663Z"
} | 5e0c31 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1637
},
"timestamp": "2026-02-10T12:55:50.439Z",
"answer": 38384
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
686531 | modular_count_residue_v1_1520064083_6685 | Let $m$ be the smallest divisor of $12673$ that is at least $2$. Let $r = 2$ and let $u = 53361$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq u$ and $n \equiv r \pmod{m}$. Let $t$ be the number of elements in $S$. Compute the remainder when $39989 \cdot t$ is divided by $57675$. | 35,876 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(53361),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(12673))))),
"r": Const(2),
"result": CountOverSet(set=Sol... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 4.662 | 2026-02-08T08:15:59.070430Z | {
"verified": true,
"answer": 35876,
"timestamp": "2026-02-08T08:16:03.732651Z"
} | 9bc761 | 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": 3610
},
"timestamp": "2026-02-13T16:55:17.827Z",
"answer": 35876
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
010f28 | modular_inverse_v1_1470522791_674 | Let $a = 647$ and $m = 1039$. Define $r$ to be the smallest positive integer $x$ such that $1 \le x \le 1038$ and
$$
647x \equiv 1 \pmod{1039}.
$$
Let $S$ be the set of all positive integers $t$ such that $12 \le t \le 9422$ and there exist positive integers $a$ and $b$ with $1 \le a \le 3923$, $1 \le b \le 523$, and
$... | 9,136 | graphs = [
Graph(
let={
"a": Const(647),
"m": Const(1039),
"upper": Const(1038),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Co... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | modular_inverse_v1 | negation_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.075 | 2026-02-08T13:10:59.402432Z | {
"verified": true,
"answer": 9136,
"timestamp": "2026-02-08T13:10:59.476957Z"
} | 863a21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 4652
},
"timestamp": "2026-02-15T10:29:20.143Z",
"answer": 9136
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cba9be | comb_count_partitions_v1_1915831931_3306 | Let $m = 9$, and let $s = \sum_{k=1}^{m} k$. Let $n$ be the sum
$$
\sum_{d \mid s} \phi(d),
$$
where $\phi(d)$ denotes Euler's totient function. Determine the value of $p(n)$, the number of integer partitions of $n$. | 89,134 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Var("k")),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K3"
] | 7bbb8e | comb_count_partitions_v1 | null | 6 | 0 | [
"K3",
"SUM_ARITHMETIC"
] | 2 | 0.003 | 2026-02-08T17:32:31.044524Z | {
"verified": true,
"answer": 89134,
"timestamp": "2026-02-08T17:32:31.047339Z"
} | 0bb498 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 840
},
"timestamp": "2026-02-18T04:31:17.113Z",
"answer": 89134
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a989c0 | nt_sum_divisors_mod_v1_124444284_5404 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1587600$. Define $n$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by 11117. | 9,360 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1587600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1111... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T06:34:30.072775Z | {
"verified": true,
"answer": 9360,
"timestamp": "2026-02-08T06:34:30.074062Z"
} | 4ed71b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 2024
},
"timestamp": "2026-02-13T02:14:16.710Z",
"answer": 9360
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3aa9e2 | sequence_lucas_compute_v1_601307018_4671 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ satisfying
$$
17b^4 + 68a^3b + 17a^4 + 68ab^3 + 102a^2b^2 = 3306177.
$$
Let $M = L_n$, where $L_n$ denotes the $n$-th Lucas number. Find the remainder when $44121 \cdot M$ is divided by $59263$. | 57,724 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Eq(Sum(Mul(Const(17), Pow(Var("b"), Const(4))),... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"POLY4_COUNT"
] | 1 | 0.003 | 2026-03-10T05:20:45.696514Z | {
"verified": true,
"answer": 57724,
"timestamp": "2026-03-10T05:20:45.699188Z"
} | adc774 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 1699
},
"timestamp": "2026-03-29T13:02:11.673Z",
"answer": 57724
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
dc5b34_n | alg_sum_ap_v1_1218484723_2660 | A secret code uses the largest prime number between 2 and 16, denoted $R$. The system generates a sequence of values $5k + R$ for $k = 0$ to $187$, and sums them. This sum is then divided by the number of integers from 1 to the largest prime $\le 7331$ that satisfy the condition: each such integer leaves the same remai... | 2,386 | ALG | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/L3C"
] | 16ce8a | alg_sum_ap_v1 | null | 4 | null | [
"L3C",
"MAX_PRIME_BELOW"
] | 2 | 0.006 | 2026-02-25T04:24:01.046485Z | null | 5fdd90 | dc5b34 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 11857
},
"timestamp": "2026-03-30T18:48:32.876Z",
"answer": 2386
},
{
"... | 1 | [
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
53d03e | sequence_count_fib_divisible_v1_1440796553_103 | Let $d = 8$ and $\text{upper} = 874$. Compute the number of positive integers $n$ such that $1 \leq n \leq 874$ and $8$ divides the $n$-th Fibonacci number. | 145 | graphs = [
Graph(
let={
"upper": Const(874),
"d": Const(8),
"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')))))),
},
go... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.074 | 2026-02-08T11:35:02.054741Z | {
"verified": true,
"answer": 145,
"timestamp": "2026-02-08T11:35:02.128305Z"
} | acd8e8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 1796
},
"timestamp": "2026-02-14T15:55:27.467Z",
"answer": 145
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemm... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
db9741 | comb_count_surjections_v1_784195855_9229 | Let $n$ be the number of integers $t$ with $7 \leq t \leq 20$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 2$ and $1 \leq b \leq 5$, such that
$$
t = 5a + 2b.
$$
Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Compute
$$
k! \cdot S(6, k... | 1,800 | 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=2)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T16:39:10.737023Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T16:39:10.739369Z"
} | 13eeb8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1083
},
"timestamp": "2026-02-17T09:21:00.226Z",
"answer": 1800
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
cbdd76 | nt_num_divisors_compute_v1_1918700295_1180 | Let $n = 65025$. Compute the number of positive divisors of $n$. | 27 | graphs = [
Graph(
let={
"n": Const(65025),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | ONE_PHI_2 | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"LIN_FORM",
"ONE_PHI_2"
] | 2 | 0.064 | 2026-02-08T05:37:59.213298Z | {
"verified": true,
"answer": 27,
"timestamp": "2026-02-08T05:37:59.277591Z"
} | d42717 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 253
},
"timestamp": "2026-02-11T23:01:51.734Z",
"answer": 75
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"s... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
bb298c_l | comb_factorial_compute_v1_168721529_1835 | Let $n = 7$. Let $f = n!$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 146$. Let $g$ be the maximum value of $xy$ over all pairs $(x, y) \in P$. Compute the value of
$$
\sum_{i=0}^{d-1} \left( \text{the } i\text{-th digit of } f \right) \cdot (i+1)^2 + g,
$$
where $d$ is the... | 5,370 | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | 51a773 | comb_factorial_compute_v1 | digits_weighted_mod | 5 | 0 | [
"B1"
] | 1 | 0.004 | 2026-02-08T13:57:05.438694Z | {
"verified": false,
"answer": 5425,
"timestamp": "2026-02-08T13:57:05.442319Z"
} | c95eeb | bb298c | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 5260
},
"timestamp": "2026-02-24T19:23:14.711Z",
"answer": 5425
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | |
af3e83 | alg_poly3_sum_v1_1218484723_84 | Let $T$ be the number of integers $t$ in the range $[7, 231]$ that can be written as $t = 3a + 4b$ for some integers $a, b$ with $1 \leq a \leq 41$, $1 \leq b \leq 27$. Compute the remainder when
$$
\sum_{\substack{1 \leq a \leq 185 \\ 1 \leq b \leq 185}} \left( 61b^3 - 93a^2b + 28a^3 + T \cdot a b^2 \right)
$$
is divi... | 13,007 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(185)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(185)))), expr=Sum(Mul(Const(... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_poly3_sum_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.07 | 2026-02-25T01:47:22.925886Z | {
"verified": true,
"answer": 13007,
"timestamp": "2026-02-25T01:47:22.995482Z"
} | c38f60 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 9359
},
"timestamp": "2026-03-10T08:03:49.553Z",
"answer": 610
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.77,
"mid": 6.8,
"hi": 9.83
} | ||
642a5c | antilemma_sum_equals_v1_1918700295_1573 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = 41$, where $1 \le i \le 40$ and $1 \le j \le 40$. Let $x$ be the number of elements in $S$. Compute the remainder when $27 - x$ is divided by $94370$. | 94,357 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(41)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(40)), right=IntegerRange(start=Const(1), end=Const(40))))),
"_c":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.02 | 2026-02-08T05:53:14.491543Z | {
"verified": true,
"answer": 94357,
"timestamp": "2026-02-08T05:53:14.511253Z"
} | 76cf2d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 558
},
"timestamp": "2026-02-24T04:42:59.735Z",
"answer": 94357
},
{
"i... | 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": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
d44c2c | sequence_fibonacci_compute_v1_601307018_7196 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ satisfying $10ab + 5a^2 + 5b^2 = 17405$. Let $M = F_n$, where $F_n$ is the $n$-th Fibonacci number. Find the remainder when $44121 \cdot M$ is divided by $94142$. | 48,431 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Eq(Sum(Mul(Const(10), Var("a"), Var("b")), Mul(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.003 | 2026-03-10T07:46:50.419638Z | {
"verified": true,
"answer": 48431,
"timestamp": "2026-03-10T07:46:50.422652Z"
} | 6a11f0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1717
},
"timestamp": "2026-04-19T06:10:15.832Z",
"answer": 48431
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
c8d2c1 | diophantine_fbi2_count_v1_865884756_669 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 8100$. Let $S$ be the set of all integers $d$ satisfying $2 \leq d \leq 61$, $d$ divides $k$, $\frac{k}{d} \geq 2$, and $\frac{k}{d} \leq \max T$, where $T$ is the set of all prime numbers $n$ such that $2 \leq ... | 55,064 | graphs = [
Graph(
let={
"_m": Const(61),
"_n": Const(44121),
"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(8100)))), e... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.009 | 2026-02-08T15:33:11.653306Z | {
"verified": true,
"answer": 55064,
"timestamp": "2026-02-08T15:33:11.662407Z"
} | cfe3b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1308
},
"timestamp": "2026-02-16T08:41:15.387Z",
"answer": 55064
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8b36cb | nt_sum_gcd_range_mod_v1_1978505735_6625 | Let $k$ be the number of positive integers $k_1$ such that $1 \le k_1 \le 7826$ and $43$ divides $k_1$. Let $N$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = k$. Let $S = \sum_{n=1}^{N} \gcd(n, 120)$. Find the remainder when $S$ is divided by $11831$. | 2,946 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("k1"), condition=And(Geq(Var("k1"), Cons... | NT | null | COMPUTE | sympy | C2 | [
"C2/B1"
] | a0cd95 | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1",
"C2"
] | 2 | 0.366 | 2026-02-08T19:43:09.306563Z | {
"verified": true,
"answer": 2946,
"timestamp": "2026-02-08T19:43:09.672654Z"
} | 845b98 | 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": 2962
},
"timestamp": "2026-02-18T23:23:20.667Z",
"answer": 2946
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1c0a0c | geo_count_lattice_rect_v1_151522320_2492 | Let $a = 32$ and $b = 50$. Let $N$ be the number of lattice points in the rectangle $[0, a] \times [0, b]$. Compute the Bell number $B_k$, where $k$ is the remainder when $|N|$ is divided by $11$. | 1 | graphs = [
Graph(
let={
"a": Const(32),
"b": Const(50),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.004 | 2026-02-08T04:50:32.074088Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T04:50:32.077834Z"
} | 29b275 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 587
},
"timestamp": "2026-02-24T01:55:38.769Z",
"answer": 1
},
{
"id": ... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
97ecf3 | diophantine_fbi2_count_v1_1978505735_455 | Let $m = 5476$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Define $T$ as the set of all values $x + y$ where $(x, y) \in S$, and let $n_{\min}$ be the minimum element of $T$. Let $k = 480$. Determine the number of positive integers $d$ satisfying the following conditions:
... | 17 | graphs = [
Graph(
let={
"_m": Const(5476),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"B3/K2"
] | 9f3175 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"K2"
] | 3 | 0.123 | 2026-02-08T15:23:32.897628Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T15:23:33.020731Z"
} | e7f9c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1729
},
"timestamp": "2026-02-16T05:37:22.303Z",
"answer": 17
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8ad8b4 | nt_count_gcd_equals_v1_1520064083_9348 | Let $n$ be a positive integer such that $1 \leq n \leq 34225$. Let $k$ be the sum of $\phi(d)$ over all positive divisors $d$ of $365$, where $\phi$ denotes Euler's totient function. Determine the number of such integers $n$ for which $\gcd(n, k) = 5$. Let this number be $r$. Compute the remainder when $39730 \cdot r$ ... | 64,808 | graphs = [
Graph(
let={
"upper": Const(34225),
"k": SumOverDivisors(n=Const(value=365), var='d', expr=EulerPhi(n=Var(name='d'))),
"d": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upp... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"K3"
] | 1 | 9.23 | 2026-02-08T10:41:47.391823Z | {
"verified": true,
"answer": 64808,
"timestamp": "2026-02-08T10:41:56.621695Z"
} | f46610 | 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": 1310
},
"timestamp": "2026-02-14T08:08:16.609Z",
"answer": 64808
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5bdbc9 | sequence_count_fib_divisible_v1_655260480_1165 | Let $n = 2$. Define $d = 15$ and let $u$ be the smallest divisor of $295927$ that is at least $n$. Compute the number of positive integers $k$ such that $1 \leq k \leq u$ and $d$ divides the $k$-th Fibonacci number.
Find the value of this count. | 27 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Ref("_n")), Divides(divisor=Var("d1"), dividend=Const(295927))))),
"d": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), co... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.033 | 2026-02-08T15:56:02.142500Z | {
"verified": true,
"answer": 27,
"timestamp": "2026-02-08T15:56:02.175011Z"
} | ef0c0d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1662
},
"timestamp": "2026-02-16T17:08:42.871Z",
"answer": 27
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6e2dc0 | comb_count_derangements_v1_1978505735_406 | Let $m = 15$. Define $S$ as the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 128$, $8$ divides $n_1$, and $\gcd(n_1, m) = 1$. Let $n$ be the largest prime number in the set $\{2, 3, \dots, |S|\}$. Compute $!n$, the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_m": Const(15),
"_n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(128)), Divides(divisor=Const(8), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Ref("_m")), Const(1))))),
"n": MaxOverSet(s... | NT | COMB | COUNT | sympy | C5 | [
"C5/MAX_PRIME_BELOW"
] | e03314 | comb_count_derangements_v1 | null | 4 | 0 | [
"C5",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T15:22:08.409055Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T15:22:08.410699Z"
} | 4f63f2 | 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": 1328
},
"timestamp": "2026-02-16T04:35:21.345Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0487dc | alg_qf_psd_count_v1_601307018_2768 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 216$ such that $$9b^2 + 25a^2 - 18ab = 234000.$$ | 11 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(216)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(216)), Eq(Sum(Mul(Const(9), Pow(Var("b"), Const(2))), Mul(Const(25), Pow(Var("a... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_DISTINCT",
"B3_CLOSEST"
] | fdd29c | alg_qf_psd_count_v1 | null | 5 | null | [
"B3_CLOSEST",
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 3 | 6.483 | 2026-03-10T03:25:10.903112Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-03-10T03:25:17.386586Z"
} | 6e560a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 4515
},
"timestamp": "2026-03-29T06:26:53.141Z",
"answer": 11
},
{
"id"... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
639e10 | comb_bell_compute_v1_784195855_2598 | Let $n$ be the number of integers $t$ such that $24 \leq t \leq 34$ and there exist integers $a$ and $b$, each between 1 and 3 inclusive, satisfying $t = 2a + 3b + 19$. Compute the Bell number $B_n$, which counts the number of partitions of a set of $n$ elements. | 21,147 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:54:07.090151Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T05:54:07.091196Z"
} | 4481b6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 936
},
"timestamp": "2026-02-24T04:47:18.517Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
1cabef | nt_count_divisors_in_range_v1_349078426_1821 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 2209$. Compute the remainder when $60055$ times the number of positive divisors $d$ of $n$ sa... | 44,461 | graphs = [
Graph(
let={
"_n": Const(60733),
"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(129600)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T13:56:57.824573Z | {
"verified": true,
"answer": 44461,
"timestamp": "2026-02-08T13:56:57.833867Z"
} | 2432af | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1861
},
"timestamp": "2026-02-15T22:40:42.292Z",
"answer": 44461
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
bbb27d | comb_binomial_compute_v1_1125832087_1287 | Let $n$ be the number of integers $t$ such that $8 \leq t \leq 30$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 3$, and $t = 3a + 5b$. Compute $\binom{n}{7}$. | 6,435 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:40:29.310766Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T03:40:29.311933Z"
} | 770137 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 805
},
"timestamp": "2026-02-10T15:22:42.670Z",
"answer": 6435
},
{
"id... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
1e48d4 | nt_max_prime_below_v1_865884756_3425 | Let $c$ be the number of positive integers $p_1$ for which there exists a positive integer $q$ such that $p_1 q = 630$, $\gcd(p_1, q) = 1$, and $p_1 < q$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p q = 72$, $\gcd(p, q) = 1$, and $p < q$. Define $r$ to be th... | 52,548 | graphs = [
Graph(
let={
"_n": Const(75023),
"upper": Const(22500),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | c90628 | nt_max_prime_below_v1 | negation_mod | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.738 | 2026-02-08T17:22:28.869900Z | {
"verified": true,
"answer": 52548,
"timestamp": "2026-02-08T17:22:30.608341Z"
} | 83d9f7 | 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": 6449
},
"timestamp": "2026-02-18T02:22:01.165Z",
"answer": 52548
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
09b24e | algebra_quadratic_discriminant_v1_1742523217_5427 | Let $a = -1$ and $c = -8$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 9$. Define $b$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the value of $b^2 - 4ac$, and let this value be $r$. Find the remainder when $44121 \cdot r$ is divided by $77978... | 20,528 | graphs = [
Graph(
let={
"_n": Const(9),
"a": Const(-1),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T10:59:15.416319Z | {
"verified": true,
"answer": 20528,
"timestamp": "2026-02-08T10:59:15.417686Z"
} | 102c24 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 530
},
"timestamp": "2026-02-14T09:46:07.173Z",
"answer": 20528
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
872b91 | lin_form_endings_v1_784195855_1852 | Let $a = 14$ and $b = 49$. Define $g = \gcd(a, b)$, and let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 49$ and $B = 9$. Define
$$
T = a' \cdot A + b' \cdot B - a' \cdot b'.
$$
Now define
$$
S = a \cdot A + b \cdot B - a - b + 1.
$$
Let $k = 19425$ and $M = ... | 32,595 | graphs = [
Graph(
let={
"a_coeff": Const(14),
"b_coeff": Const(49),
"A_val": Const(49),
"B_val": Const(9),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:22:19.251286Z | {
"verified": true,
"answer": 32595,
"timestamp": "2026-02-08T05:22:19.252793Z"
} | 193a41 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 958
},
"timestamp": "2026-02-12T06:53:52.563Z",
"answer": 32595
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
53bc7d | antilemma_v8_lucas_677425708_1132 | Compute the number of integers $j$ with $0 \leq j \leq 95997$ such that the remainder when $\binom{95997}{j}$ is divided by $2$ is equal to $\phi(2)$, where $\phi$ denotes Euler's totient function. Determine the value of this number. | 8,192 | graphs = [
Graph(
let={
"_n": Const(95997),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(95997), k=Var("j")), modulus=Const(2)), EulerPhi(n=Const(2)))), domain='nonnegative_integers')),
... | NT | COMB | COMPUTE | sympy | ONE_PHI_2 | [
"ONE_PHI_2",
"V8"
] | 299d97 | antilemma_v8_lucas | null | 6 | 0 | [
"ONE_PHI_2",
"V8"
] | 2 | 0.002 | 2026-02-08T04:00:35.049303Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T04:00:35.051164Z"
} | 19bb93 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 916
},
"timestamp": "2026-02-09T16:03:58.744Z",
"answer": 8192
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
fe08b7 | nt_count_digit_sum_v1_971394319_346 | Let $S$ be the set of all integers $t$ such that $25 \leq t \leq 52$ and there exist positive integers $a \leq 10$ and $b \leq 4$ satisfying $t = 2a + 3b + 20$. Let $\sigma$ be the number of elements in $S$. Determine the number of positive integers $n \leq 99999$ such that the sum of the decimal digits of $n$ is equal... | 5,280 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=10))... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 3.926 | 2026-02-08T13:02:31.060518Z | {
"verified": true,
"answer": 5280,
"timestamp": "2026-02-08T13:02:34.986215Z"
} | 5b9c01 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3097
},
"timestamp": "2026-02-15T08:51:02.282Z",
"answer": 5280
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d651f5 | nt_sum_divisors_mod_v1_1439011603_236 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 75600$ and $11$ divides the $n_1$-th Fibonacci number. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by 10039. | 8,722 | graphs = [
Graph(
let={
"_n": Const(75600),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Divides(divisor=Const(11), dividend=Fibonacci(arg=Var(name='n1')))))),
"M": Const(10039),
"sigma": ... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T15:22:13.066839Z | {
"verified": true,
"answer": 8722,
"timestamp": "2026-02-08T15:22:13.068549Z"
} | e9eab4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1263
},
"timestamp": "2026-02-16T05:14:39.545Z",
"answer": 8722
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ba19a7 | alg_telescope_v1_1419126231_346 | Find the remainder when $\sum_{k=0}^{\min\{ x + y : x > 0,\, y > 0,\, xy = 724201 \}} (4k^3 + 6k^2 + 4k + 1)$ is divided by $3618$. | 3,013 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=Summation(var="k", start=Const(0), end=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"... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_telescope_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.138 | 2026-02-25T09:51:30.007845Z | {
"verified": true,
"answer": 3013,
"timestamp": "2026-02-25T09:51:30.146126Z"
} | 1dc107 | 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": 12823
},
"timestamp": "2026-03-30T08:09:36.087Z",
"answer": 3013
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
98a5c9 | alg_poly4_count_v1_1419126231_91 | Let $ S $ be the set of integers $ v $ such that $ 25 \leq v \leq 3025 $ and there exist integers $ a, b \in [1,11] $ satisfying $ 20a^2 + 5b^2 = v $. Let $ A = |S| $. Find the number of ordered pairs $ (a, b) $ with $ 1 \leq a \leq A $, $ 1 \leq b \leq 102 $, and $ 82a^4 = 5874422272 $. | 102 | graphs = [
Graph(
let={
"_n": Const(3025),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(25)), Leq(Var("v"), Ref("_n"... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_poly4_count_v1 | null | 5 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 9.035 | 2026-02-25T09:37:54.021495Z | {
"verified": true,
"answer": 102,
"timestamp": "2026-02-25T09:38:03.056962Z"
} | bae237 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 3447
},
"timestamp": "2026-03-30T06:57:01.958Z",
"answer": 102
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
f0df3f | nt_count_divisible_and_v1_2051736721_3227 | Let $d_1 = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function, and let $d_2 = 9$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 7722$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Find the value of $N$. | 429 | graphs = [
Graph(
let={
"upper": Const(7722),
"d1": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"d2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 3 | 0 | [
"K2"
] | 1 | 3.117 | 2026-02-08T17:12:06.080994Z | {
"verified": true,
"answer": 429,
"timestamp": "2026-02-08T17:12:09.198487Z"
} | eb5710 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 466
},
"timestamp": "2026-02-16T09:07:13.540Z",
"answer": null
},
{
"id": 11,... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
211e10 | comb_catalan_compute_v1_458359167_5237 | Let $n$ be the number of integers $t$ with $21 \leq t \leq 60$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 6a + 15b$. Let $Q$ be the remainder when $\left( \text{the number of ordered pairs } (i,j) \text{ of positive integers such that } i+j = 42,\ 1 \leq... | 70,796 | graphs = [
Graph(
let={
"_n": Const(87551),
"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 | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | afd3ec | comb_catalan_compute_v1 | negation_mod | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.01 | 2026-02-08T12:21:05.541947Z | {
"verified": true,
"answer": 70796,
"timestamp": "2026-02-08T12:21:05.552433Z"
} | 4486c4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 914
},
"timestamp": "2026-02-24T15:37:29.334Z",
"answer": 70796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
bdc2d9 | antilemma_k2_v1_124444284_2601 | Let $x = \sum_{k=1}^{181} \phi(k) \left\lfloor \frac{181}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the smallest positive integer $m$ such that the $m$th Fibonacci number is divisible by $|x| + 2$. Compute $Q$. | 612 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(181), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(181), Var("k"))))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T04:50:14.970072Z | {
"verified": true,
"answer": 612,
"timestamp": "2026-02-08T04:50:14.970594Z"
} | 7278ae | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 3087
},
"timestamp": "2026-02-11T22:17:04.697Z",
"answer": 612
},
{
"i... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f28f27 | nt_count_divisors_in_range_v1_1353956133_252 | Let $n = 221760$. Compute the number of positive divisors $d$ of $n$ such that $15 \leq d \leq 1588$. | 103 | graphs = [
Graph(
let={
"n": Const(221760),
"a": Const(15),
"b": Const(1588),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
},
... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.976 | 2026-02-08T11:21:32.764977Z | {
"verified": true,
"answer": 103,
"timestamp": "2026-02-08T11:21:33.740572Z"
} | ab707b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 4029
},
"timestamp": "2026-02-14T13:18:08.325Z",
"answer": 103
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
996c5f | antilemma_k2_v1_397696148_2053 | Compute the value of
$$
\sum_{k=1}^{125} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 125} \phi(d) \right\rfloor,
$$
where $\phi(n)$ denotes Euler's totient function and the inner sum is over all positive divisors $d$ of $125$. | 7,875 | graphs = [
Graph(
let={
"_n": Const(125),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=125), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 7 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.004 | 2026-02-08T12:55:48.903269Z | {
"verified": true,
"answer": 7875,
"timestamp": "2026-02-08T12:55:48.907233Z"
} | 714172 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 859
},
"timestamp": "2026-02-15T07:37:20.024Z",
"answer": 7875
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
07bce8 | geo_count_lattice_rect_v1_655260480_1586 | Compute the number of lattice points in the rectangle defined by $0 \leq x \leq 47$ and $0 \leq y \leq 41$. | 2,016 | graphs = [
Graph(
let={
"a": Const(47),
"b": Const(41),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.003 | 2026-02-08T16:13:48.793142Z | {
"verified": true,
"answer": 2016,
"timestamp": "2026-02-08T16:13:48.796114Z"
} | eb9122 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 188
},
"timestamp": "2026-02-24T20:22:36.250Z",
"answer": 2016
},
{
"i... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.