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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
4aa411 | sequence_lucas_compute_v1_1742523217_3759 | Let $P$ be the set of all prime numbers $n$ such that $2 \leq n \leq 5$. Let $p$ be the maximum element of $P$. Define $T$ as the set of all positive integers $n$ such that $1 \leq n \leq 115$ and $p$ divides the $n$-th Fibonacci number. Let $t$ be the number of elements in $T$. Compute the $t$-th Lucas number, multipl... | 8,853 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(51202),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(115)), Divides(divisor=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")),... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COUNT_FIB_DIVISIBLE"
] | 97eb89 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T06:05:02.431741Z | {
"verified": true,
"answer": 8853,
"timestamp": "2026-02-08T06:05:02.433807Z"
} | 8cdf8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1436
},
"timestamp": "2026-02-12T19:19:02.620Z",
"answer": 8853
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7a22a4 | modular_sum_quadratic_residues_v1_397696148_1672 | Let $ d $ be the smallest positive divisor of 89951 that is at least 2. Define $ x = \frac{d(d-1)}{4} $. Compute the remainder when $ 44121 \cdot x $ is divided by 57349. | 26,274 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(89951))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
"Q": Mod(value=... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T12:42:34.904553Z | {
"verified": true,
"answer": 26274,
"timestamp": "2026-02-08T12:42:34.905940Z"
} | 916050 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 3594
},
"timestamp": "2026-02-15T04:05:34.477Z",
"answer": 26274
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5e49a7 | comb_catalan_compute_v1_153355830_2711 | Let $T$ be the set of all integers $t$ such that $27 \leq t \leq 120$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 13$, and $t = 21a + 6b$. Let $m$ be the number of elements in $T$. Let $P$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2... | 58,786 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS"
] | eb862e | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.011 | 2026-02-08T07:17:44.097276Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T07:17:44.107842Z"
} | 557d30 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 31497
},
"timestamp": "2026-02-24T07:55:21.818Z",
"answer": 58786
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
fd73d1 | antilemma_sum_equals_v1_655260480_997 | Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 20$ and $1 \leq j \leq 20$ such that $i + j = 20$. Compute the remainder when $13503x$ is divided by $69764$. | 47,265 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(20)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=Const(1), end=Const(20))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.028 | 2026-02-08T15:51:40.562408Z | {
"verified": true,
"answer": 47265,
"timestamp": "2026-02-08T15:51:40.590844Z"
} | 431b99 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 480
},
"timestamp": "2026-02-24T18:50:27.676Z",
"answer": 47265
},
{
"... | 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",
"status":... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
f9252e | nt_min_phi_inverse_v1_1978505735_1379 | Let $T$ be the set of all integers $t$ such that $24 \leq t \leq 195$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 15$, and $t = 15a + 9b$. Let $u$ be the number of elements in $T$. Find the smallest positive integer $n$ such that $1 \leq n \leq u$ and $\phi(n) = 22$, where $\phi... | 23 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(val... | NT | null | EXTREMUM | sympy | COMB1 | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.09 | 2026-02-08T16:06:26.722443Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T16:06:26.812057Z"
} | c39704 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2857
},
"timestamp": "2026-02-16T20:58:27.845Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8fd381 | nt_sum_divisors_mod_v1_124444284_7936 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10559$. | 2,880 | 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(176400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10559... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T09:27:11.723633Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T09:27:11.725474Z"
} | d49661 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 372
},
"timestamp": "2026-02-15T20:41:57.931Z",
"answer": 3600
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
67e8eb | nt_count_digit_sum_v1_458359167_2949 | Let $\text{upper}$ be the number of integers $t$ with $37 \leq t \leq 20081$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 1416$, $1 \leq b \leq 422$, such that $t = 10a + 14b + 13$. Let $\text{target\_sum}$ be the number of integers $t$ with $5 \leq t \leq 19$ for which there exist positive i... | 16,238 | graphs = [
Graph(
let={
"_m": Const(62609),
"_n": Const(44121),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a')... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.357 | 2026-02-08T06:52:00.694551Z | {
"verified": true,
"answer": 16238,
"timestamp": "2026-02-08T06:52:01.051158Z"
} | 58db73 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 7112
},
"timestamp": "2026-02-13T05:29:01.226Z",
"answer": 16238
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
bdb67a | nt_max_prime_below_v1_1439011603_2802 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p,q) = 1$, and $p < q$. Let $c$ be the number of elements in $P$. Let $Q$ be the set of all prime numbers $n$ such that $c \le n \le 24649$. Let $p_{\text{max}}$ be the largest element in $Q$. Find $... | 33,933 | graphs = [
Graph(
let={
"upper": Const(24649),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.029 | 2026-02-08T17:00:11.857176Z | {
"verified": true,
"answer": 33933,
"timestamp": "2026-02-08T17:00:12.885928Z"
} | a2a4e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2723
},
"timestamp": "2026-02-17T17:40:57.225Z",
"answer": 33933
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0c701e | antilemma_sum_equals_v1_784195855_8760 | Let $n$ be the number of integers $t$ with $27 \le t \le 252$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 12$, $1 \le b \le 6$, and $t = 15a + 12b$. Compute the number of ordered pairs $(i,j)$ of positive integers such that $i + j = n$ and $1 \le i \le 64$, $1 \le j \le 64$. | 63 | 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=12)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.036 | 2026-02-08T16:18:07.989565Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T16:18:08.025088Z"
} | 546569 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 3660
},
"timestamp": "2026-02-24T20:37:25.946Z",
"answer": 63
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
ffbb46 | nt_sum_totient_over_divisors_v1_1820931509_834 | Let $n = 90294$. Define $\sigma$ to be the sum
$$
\sum_{d \mid n} \phi(d),
$$
where $\phi(d)$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $n$. Let $C$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 10006$. Compute the remainder whe... | 6,690 | graphs = [
Graph(
let={
"n": Const(90294),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Mod(value=Ref("result"), modulus=Const(293)), Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), c... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | cc201f | nt_sum_totient_over_divisors_v1 | two_moduli | 5 | 0 | [
"COMB1"
] | 1 | 0.006 | 2026-02-08T11:55:39.165134Z | {
"verified": true,
"answer": 6690,
"timestamp": "2026-02-08T11:55:39.171361Z"
} | fc8fee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1002
},
"timestamp": "2026-02-14T20:54:19.738Z",
"answer": 6690
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3696c9 | nt_count_digit_sum_v1_1874849503_70 | Let $m = 289$ and $d = 34$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. For each such pair, compute $x + y$, and let $t$ be the minimum value of $x + y$ over all such pairs. Define $T$ to be the set of all positive integers $n$ such that $1 \leq n \leq t$ and $n \equiv 0 \p... | 2,783 | graphs = [
Graph(
let={
"_m": Const(289),
"_n": Const(34),
"upper": Const(195364),
"target_sum": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("... | NT | null | COUNT | sympy | B3 | [
"B3/SUM_DIVISIBLE"
] | 138b1a | nt_count_digit_sum_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 8.311 | 2026-02-08T12:47:19.527287Z | {
"verified": true,
"answer": 2783,
"timestamp": "2026-02-08T12:47:27.838409Z"
} | a17488 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 6842
},
"timestamp": "2026-02-10T02:33:32.085Z",
"answer": 2783
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"... | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
975b07 | modular_modexp_compute_v1_601307018_6301 | Let $M$ be the number of positive integers $n$ with $1 \leq n \leq \max\{ d : d \mid 213906,\ d^2 \leq 213906 \}$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $e$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ with $x + y = M$. Let $R = 7^e \bmod 13861$. Find the ... | 9,540 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(213906)), Leq(Mul(Var("d"), Var("d")), Const(21... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/L3C/B1"
] | 75239c | modular_modexp_compute_v1 | null | 6 | 0 | [
"B1",
"B3_CLOSEST",
"L3C"
] | 3 | 0.009 | 2026-03-10T06:54:49.538245Z | {
"verified": true,
"answer": 9540,
"timestamp": "2026-03-10T06:54:49.546811Z"
} | 63f7fb | 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": 5209
},
"timestamp": "2026-04-19T04:05:36.107Z",
"answer": 9540
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
303a3f | nt_sum_divisors_mod_v1_2051736721_1969 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. For each such pair, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Find the remainder when $\sigma(n)$ is divided by 10753. | 2,880 | 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(176400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10753... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T16:23:17.409283Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T16:23:17.414426Z"
} | 1bc613 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1349
},
"timestamp": "2026-02-17T02:41:04.329Z",
"answer": 2880
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d6832a | comb_count_derangements_v1_1978505735_2997 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 5136$ and $\binom{5136}{j}$ is odd. Compute the subfactorial of $n$, denoted $!n$, which counts the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_n": Const(5136),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(5136)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T17:17:43.418010Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T17:17:43.419393Z"
} | 5264a2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 2005
},
"timestamp": "2026-02-17T22:53:33.864Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
c9ab3c | comb_catalan_compute_v1_784195855_2636 | Let $S$ be the set of all ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 20$. Let $n$ be the number of such pairs. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $22238 \cdot C_n$ is divided by $93345$. | 36,103 | graphs = [
Graph(
let={
"_n": Const(93345),
"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")),... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T05:54:46.775473Z | {
"verified": true,
"answer": 36103,
"timestamp": "2026-02-08T05:54:46.777155Z"
} | cdba3e | 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": 1390
},
"timestamp": "2026-02-24T04:48:18.762Z",
"answer": 36103
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
1bbd67 | lin_form_endings_v1_784195855_92 | Let $a = 21$ and $b = 35$. 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 $A = 31$ and $B = 32$. Compute the remainder when
$$
8090 \cdot (a' A + b' B - a' b')
$$
is divided by $55946$. | 23,256 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(35),
"A_val": Const(31),
"B_val": Const(32),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:57:23.734292Z | {
"verified": true,
"answer": 23256,
"timestamp": "2026-02-08T02:57:23.735553Z"
} | 7f03c5 | 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": 863
},
"timestamp": "2026-02-10T11:55:58.483Z",
"answer": 23256
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -1,
"mid": 0.94,
"hi": 2.59
} | ||
921d9a | alg_poly_preperiod_count_v1_1218484723_1464 | For a non-negative integer $a$, define $f(x) = x^5 + 2x^4 - 3x^3 + 4x^2 + 5x + 1$. Let $N = f(a) \bmod 41$, $M = f(N) \bmod 41$, $R = f(M) \bmod 41$, and $S = f(R) \bmod 41$. Find the number of integers $a$ with $0 \leq a \leq 36284$ such that $S = N$, $M \neq N$, and $R \neq N$. | 5,310 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(5)), Mul(Const(2), Pow(Var("a"), Const(4))), Mul(Const(-3), Pow(Var("a"), Const(3))), Mul(Const(4), Pow(Var("a"), Const(2))), Mul(Const(5), Var("a")), Const(1)), modulus=Const(41)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Con... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.071 | 2026-02-25T03:10:37.703782Z | {
"verified": true,
"answer": 5310,
"timestamp": "2026-02-25T03:10:37.775241Z"
} | 5bc353 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 17608
},
"timestamp": "2026-03-10T03:53:43.668Z",
"answer": 5310
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
92482c | nt_count_primes_v1_1520064083_4854 | Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $N = |T|$. Let $S$ be the set of all prime numbers $n$ such that $N \leq n \leq 15129$. Compute the remainder when $99049 \cdot |S|$ is divided by $64633$. | 23,636 | graphs = [
Graph(
let={
"upper": Const(15129),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.652 | 2026-02-08T06:27:45.349560Z | {
"verified": true,
"answer": 23636,
"timestamp": "2026-02-08T06:27:47.001230Z"
} | 6884b0 | 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": 1602
},
"timestamp": "2026-02-13T00:26:31.591Z",
"answer": 23636
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e50544 | modular_mod_compute_v1_784195855_8527 | Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 3694084$. Let $m$ be the number of integers $t$ with $12 \leq t \leq 5660$ that can be expressed as $t = 7a + 5b$ for some integers $a, b$ satisfying $1 \leq a \leq 730$ and $1 \leq b \leq 110$. Let $r$ be the remainder... | 68,336 | graphs = [
Graph(
let={
"_n": Const(89854),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(3694084)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | modular_mod_compute_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T16:08:44.803835Z | {
"verified": true,
"answer": 68336,
"timestamp": "2026-02-08T16:08:44.807600Z"
} | 53f683 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 5885
},
"timestamp": "2026-02-16T22:24:35.643Z",
"answer": 68336
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cf1519 | diophantine_fbi2_min_v1_677425708_318 | Let $k = 32$ and let $u$ be the largest integer such that $23^u$ divides $1280517755401610942554593344683883498184411818540470887 \times 12167$. Let $d$ be the smallest integer satisfying $6 \leq d \leq u$, $d \mid k$, and $\frac{k}{d} \geq 4$. Define $Q$ as the sum of $56169$ and the sum over each digit of $|d|$, wher... | 56,177 | graphs = [
Graph(
let={
"_n": Const(6),
"k": Const(32),
"upper": MaxKDivides(target=Mul(Const(128051775540161094255459334683883498184411818540470887), Const(12167)), base=Const(23)),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"... | NT | null | EXTREMUM | sympy | K13 | [
"K13"
] | 8d970a | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"K13"
] | 1 | 0.006 | 2026-02-08T03:13:16.271172Z | {
"verified": true,
"answer": 56177,
"timestamp": "2026-02-08T03:13:16.276786Z"
} | a7d67b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 2693
},
"timestamp": "2026-02-10T02:02:28.322Z",
"answer": 56177
},
{
... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
7e32b2 | comb_count_partitions_v1_238844314_64 | Let $m = 2$. Let $n$ be the largest prime number less than or equal to 7487. Let $p(n)$ denote the number of integer partitions of $n$. Compute $p(42)$. Let $c$ be the largest prime number such that $2 \le c \le n$. Find the remainder when $c \cdot p(42)$ is divided by 60005. | 40,568 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(7487)), IsPrime(Var("n"))))),
"n": Const(42),
"result": Partition(arg=Ref(name='n')),
"_c": MaxOverS... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 8237f8 | comb_count_partitions_v1 | affine_mod | 7 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:06:33.258348Z | {
"verified": true,
"answer": 40568,
"timestamp": "2026-02-08T13:06:33.260707Z"
} | e1580a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1397
},
"timestamp": "2026-02-15T09:33:02.607Z",
"answer": 40568
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
76c02c | diophantine_fbi2_min_v1_1978505735_440 | Let $k = 125$ and let $u = 135$. Define $D$ as the set of all integers $d$ such that $2 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Let $m$ be the smallest element of $D$. Compute the sum $\sum_{i=0}^{t} d_i (i+1)^2$, where $d_i$ denotes the $i$-th decimal digit of $|m|$ (starting from the units digit as... | 2,023 | graphs = [
Graph(
let={
"k": Const(125),
"upper": Const(135),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3))))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 8e300c | diophantine_fbi2_min_v1 | digits_weighted_mod | 5 | 0 | [
"B3"
] | 1 | 0.015 | 2026-02-08T15:23:29.481020Z | {
"verified": true,
"answer": 2023,
"timestamp": "2026-02-08T15:23:29.496155Z"
} | 9d4166 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 840
},
"timestamp": "2026-02-16T05:38:16.166Z",
"answer": 2023
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f9f76 | nt_count_divisible_and_v1_865884756_245 | Let $d_1$ be the number of positive integers $n$ such that $n \le 43$ and $\gcd(n, 30) = 1$. Let $d_2 = 18$. Determine the value of the number of positive integers $n_1$ such that $n_1 \le 16524$, $n_1$ is divisible by $d_1$, and $n_1$ is divisible by $d_2$. | 459 | graphs = [
Graph(
let={
"upper": Const(16524),
"d1": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(43)), Eq(GCD(a=Var("n"), b=Const(30)), Const(1))))),
"d2": Const(18),
"result": CountOverSet(set=Solutio... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.542 | 2026-02-08T15:16:13.608557Z | {
"verified": true,
"answer": 459,
"timestamp": "2026-02-08T15:16:14.150277Z"
} | 0779df | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1113
},
"timestamp": "2026-02-10T06:04:02.604Z",
"answer": 459
},
{
"id... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
27a7ed | sequence_count_fib_divisible_v1_124444284_699 | Let $u$ be the number of prime numbers $n$ such that $2 \leq n \leq 1483$. Determine the number of positive integers $n \leq u$ for which $10$ divides the $n$th Fibonacci number. | 15 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1483)), IsPrime(Var("n"))))),
"d": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)... | NT | null | COUNT | sympy | LIN_FORM | [
"COUNT_PRIMES"
] | 07c874 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"LIN_FORM"
] | 2 | 0.076 | 2026-02-08T03:27:36.375067Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T03:27:36.451221Z"
} | ddf97c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 5108
},
"timestamp": "2026-02-23T19:48:49.656Z",
"answer": 15
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
dc3e89 | comb_binomial_compute_v1_2051736721_5290 | Let $u_1 = 1$, $n_2 = u_1 + 1$, and $$h = \sum_{k_1=0}^{n_2} (-1)^{k_1} \binom{n_2}{k_1}.$$ Let $n_1 = 0$ and $$u = \sum_{k_2=0}^{n_1} (-1)^{k_2} \binom{n_1}{k_2}.$$ Define $n = 12u$ and $k = 5 + h$. Compute $\binom{n}{k}$. | 792 | graphs = [
Graph(
let={
"u1": Const(1),
"n2": Sum(Ref("u1"), Const(1)),
"h": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"n1": Const(0),
"u": Summation(var="k2", start=Co... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_binomial_compute_v1 | null | 2 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T18:28:37.810403Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T18:28:37.811673Z"
} | c71485 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 785
},
"timestamp": "2026-02-24T23:57:50.063Z",
"answer": 792
},
{
... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -10,
"mid": -7.4,
"hi": -4.8
} | ||
027ec1 | lin_form_endings_v1_2051736721_900 | Let $a = 75$ and $b = 60$. Let $g$ be the greatest common divisor of $a$ and $b$. Compute the remainder when $12283 \cdot g$ is divided by 99599. | 84,646 | graphs = [
Graph(
let={
"a_coeff": Const(75),
"b_coeff": Const(60),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(12283),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(99599),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T15:45:11.876537Z | {
"verified": true,
"answer": 84646,
"timestamp": "2026-02-08T15:45:11.877458Z"
} | 367b7c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 445
},
"timestamp": "2026-02-16T06:18:01.258Z",
"answer": 84646
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
15e935 | comb_factorial_compute_v1_1874849503_108 | Let $n$ be the number of positive integers $k$ such that $\gcd(k, 6) = 1$ and $1 \leq k \leq p$, where $p$ is the largest prime number at most $21$. Compute the value of $n!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(21)), IsPrime(Var("n"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2)... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/C4",
"ONE_PHI_2"
] | 7c31e7 | comb_factorial_compute_v1 | null | 5 | 0 | [
"C4",
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 3 | 0.004 | 2026-02-08T12:48:43.612544Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T12:48:43.616676Z"
} | dafbd5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 3561
},
"timestamp": "2026-02-09T13:52:07.217Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{... | {
"lo": -6.51,
"mid": -0.38,
"hi": 5.12
} | ||
47904d | sequence_lucas_compute_v1_1439011603_383 | Let $t$ be a positive integer. Define $n$ to be the number of values of $t$ with $7 \le t \le 32$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 11$, $1 \le b \le 2$, and $t = 2a + 5b$. Let $L_n$ denote the $n$-th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k... | 1,741 | graphs = [
Graph(
let={
"_n": Const(16831),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(left=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T15:26:11.243784Z | {
"verified": true,
"answer": 1741,
"timestamp": "2026-02-08T15:26:11.247568Z"
} | 3fe3cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1293
},
"timestamp": "2026-02-16T06:29:42.339Z",
"answer": 1741
},
{... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
021055 | sequence_lucas_compute_v1_1520064083_148 | Let $n$ be the number of integers $t$ such that $14 \leq t \leq 62$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 4$, and $t = 6a + 8b$. Compute the $n$th Lucas number. | 9,349 | 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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T03:06:30.801839Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T03:06:30.805824Z"
} | e0e078 | 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": 2714
},
"timestamp": "2026-02-10T12:58:22.907Z",
"answer": 9349
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
b572a2 | nt_count_coprime_and_v1_1439011603_1640 | Let $ k_1 $ be the number of ordered pairs $ (i, j) $ of integers with $ 1 \leq i \leq 6 $ and $ 1 \leq j \leq 6 $ such that $ i + j = 6 $. Let $ k_2 $ be the largest prime number $ n $ satisfying $ 2 \leq n \leq 12 $. Define $ N $ to be the number of positive integers $ n_1 $ with $ 1 \leq n_1 \leq 40173 $ such that $... | 29,217 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(12),
"upper": Const(40173),
"k1": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"MAX_PRIME_BELOW"
] | a9245e | nt_count_coprime_and_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"MAX_PRIME_BELOW"
] | 2 | 5.176 | 2026-02-08T16:12:02.427050Z | {
"verified": true,
"answer": 29217,
"timestamp": "2026-02-08T16:12:07.602791Z"
} | 8bfe5e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 2353
},
"timestamp": "2026-02-16T22:54:37.021Z",
"answer": 29217
},
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b0107c | nt_sum_over_divisible_v1_1915831931_2604 | Compute the sum of all positive integers $n$ such that $n \leq 5555$ and $n$ is divisible by 162. | 96,390 | graphs = [
Graph(
let={
"upper": Const(5555),
"divisor": Const(162),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
},
go... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | nt_sum_over_divisible_v1 | null | 2 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 6.156 | 2026-02-08T16:58:07.500400Z | {
"verified": true,
"answer": 96390,
"timestamp": "2026-02-08T16:58:13.656872Z"
} | 9c74b4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 533
},
"timestamp": "2026-02-16T08:54:25.088Z",
"answer": 96770
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
769437 | antilemma_k3_v1_784195855_595 | Let $n = 7965$. Compute the sum of $\varphi(d)$ over all positive divisors $d$ of $n$, where $\varphi$ denotes Euler's totient function. | 7,965 | graphs = [
Graph(
let={
"_n": Const(7965),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:29:21.856841Z | {
"verified": true,
"answer": 7965,
"timestamp": "2026-02-08T04:29:21.857080Z"
} | 0a51de | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 332
},
"timestamp": "2026-02-10T16:51:17.868Z",
"answer": 7965
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
6008ac | comb_sum_binomial_row_v1_677425708_1127 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 28$. Let $r$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Define $s = r^n$. Compute the remainder when $44121 \cdot s$ is divide... | 14,413 | graphs = [
Graph(
let={
"_m": Const(70297),
"_n": Const(28),
"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')), ... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"COMB1"
] | d35293 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COMB1",
"COPRIME_PAIRS"
] | 2 | 0.002 | 2026-02-08T04:00:24.716752Z | {
"verified": true,
"answer": 14413,
"timestamp": "2026-02-08T04:00:24.718511Z"
} | e8d3f8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 2002
},
"timestamp": "2026-02-09T15:58:53.345Z",
"answer": 14413
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"l... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
588e30 | antilemma_v1_legendre_151522320_134 | Let $N=38060$. Let $x$ be the largest integer $k$ such that $5^k$ divides $N!$.
Consider all integers $t$ such that $5\le t\le17$ and there exist integers $a$ and $b$ with $1\le a\le4$ and $1\le b\le3$ satisfying
$$t=2a+3b.$$
Let $M$ be the number of such integers $t$.
Let $S$ be the set of all integers $n$ such that... | 4,140 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(38060),
"x": MaxKDivides(target=Factorial(Ref("_n")), base=Const(5)),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"V1"
] | b1eb50 | antilemma_v1_legendre | bell_mod | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"V1"
] | 3 | 0.005 | 2026-02-08T02:59:58.145002Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T02:59:58.149667Z"
} | 56e4fd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 350,
"completion_tokens": 1214
},
"timestamp": "2026-02-08T23:32:53.311Z",
"answer": 4140
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
1d7acb | sequence_count_fib_divisible_v1_1978505735_354 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 683$ and the sum of the digits of $n$ is even. Let $a = |A|$. Let $B$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq a$ and $3$ divides the $n_1$-th Fibonacci number. Let $b = |B|$. Compute the remainder when $44566 \cdot b$ ... | 38,160 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(683)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"d": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var(... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.038 | 2026-02-08T15:20:14.855318Z | {
"verified": true,
"answer": 38160,
"timestamp": "2026-02-08T15:20:14.892907Z"
} | e1f1c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2800
},
"timestamp": "2026-02-16T04:30:27.251Z",
"answer": 38160
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d597d7 | diophantine_sum_product_min_v1_2051736721_887 | Let $S = 36$ and $P = 324$. Compute the minimum value of $x$ such that $1 \leq x \leq 35$ and $x(S - x) = P$. | 18 | graphs = [
Graph(
let={
"S": Const(36),
"P": Const(324),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(35)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),
... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"C4/C4/C2/K13"
] | 824bf5 | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"C2",
"C4",
"K13",
"LIN_FORM"
] | 4 | 0.139 | 2026-02-08T15:44:02.739918Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T15:44:02.878806Z"
} | e5abd0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 313
},
"timestamp": "2026-02-16T12:31:52.707Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3a51b3 | algebra_poly_eval_v1_1978505735_1847 | Let $k = 16$. Compute the value of
$$
\frac{2k^5 - 18k^4 - 24k^3 + m k^2 + 2k - 16}{34},
$$
where $m$ is the number of positive integers $k_1 \leq t$ that are divisible by $36$, and $t$ is the number of positive integers $k_2 \leq 8568$ that are divisible by $17$. Let $r$ be the absolute value of this result. Compute t... | 1 | graphs = [
Graph(
let={
"_n": Const(11),
"k": Const(16),
"result": Div(Sum(Mul(Const(2), Pow(Ref("k"), Const(5))), Mul(Const(-18), Pow(Ref("k"), Const(4))), Mul(Const(-24), Pow(Ref("k"), Const(3))), Mul(CountOverSet(set=SolutionsSet(var=Var("k1"), condition=And(Geq(Var("k... | COMB | NT | COMPUTE | sympy | C2 | [
"C2/C2"
] | c8a699 | algebra_poly_eval_v1 | null | 6 | 0 | [
"C2"
] | 1 | 0.01 | 2026-02-08T16:28:33.726897Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:28:33.736601Z"
} | 2db357 | 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": 1011
},
"timestamp": "2026-02-17T04:59:00.284Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fe06f7 | comb_count_surjections_v1_1439011603_3033 | Let $n_1 = 1$ and $n_2 = 0$. Define
$$
c = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k} \quad \text{and} \quad e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $k = 6 + c$ and $n = 7$. Compute the remainder when $71168 \cdot k! \cdot S(n, k)$ is divided by $93213 \cdot e$, where $S(n, k)$ denotes the Stirling number of the... | 9,288 | graphs = [
Graph(
let={
"n2": Const(0),
"e": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"u": Const(0),
"n1": Sum(Ref("u"), Factorial(Const(0))),
"c": Summation(var="k2",... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0",
"ZERO_BINOM_0"
] | 6c8df4 | comb_count_surjections_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0",
"ZERO_BINOM_0"
] | 3 | 0.006 | 2026-02-08T17:10:44.059111Z | {
"verified": true,
"answer": 9288,
"timestamp": "2026-02-08T17:10:44.064640Z"
} | 73b307 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1203
},
"timestamp": "2026-02-17T22:04:31.256Z",
"answer": 9288
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b4c545 | sequence_count_fib_divisible_v1_601307018_5200 | Let $F_n$ denote the $n$-th Fibonacci number. Let $d$ be the number of integers $j$ with $0 \le j \le 1036$ such that $\binom{1036}{j}$ is odd. Let $M$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers with $xy = 1486949$. Find the number of positive integers $n$ with $1 \le n \le M... | 143 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1486949)))), expr=Abs(arg=Sub(left=Var(n... | NT | null | COUNT | sympy | B3_DIFF | [
"B3_DIFF",
"V8"
] | 1cc898 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3_DIFF",
"V8"
] | 2 | 0.031 | 2026-03-10T05:54:01.347080Z | {
"verified": true,
"answer": 143,
"timestamp": "2026-03-10T05:54:01.377661Z"
} | df7256 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 9824
},
"timestamp": "2026-04-19T01:31:56.340Z",
"answer": 143
},
{
"i... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"le... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
fea6c1 | nt_num_divisors_compute_v1_1742523217_3725 | Let $n = 41209$. Let $d(n)$ denote the number of positive divisors of $n$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1119364$. Let $c$ be the minimum value of $x + y$ over all such pairs. Compute $c - d(n)$. | 2,107 | graphs = [
Graph(
let={
"n": Const(41209),
"result": NumDivisors(n=Ref("n")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_num_divisors_compute_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T06:04:46.213271Z | {
"verified": true,
"answer": 2107,
"timestamp": "2026-02-08T06:04:46.214700Z"
} | d3d225 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1401
},
"timestamp": "2026-02-12T18:41:21.979Z",
"answer": 2107
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4e78a9 | alg_poly_orbit_count_v1_1419126231_390 | Let $N \equiv 3a^3 + a^2 + 4a - 1 \pmod{23}$ and $M \equiv 3N^3 + N^2 + 4N - 1 \pmod{23}$. Find the number of non-negative integers $a$ with $0 \le a \le 40985$ such that $M \equiv a \pmod{23}$ and $N \not\equiv a \pmod{23}$. | 10,692 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(3))), Pow(Var("a"), Const(2)), Mul(Const(4), Var("a")), Const(-1)), modulus=Const(23)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(3))), Pow(Ref("p1"), Const(2)), Mul(Const(4), Ref("p1")), Const... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.021 | 2026-02-25T09:55:35.093484Z | {
"verified": true,
"answer": 10692,
"timestamp": "2026-02-25T09:55:35.114142Z"
} | 6e0b80 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 5663
},
"timestamp": "2026-03-30T08:19:16.157Z",
"answer": 10692
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
38fce9 | antilemma_k2_v1_458359167_2696 | Compute the remainder when
$$
88713 \sum_{k=1}^{146} \phi(k) \left\lfloor \frac{146}{k} \right\rfloor
$$
is divided by $60529$. | 39,620 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(146), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(146), Var("k"))))),
"Q": Mod(value=Mul(Const(88713), Ref("x")), modulus=Const(60529)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T06:44:19.306362Z | {
"verified": true,
"answer": 39620,
"timestamp": "2026-02-08T06:44:19.306714Z"
} | e8249d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 1929
},
"timestamp": "2026-02-13T03:57:45.378Z",
"answer": 39620
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
9c0e90 | algebra_poly_eval_v1_2051736721_4521 | Let $x = 8$. Define $$
= \frac{8x^5 - 50x^4 + 43x^3 - 69x^2 + 67x + 55}{5}.$$
Let $S$ be the set of all ordered pairs $(x_1, y)$ of positive integers such that $x_1 y = 3694084$. Let $T$ be the set of all values $x_1 + y$ where $(x_1, y) \in S$. Compute the remainder when $$n^2 + 23n + \min(T)$$ is divided by $94869$. | 33,333 | graphs = [
Graph(
let={
"_n": Const(55),
"x": Const(8),
"result": Div(Sum(Mul(Const(8), Pow(Ref("x"), Const(5))), Mul(Const(-50), Pow(Ref("x"), Const(4))), Mul(Const(43), Pow(Ref("x"), Const(3))), Mul(Const(-69), Pow(Ref("x"), Const(2))), Mul(Const(67), Ref("x")), Ref("_n... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | d720b5 | algebra_poly_eval_v1 | quadratic_mod | 4 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T18:01:57.967436Z | {
"verified": true,
"answer": 33333,
"timestamp": "2026-02-08T18:01:57.973277Z"
} | 28c5df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2117
},
"timestamp": "2026-02-18T12:08:00.342Z",
"answer": 33333
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bebf3b | nt_count_digit_sum_v1_784195855_612 | Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq 256$ and $128$ divides $k$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all positive integers $d$ such that $d \geq m$ and $d$ divides $10051$. Let $n$ be the smallest element of $T$. Let $U$ be the set of all ordered pairs $(i... | 16,216 | graphs = [
Graph(
let={
"_c": Const(128),
"_m": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(256)), Divides(divisor=Ref("_c"), dividend=Var("k"))), domain='positive_integers')),
"_n": MinOverSet(set=SolutionsSet(va... | NT | null | COUNT | sympy | C2 | [
"C2/MIN_PRIME_FACTOR/COUNT_SUM_EQUALS"
] | da0884 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"C2",
"COUNT_SUM_EQUALS",
"MIN_PRIME_FACTOR"
] | 3 | 18.365 | 2026-02-08T04:29:37.869319Z | {
"verified": true,
"answer": 16216,
"timestamp": "2026-02-08T04:29:56.234445Z"
} | ba1a64 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 306,
"completion_tokens": 5923
},
"timestamp": "2026-02-10T16:51:57.220Z",
"answer": 16216
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f9d63c | sequence_count_fib_divisible_v1_2051736721_2794 | Let $n$ be a positive integer. Define $\phi(n)$ to be Euler's totient function. Let $N = 949$ and let
$$
S = \sum_{d \mid N} \phi(d).
$$
Let $d = 4$. Determine the number of positive integers $n$ such that $1 \leq n \leq S$ and $d$ divides the $n$-th Fibonacci number $F_n$. Compute this number. | 158 | graphs = [
Graph(
let={
"_n": Const(949),
"upper": SumOverDivisors(n=Ref(name='_n'), var='d1', expr=EulerPhi(n=Var(name='d1'))),
"d": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("uppe... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.136 | 2026-02-08T16:55:06.550185Z | {
"verified": true,
"answer": 158,
"timestamp": "2026-02-08T16:55:06.686634Z"
} | 83802d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 872
},
"timestamp": "2026-02-17T14:48:48.254Z",
"answer": 158
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
84e190 | algebra_vieta_sum_v1_1520064083_1814 | Let $d_{\max}$ be the largest positive divisor of $153$ that is at most $9$. Find all real numbers $x$ such that
$$
x^3 + d_{\max} x^2 - 36x - 324 = 0.
$$
Let $P$ be the product of all such real solutions. Compute $P$. | 324 | graphs = [
Graph(
let={
"_n": Const(9),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=3)), Mul(MaxOverSet(set=SolutionsSet(var=Var(name='d'), condition=And(Geq(left=Var(name='d'), right=Const(value=1)), Leq(... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"MAX_DIVISOR"
] | 51757e | algebra_vieta_sum_v1 | null | 4 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_DIVISOR"
] | 2 | 0.021 | 2026-02-08T04:19:06.028406Z | {
"verified": true,
"answer": 324,
"timestamp": "2026-02-08T04:19:06.049550Z"
} | afdcd7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 882
},
"timestamp": "2026-02-10T16:04:15.251Z",
"answer": 324
},
{
"id... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
209ff2 | nt_count_primes_v1_151522320_1302 | Let $m = 56372$. Define $r$ to be the number of prime numbers $n$ such that $2 \leq n \leq 12720$.
Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 4$. Let $s$ be the minimum value of $x + y$ over all such pairs.
Let $t$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \l... | 2,744 | graphs = [
Graph(
let={
"_m": Const(56372),
"_n": Const(2),
"upper": Const(12720),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Sum(Po... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"B3"
] | b257a6 | nt_count_primes_v1 | quadratic_mod | 4 | 0 | [
"B3",
"COUNT_CARTESIAN"
] | 2 | 1.66 | 2026-02-08T03:52:29.314878Z | {
"verified": true,
"answer": 2744,
"timestamp": "2026-02-08T03:52:30.975358Z"
} | 2e2f4f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1513
},
"timestamp": "2026-02-11T20:21:16.302Z",
"answer": 2744
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
818092 | lin_form_endings_v1_1742523217_2218 | Let $a = 63$ and $b = 36$. Define $g = \gcd(a, b)$. Let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 31$ and $B = 48$. Define
$$
T = a' \cdot A + b' \cdot B - a' \cdot b'.
$$
Now define
$$
S = a \cdot A + b \cdot B - a - b + 1.
$$
Compute $S - T$. | 3,202 | graphs = [
Graph(
let={
"a_coeff": Const(63),
"b_coeff": Const(36),
"A_val": Const(31),
"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": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T04:35:49.941981Z | {
"verified": true,
"answer": 3202,
"timestamp": "2026-02-08T04:35:49.945670Z"
} | cd9e6e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 625
},
"timestamp": "2026-02-10T17:13:30.838Z",
"answer": 3202
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
3d6a96 | comb_factorial_compute_v1_655260480_5037 | Let $n = 8$, and let $f = n!$. Let $d$ be the smallest divisor of $537251$ that is at least $2$. Compute the Bell number $B_k$, where $k$ is the remainder when $|f|$ is divided by $d$. | 52 | graphs = [
Graph(
let={
"n": Const(8),
"result": Factorial(Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(537251))))))),
... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | comb_factorial_compute_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.019 | 2026-02-08T18:15:25.794744Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T18:15:25.813715Z"
} | 72b0c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 1345
},
"timestamp": "2026-02-18T15:31:03.429Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0547a6 | algebra_poly_eval_v1_1918700295_1961 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $k$ be the maximum value of $xy$ over all such pairs. Compute the remainder when $52428(k^4 + k^3 + 2k^2 - 10k - 7)$ is divided by $94313$. | 56,396 | graphs = [
Graph(
let={
"_n": Const(2),
"k": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T06:12:00.664111Z | {
"verified": true,
"answer": 56396,
"timestamp": "2026-02-08T06:12:00.666220Z"
} | 53210d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1150
},
"timestamp": "2026-02-13T11:26:39.291Z",
"answer": 56396
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
5c2c8a | geo_count_lattice_rect_v1_1439011603_821 | Compute the number of lattice points in the rectangle $[0, 484] \times [0, 123]$. Multiply this number by $79157$, and find the remainder when the result is divided by $91730$. | 81,900 | graphs = [
Graph(
let={
"a": Const(484),
"b": Const(123),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(79157),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(91730)),
},
goal=Ref("Q"),
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.006 | 2026-02-08T15:45:37.614780Z | {
"verified": true,
"answer": 81900,
"timestamp": "2026-02-08T15:45:37.620766Z"
} | c8088d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1700
},
"timestamp": "2026-02-24T18:29:47.904Z",
"answer": 81900
},
{
... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
9ce7ae | sequence_fibonacci_compute_v1_655260480_6206 | Let $T$ be the set of all integers $t$ such that $18 \leq t \leq 90$ and $t = 8a + 10b$ for some integers $a$ and $b$ with $1 \leq a \leq 5$ and $1 \leq b \leq 5$. Let $n$ be the number of elements in $T$. Let $F_n$ denote the $n$-th Fibonacci number, with $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq... | 308 | 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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:54:58.646634Z | {
"verified": true,
"answer": 308,
"timestamp": "2026-02-08T18:54:58.648984Z"
} | ab924f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 3798
},
"timestamp": "2026-02-18T20:28:47.376Z",
"answer": 308
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
191120 | modular_mod_compute_v1_784195855_8729 | Let $ S $ be the set of all integers $ t $ such that $ 7 \leq t \leq 235 $ and there exist positive integers $ a $ and $ b $ with $ 1 \leq a \leq 90 $, $ 1 \leq b \leq 11 $, and $ t = 2a + 5b $. Let $ a $ be the number of elements in $ S $. Compute the remainder when $ a $ is divided by $ 37675 $. | 225 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=90)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T16:17:37.463695Z | {
"verified": true,
"answer": 225,
"timestamp": "2026-02-08T16:17:37.467525Z"
} | f37cfa | 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": 3320
},
"timestamp": "2026-02-17T01:06:57.565Z",
"answer": 225
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6dd006 | alg_qf_psd_count_v1_601307018_4097 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1 \le 35$ and $1 \le b_1 \le 35$ such that $16 b_1^2 = \max\{ d \ge 1 : d \mid 332352 \text{ and } d^2 \le 332352 \}$. Let $B = |S|$. Let $T$ be the set of ordered pairs $(a_1, b_1)$ with $1 \le a_1 \le 35$, $1 \le b_1 \le B$, such that... | 12 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(16),
"_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(468)), Geq(Var("b"), Const(1)), Leq(Var("b"), ... | NT | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"B3_CLOSEST/QF_PSD_COUNT/QF_PSD_COUNT_LEQ"
] | b15f26 | alg_qf_psd_count_v1 | null | 7 | 0 | [
"B3_CLOSEST",
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 2.969 | 2026-03-10T04:42:25.612241Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-03-10T04:42:28.581464Z"
} | 7e8d35 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 348,
"completion_tokens": 13094
},
"timestamp": "2026-03-29T10:57:49.031Z",
"answer": 12
},
{
"id... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"statu... | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
9f36dc | modular_mod_compute_v1_1918700295_696 | Let $T$ be the set of all positive integers $t$ such that $9 \leq t \leq 168$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 37$, $1 \leq b \leq 4$, and $t = 4a + 5b$. Let $n$ be the number of elements in $T$.
Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = n$... | 54,741 | graphs = [
Graph(
let={
"_m": Const(84339),
"_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=37)), Geq(left=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | modular_mod_compute_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T03:23:19.922723Z | {
"verified": true,
"answer": 54741,
"timestamp": "2026-02-08T03:23:19.928119Z"
} | cecd89 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 3890
},
"timestamp": "2026-02-10T13:24:47.905Z",
"answer": 54741
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
82a9c1 | antilemma_sum_equals_v1_784195855_3439 | Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 52$ and $t = 3a + 5b$ for some integers $a$ and $b$ with $1 \leq a \leq 9$ and $1 \leq b \leq 5$. Let $n = |T|$. Define $S$ as the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 37$ and $1 \leq j \leq 37$ such that $i + j = n$. Compute t... | 36 | 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=9)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T06:26:00.470019Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T06:26:00.477656Z"
} | 14f995 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 2643
},
"timestamp": "2026-02-24T06:11:34.128Z",
"answer": 36
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
405d88 | nt_gcd_compute_v1_1439011603_372 | Let $m = 3249$ and $n = 93563$. Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = m$. Define $T$ as the set of all values of $x_1 + y_1$ where $(x_1, y_1) \in S$. Let $s$ be the minimum value in $T$. Now, let $U$ be the set of all ordered pairs $(x, y)$ of positive integers ... | 19,495 | graphs = [
Graph(
let={
"_m": Const(3249),
"_n": Const(93563),
"a": Const(1005121),
"b": Const(1623657),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), ... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 6cdf3d | nt_gcd_compute_v1 | negation_mod | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T15:25:50.677288Z | {
"verified": true,
"answer": 19495,
"timestamp": "2026-02-08T15:25:50.680758Z"
} | cfae10 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 1308
},
"timestamp": "2026-02-16T06:29:40.496Z",
"answer": 19495
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a37a3f | antilemma_sum_equals_v1_865884756_2153 | Let $c = 118$. Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = c$. Let $n$ be the number of ordered pairs $(i, j)$ with $1 \leq i, j \leq 59$ such that $i + j = m$. Compute the number of ordered pairs $(i_1, j_1)$ with $1 \leq i_1, j_1 \leq 57$ such that $i_1 + j_1 = ... | 57 | graphs = [
Graph(
let={
"_c": Const(118),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | a57484 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.114 | 2026-02-08T16:35:07.776878Z | {
"verified": true,
"answer": 57,
"timestamp": "2026-02-08T16:35:07.890904Z"
} | c7b1a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1151
},
"timestamp": "2026-02-17T07:58:47.677Z",
"answer": 57
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
9f1287 | alg_poly_orbit_hensel_v1_601307018_3753 | Let $N = (a^3 - 5a) \bmod 169$ and $M = (N^3 - 5N) \bmod 169$. Find the number of non-negative integers $a$ with $0 \le a \le 112553$ such that $M = a$ and $N \ne a$. | 1,332 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-5), Var("a"))), modulus=Const(169)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-5), Ref("p1"))), modulus=Const(169)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), condit... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.034 | 2026-03-10T04:19:56.627622Z | {
"verified": true,
"answer": 1332,
"timestamp": "2026-03-10T04:19:56.661340Z"
} | 1360eb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 9827
},
"timestamp": "2026-03-29T09:54:14.918Z",
"answer": 2
},
{
"i... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
94958a | modular_sum_quadratic_residues_v1_1742523217_3703 | Let $m = 514$. Let $d_{\text{max}}$ be the largest positive divisor $d$ of $268822$ such that $d \leq m$. Let $p$ be the number of positive integers $n$ such that $1 \leq n \leq d_{\text{max}}$ and the sum of the decimal digits of $n$ is divisible by $2$. Compute $\frac{p(p-1)}{4}$. | 16,448 | graphs = [
Graph(
let={
"_m": Const(514),
"_n": Const(2),
"p": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_m")), Divid... | NT | null | SUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/L3B"
] | fd7fc9 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"L3B",
"MAX_DIVISOR"
] | 2 | 0.004 | 2026-02-08T06:03:24.318961Z | {
"verified": true,
"answer": 16448,
"timestamp": "2026-02-08T06:03:24.322553Z"
} | 4308e6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 3058
},
"timestamp": "2026-02-12T18:41:37.261Z",
"answer": 16448
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "MAX_DIVISOR",
"status": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
829aab | nt_min_phi_inverse_v1_1520064083_10384 | Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 113$. Let $m = |S|$. Define $T$ as the set of all positive integers $n$ such that $1 \leq n \leq m$ and $\phi(n) = 10$. Let $a$ be the smallest element of $T$. Let $B$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y ... | 5,648 | graphs = [
Graph(
let={
"_n": Const(113),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"k": Const(10),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=... | NT | null | EXTREMUM | sympy | B3 | [
"B3",
"COUNT_PRIMES"
] | 50074e | nt_min_phi_inverse_v1 | two_stage_modexp | 7 | 0 | [
"B3",
"COUNT_PRIMES"
] | 2 | 0.006 | 2026-02-08T11:22:35.402233Z | {
"verified": true,
"answer": 5648,
"timestamp": "2026-02-08T11:22:35.408695Z"
} | e07f6d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 2555
},
"timestamp": "2026-02-14T13:25:12.065Z",
"answer": 5648
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bcc259 | antilemma_k3_v1_1520064083_3122 | Let $S$ be the set of all real numbers $x$ such that $x^2 - 3582x + 152177 = 0$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of the sum of the elements of $S$. Compute the remainder when $37331n$ is divided by $53142$. | 14,370 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=SumOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=2)), Mul(Const(value=-3582), Var(name='x')), Const(value=152177)), right=Const(value=0)))), var='d', expr=EulerPhi(n=Var(name='d'))),
... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K3",
"K3"
] | 78a626 | antilemma_k3_v1 | null | 6 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T05:28:46.108833Z | {
"verified": true,
"answer": 14370,
"timestamp": "2026-02-08T05:28:46.109823Z"
} | c45750 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1749
},
"timestamp": "2026-02-12T09:22:11.380Z",
"answer": 14370
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"le... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ac512f | nt_num_divisors_compute_v1_1915831931_2464 | Let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 4019$. Compute the number of positive divisors of $n$. | 8 | graphs = [
Graph(
let={
"_n": Const(4019),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"COUNT_PRIMES"
] | 07c874 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"LIN_FORM"
] | 2 | 0.047 | 2026-02-08T16:51:10.533422Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T16:51:10.580415Z"
} | 933a77 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 83,
"completion_tokens": 3042
},
"timestamp": "2026-02-17T15:17:48.674Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ff8f2b | nt_count_intersection_v1_1125832087_1208 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6250000$. Define $N$ to be the minimum value of $x + y$ over all such pairs. Let $a = 9$ and $b = 16$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. | 278 | 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(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(9),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.167 | 2026-02-08T03:36:47.609643Z | {
"verified": true,
"answer": 278,
"timestamp": "2026-02-08T03:36:47.776312Z"
} | b94602 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1509
},
"timestamp": "2026-02-10T15:09:28.576Z",
"answer": 278
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
224580 | antilemma_k3_v1_1520064083_7168 | Let $n = 98305$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 98,305 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=98305), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T08:49:33.093577Z | {
"verified": true,
"answer": 98305,
"timestamp": "2026-02-08T08:49:33.094337Z"
} | fec3b6 | 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": 1666
},
"timestamp": "2026-02-13T21:57:20.592Z",
"answer": 98305
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
618cc4 | comb_sum_binomial_row_v1_124444284_943 | Let $n = 12$. Define $S$ to be 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 $r = |S|$. Compute the remainder when $44121 \cdot r^{12}$ is divided by $96412$. | 43,528 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": Const(12),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T03:36:24.737117Z | {
"verified": true,
"answer": 43528,
"timestamp": "2026-02-08T03:36:24.738152Z"
} | 6f52a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 1536
},
"timestamp": "2026-02-10T00:24:03.692Z",
"answer": 43528
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
833452 | diophantine_fbi2_min_v1_2051736721_4320 | Let $k$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 32400$. Let $d$ be a positive integer satisfying $7 \leq d \leq 370$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. Define $r$ to be the smallest such $d$. Compute the value of $\sum_{n=1}^{r} \phi(n)$, where $\phi(n)... | 22 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(37... | NT | null | EXTREMUM | sympy | C2 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3",
"C2"
] | 2 | 0.103 | 2026-02-08T17:54:54.449672Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T17:54:54.552585Z"
} | ce0dd4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1289
},
"timestamp": "2026-02-18T10:05:01.421Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e0d2ce_n | alg_sum_ap_v1_1218484723_7711 | A delivery service packs boxes with combinations of two types of items: Type A (5 units per item) and Type B (2 units per item). Each shipment uses between 1 and 711 Type A items and between 1 and 2733 Type B items. The total unit count of a shipment is $t = 5a + 2b$, and only shipments with between 7 and 9021 units ar... | 3,779 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sum_ap_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.037 | 2026-02-25T09:13:47.201119Z | null | c1de1f | e0d2ce | narrative | 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": 23941
},
"timestamp": "2026-03-31T02:59:36.676Z",
"answer": 3779
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
8c4107 | nt_lcm_compute_v1_1439011603_2485 | Let $a = 1375$ and let $$b = \sum_{k=1}^{32} \varphi(k) \left\lfloor \frac{32}{k} \right\rfloor,$$ where $\varphi(k)$ denotes Euler's totient function. Compute $\text{lcm}(a, b)$. | 66,000 | graphs = [
Graph(
let={
"a": Const(1375),
"b": Summation(var="k", start=Const(1), end=Const(32), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(32), Var("k"))))),
"result": LCM(a=Ref("a"), b=Ref("b")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_lcm_compute_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T16:49:58.246546Z | {
"verified": true,
"answer": 66000,
"timestamp": "2026-02-08T16:49:58.248794Z"
} | b07d79 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 776
},
"timestamp": "2026-02-17T13:29:27.163Z",
"answer": 66000
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c49d68 | alg_qf_psd_orbit_v1_1218484723_2960 | Let $V$ be the number of integers $v$ with $13 \leq v \leq 1105$ for which there exist integers $a, b$ with $1 \leq a, b \leq 8$ such that $17a^2 - 24ab + 20b^2 = v$. Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \leq a \leq b \leq c \leq 34$ such that
$$
V \cdot c^2 + 60a^2 + 60b^2 + 68ab... | 5 | graphs = [
Graph(
let={
"_n": Const(34),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(34)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Geq(Var("c"), Const(1)), Leq(Var("c... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 13.46 | 2026-02-25T04:42:03.096746Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-25T04:42:16.556975Z"
} | a3ec1b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T07:34:14.780Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
d18cf9 | nt_euler_phi_compute_v1_349078426_493 | Let $n = 44944$. Define $\phi(n)$ to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14494$. Compute the remainder when $c \cdot \phi(n)$ is divided by $96312$. | 248 | graphs = [
Graph(
let={
"_n": Const(96312),
"n": Const(44944),
"result": EulerPhi(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(a... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 54ff32 | nt_euler_phi_compute_v1 | affine_mod | 3 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T13:06:08.049133Z | {
"verified": true,
"answer": 248,
"timestamp": "2026-02-08T13:06:08.051846Z"
} | 6b65ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 2955
},
"timestamp": "2026-02-15T09:26:22.657Z",
"answer": 248
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dfce10 | antilemma_sum_equals_v1_1742523217_3436 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 100$, $1 \leq j \leq 100$, and $i + j = 101$. Compute the remainder when
$$
(x \bmod 317) + 7001 \cdot (x \bmod 313)
$$
is divided by $60730$. | 32,170 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(101)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(100)), right=IntegerRange(start=Const(1), end=Const(100))))),
"Q... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.003 | 2026-02-08T05:52:01.313302Z | {
"verified": true,
"answer": 32170,
"timestamp": "2026-02-08T05:52:01.315865Z"
} | b376c9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T04:53:20.977Z",
"answer": null
},
{
... | 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",
"status":... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
037949 | comb_count_derangements_v1_48377204_2249 | Let $n$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $pq = 154350$ and $\gcd(p, q) = 1$. Let $D_n$ denote the number of derangements of $n$ elements. Compute the remainder when $26265 \cdot D_n$ is divided by $55583$. | 7,498 | graphs = [
Graph(
let={
"_n": Const(26265),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=154350)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:41:37.650788Z | {
"verified": true,
"answer": 7498,
"timestamp": "2026-02-08T16:41:37.653105Z"
} | f730c1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 2401
},
"timestamp": "2026-02-17T09:19:46.394Z",
"answer": 7498
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab4315 | diophantine_fbi2_count_v1_1915831931_2962 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 57600$. For each pair $(x, y)$ in $P$, compute $x + y$. Let $k$ be the minimum value among all such sums. Let $T$ be the set of positive integers $d$ such that $3 \leq d \leq 123$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 124$. C... | 18 | graphs = [
Graph(
let={
"_n": Const(4),
"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(57600)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | C5 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"B3",
"C5"
] | 2 | 0.14 | 2026-02-08T17:16:23.434413Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T17:16:23.574348Z"
} | 8f9e29 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1721
},
"timestamp": "2026-02-17T22:38:31.639Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fb587c | modular_count_residue_v1_784195855_6332 | Let $m = \sum_{k=1}^{7} \phi(k) \left\lfloor \frac{7}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n$ such that $1 \leq n \leq 32400$ and $n \equiv 8 \pmod{m}$. Find the value of this count. | 1,157 | graphs = [
Graph(
let={
"upper": Const(32400),
"m": Summation(var="k", start=Const(1), end=Const(7), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(7), Var("k"))))),
"r": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | modular_count_residue_v1 | null | 5 | 0 | [
"K2"
] | 1 | 1.398 | 2026-02-08T08:35:17.212137Z | {
"verified": true,
"answer": 1157,
"timestamp": "2026-02-08T08:35:18.610216Z"
} | 9bad89 | 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": 1095
},
"timestamp": "2026-02-13T19:59:51.570Z",
"answer": 1157
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
a957f2 | nt_count_gcd_equals_v1_1520064083_9391 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 17909824$. Define $\alpha$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $d$ be the sum of all positive integers $x$ such that $x^2 - 277x + 9082 = 0$. Determine the value of $\beta$, where $\beta$ is the number ... | 959 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(17909824))))... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"VIETA_SUM",
"B3"
] | 8cbb22 | nt_count_gcd_equals_v1 | quadratic_mod | 7 | 0 | [
"B3",
"LIN_FORM",
"VIETA_SUM"
] | 3 | 0.657 | 2026-02-08T10:42:52.590420Z | {
"verified": true,
"answer": 959,
"timestamp": "2026-02-08T10:42:53.247260Z"
} | d5256b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 2432
},
"timestamp": "2026-02-14T08:12:47.100Z",
"answer": 959
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6e34de | sequence_count_fib_divisible_v1_865884756_3528 | Let $d$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 9$. Compute the number of positive integers $n$ such that $1 \leq n \leq 787$ and $d$ divides the $n$-th Fibonacci number. | 65 | graphs = [
Graph(
let={
"upper": Const(787),
"d": 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(9)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.142 | 2026-02-08T17:29:51.894223Z | {
"verified": true,
"answer": 65,
"timestamp": "2026-02-08T17:29:52.036103Z"
} | 9732dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 1750
},
"timestamp": "2026-02-18T02:42:30.331Z",
"answer": 65
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1ac037 | geo_count_lattice_rect_v1_865884756_2488 | Let $a = 111$ and $b = 239$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries. Compute $68644 - \text{result}$. | 41,764 | graphs = [
Graph(
let={
"a": Const(111),
"b": Const(239),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Sub(Const(68644), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.004 | 2026-02-08T16:47:30.143536Z | {
"verified": true,
"answer": 41764,
"timestamp": "2026-02-08T16:47:30.147157Z"
} | cda6f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 636
},
"timestamp": "2026-02-17T11:47:44.821Z",
"answer": 41764
},
{... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||||
e202b1 | nt_count_divisible_v1_1125832087_453 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 18$. Let $P$ be the maximum value of $xy$ over all $(x, y) \in S$. Let $T$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = P$. Let $d$ be the minimum value of $x + y$ over all $(x, y) \in T$. Compute t... | 2,005 | graphs = [
Graph(
let={
"_n": Const(18),
"upper": Const(36100),
"divisor": 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")), MaxOverS... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_divisible_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 1.151 | 2026-02-08T03:06:49.491112Z | {
"verified": true,
"answer": 2005,
"timestamp": "2026-02-08T03:06:50.641634Z"
} | a3f84e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 867
},
"timestamp": "2026-02-10T13:01:06.900Z",
"answer": 2005
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lem... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
747611 | antilemma_k3_v1_717093673_704 | Let $n = 82603$. Compute $$\sum_{d \mid n} \phi(d),$$ where the sum is taken over all positive divisors $d$ of $n$, and $\phi(d)$ denotes Euler's totient function. | 82,603 | graphs = [
Graph(
let={
"_n": Const(82603),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:36:39.708823Z | {
"verified": true,
"answer": 82603,
"timestamp": "2026-02-08T15:36:39.710099Z"
} | d8fb44 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 574
},
"timestamp": "2026-02-16T06:13:09.589Z",
"answer": 82608
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
fd6d22 | geo_count_lattice_triangle_v1_1125832087_109 | Consider the triangle with vertices at $(0, 0)$, $(144, 4)$, and $(34, 139)$. Let $A$ be twice the area of this triangle. Let $B$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along each side:
- $\gcd(|144|, |4|)$,
- $\gcd(|34 - 144|, |139 - 4|)$,
- $\gcd(|0 - 34|, ... | 9,936 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=139)), Mul(Const(value=34), Sub(left=Const(value=0), right=Const(value=4))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(value=4))), GCD(a=Abs(arg=Sub(left=Const(value=34), right=C... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.003 | 2026-02-08T02:52:22.656702Z | {
"verified": true,
"answer": 9936,
"timestamp": "2026-02-08T02:52:22.659483Z"
} | 7536e4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1027
},
"timestamp": "2026-02-10T11:43:15.264Z",
"answer": 9936
},
{
"i... | 1 | [] | {
"lo": -4.35,
"mid": -2.1,
"hi": 0.01
} | ||||
15a44f_l | comb_count_permutations_fixed_v1_717093673_3743 | Let $n = 9$ and let $k$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 1088$ and $\binom{1088}{j}$ is odd. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 0 | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T17:49:38.616387Z | {
"verified": false,
"answer": 5544,
"timestamp": "2026-02-08T17:49:38.619000Z"
} | 3f3c8b | 15a44f | legacy_text | CC BY 4.0 | [
{
"id": 5,
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"score": 3,
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},
"usage": {
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"completion_tokens": 1230
},
"timestamp": "2026-02-18T08:55:01.627Z",
"answer": 5544
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
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"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.38,
"mid": 1.74,
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} | |
34b26b | comb_sum_binomial_row_v1_168721529_158 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 324$. Let $s$ be the minimum value of $x + y$ as $(x, y)$ ranges over $P$. Now, let $Q$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = s$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over ... | 59,782 | graphs = [
Graph(
let={
"_n": Const(90937),
"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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var... | NT | null | SUM | sympy | B3 | [
"B3/B3"
] | 8ffef9 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T12:52:11.661214Z | {
"verified": true,
"answer": 59782,
"timestamp": "2026-02-08T12:52:11.664458Z"
} | a66489 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1854
},
"timestamp": "2026-02-09T02:04:30.847Z",
"answer": 59782
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.84
} | ||
368c0d | nt_count_gcd_equals_v1_784195855_67 | Let $d$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Determine the number of positive integers $n$ at most $7396$ such that $\gcd(n, 396) = d$. | 373 | graphs = [
Graph(
let={
"_n": Const(36),
"upper": Const(7396),
"k": Const(396),
"d": 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"... | NT | null | COUNT | sympy | LIN_FORM | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 2.932 | 2026-02-08T02:56:49.004656Z | {
"verified": true,
"answer": 373,
"timestamp": "2026-02-08T02:56:51.936505Z"
} | f6771f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1673
},
"timestamp": "2026-02-10T11:54:55.513Z",
"answer": 373
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -0.91,
"mid": 1.09,
"hi": 2.86
} | ||
b7b5a6 | sequence_lucas_compute_v1_458359167_3130 | Let $m = 2$, and let $N$ be the sum of all prime numbers $n$ such that $m \leq n \leq 23$. Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = N$. Compute the $n$-th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $... | 15,127 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(23)), IsPrime(Var("n"))))),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condit... | NT | null | COMPUTE | sympy | SUM_PRIMES | [
"SUM_PRIMES/B3"
] | dc18e5 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"B3",
"SUM_PRIMES"
] | 2 | 0.002 | 2026-02-08T06:59:19.123274Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T06:59:19.125000Z"
} | 28a636 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 981
},
"timestamp": "2026-02-13T07:02:32.778Z",
"answer": 15127
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
b4aea7 | comb_count_partitions_v1_124444284_841 | Let $ n $ be the number of integers $ t $ such that $ 18 \leq t \leq 106 $ and there exist positive integers $ a \leq 16 $ and $ b \leq 3 $ satisfying $ t = 4a + 14b $. Let $ Q $ be the number of integer partitions of $ n $. Compute $ Q $. | 31,185 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=16)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:32:55.041707Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T03:32:55.044122Z"
} | 4377f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 3340
},
"timestamp": "2026-02-09T22:53:48.973Z",
"answer": 53174
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
a5ffe9 | geo_count_lattice_triangle_v1_124444284_9919 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(256,300)$, and $(43,121)$, multiplied by 2. Let $B$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along each side of the triangle. Specifically,
$$
B = \gcd(256, 300) + \gcd(|43 - 256|, |y - 300|) + \gcd... | 9,036 | graphs = [
Graph(
let={
"_n": Const(121),
"area_2x": Abs(arg=Sum(Mul(Const(value=256), Const(value=121)), Mul(Const(value=43), Sub(left=Const(value=0), right=Const(value=300))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=256)), b=Abs(arg=Const(value=300))), GCD(a=Abs(arg... | ALG | NT | COUNT | sympy | B1 | [
"B1"
] | 5b950e | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B1"
] | 1 | 0.007 | 2026-02-08T12:43:38.882556Z | {
"verified": true,
"answer": 9036,
"timestamp": "2026-02-08T12:43:38.889185Z"
} | 5266d5 | 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": 918
},
"timestamp": "2026-02-15T04:32:02.418Z",
"answer": 9036
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6c6ab8 | algebra_quadratic_discriminant_v1_784195855_8931 | Let $a = 5$, $b = 2$, and $c = -2$. Define $D = b^2 - 4ac$. Let $r$ be the sum of $2$ times the indicator that $D > 0$ and the indicator that $D = 0$. Let $p$ be the largest prime number at most 12. Compute the Bell number of the absolute value of $r$ modulo $p$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(5),
"b": Const(2),
"c": Const(-2),
"D": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | algebra_quadratic_discriminant_v1 | bell_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.042 | 2026-02-08T16:25:33.158664Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:25:33.200228Z"
} | 5bd1ed | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 458
},
"timestamp": "2026-02-16T07:24:44.619Z",
"answer": 75
},
{
"id": 11,
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
9869e2 | nt_count_coprime_and_v1_1978505735_7618 | Let $k_1$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 44100$, $\gcd(p, q) = 1$, and $p < q$. Let $k_2 = 9$. Determine the value of the number of positive integers $n \leq 45672$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. | 15,224 | graphs = [
Graph(
let={
"upper": Const(45672),
"k1": 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=44100)), Eq(left=GCD(a=Var(name='p'), b=V... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_coprime_and_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 4.114 | 2026-02-08T20:21:49.376358Z | {
"verified": true,
"answer": 15224,
"timestamp": "2026-02-08T20:21:53.490627Z"
} | 2902d5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 4914
},
"timestamp": "2026-02-19T00:24:24.291Z",
"answer": 15224
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fb70af | comb_sum_binomial_row_v1_1470522791_1872 | Let $n$ be the number of integers $t$ with $15 \leq t \leq 60$ for which there exist integers $a$ and $b$, each between 1 and 4 inclusive, such that $t = 9a + 6b$. Let $d_{\max}$ be the largest positive divisor of 6 that is at most 2. Compute $d_{\max}^n$, and let $Q$ be the remainder when $95693$ times this value is d... | 37,442 | graphs = [
Graph(
let={
"_n": Const(95693),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Va... | NT | null | SUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR",
"LIN_FORM"
] | 35b5d8 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 0.002 | 2026-02-08T14:02:33.261043Z | {
"verified": true,
"answer": 37442,
"timestamp": "2026-02-08T14:02:33.263442Z"
} | 3cb1d7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1896
},
"timestamp": "2026-02-15T23:49:34.998Z",
"answer": 37442
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
be0db7 | antilemma_sum_equals_v1_458359167_2931 | Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 20$ and $1 \leq j \leq 20$ such that $i + j = 22$. Let $Q$ be the remainder when $x$ times the number of ordered pairs $(x_1, x_2)$ of positive odd integers satisfying $x_1 + x_2 = 17942$ is divided by 65547. Find the value of $Q$. | 39,355 | graphs = [
Graph(
let={
"_n": Const(22),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | a8cbfb | antilemma_sum_equals_v1 | affine_mod | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.009 | 2026-02-08T06:50:32.971688Z | {
"verified": true,
"answer": 39355,
"timestamp": "2026-02-08T06:50:32.980784Z"
} | 4f3fab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1304
},
"timestamp": "2026-02-24T07:10:32.361Z",
"answer": 39355
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
9c2db1 | comb_count_derangements_v1_1419126231_687 | Let $D_n$ denote the number of derangements of $n$ elements. Let $M$ be the number of non-negative integers $a$ with $0 \leq a \leq 9408$ such that $\left(a^{2} - 4451 \bmod 9409\right)^{2} - 4451 \bmod 9409 = a$ and $a^{2} - 4451 \bmod 9409 \neq a$. Let $n = \sum_{k=0}^{2} M^{k}$. Compute the remainder when $12423 \cd... | 45,210 | graphs = [
Graph(
let={
"_m": Const(50744),
"_n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(9408)), Eq(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-4451)), modulus=Const(9409)), Const(2)), Const(-4451)), ... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/SUM_GEOM"
] | 8a1734 | comb_count_derangements_v1 | null | 5 | 0 | [
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 2 | 0.002 | 2026-02-25T10:09:33.602456Z | {
"verified": true,
"answer": 45210,
"timestamp": "2026-02-25T10:09:33.604462Z"
} | e4bd9b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T09:40:49.165Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
},
{
"lemma": "V8",
... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
ab4a79 | comb_count_permutations_fixed_v1_238844314_664 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 81$. Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Compute $\binom{m}{6} \cdot !(m - 6)$, where $!k$ denotes the number of derangements of $k$ elements. | 168 | 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(81)))), expr=Sum(Var("x"), Var("y")))),
"n": CountOverSet(s... | COMB | null | COUNT | sympy | B3 | [
"B3/COMB1"
] | e26f7e | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.003 | 2026-02-08T13:29:32.656726Z | {
"verified": true,
"answer": 168,
"timestamp": "2026-02-08T13:29:32.659800Z"
} | 66b18b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 933
},
"timestamp": "2026-02-24T18:36:03.067Z",
"answer": 168
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
454c98 | comb_binomial_compute_v1_655260480_5577 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 16$. Let $k = 5$. Compute $\binom{n}{k}$. | 1,287 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(16)), IsPrime(Var("n1"))))),
"k": Const(5),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=R... | NT | null | COMPUTE | sympy | LIN_FORM | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.033 | 2026-02-08T18:34:07.481394Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T18:34:07.514516Z"
} | a79e0e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 437
},
"timestamp": "2026-02-16T12:25:39.718Z",
"answer": 1287
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
d4fa4c | comb_count_surjections_v1_1915831931_2046 | Let $ k $ be the number of ordered pairs $ (i, j) $ of integers such that $ 1 \leq i \leq 4 $, $ 1 \leq j \leq 4 $, and $ i + j = 6 $. Compute $ k! \cdot S(5, k) $, where $ S(n, k) $ denotes the Stirling number of the second kind. | 150 | graphs = [
Graph(
let={
"n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(4... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.027 | 2026-02-08T16:36:04.889361Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T16:36:04.916243Z"
} | 24e95a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 769
},
"timestamp": "2026-02-17T07:35:38.480Z",
"answer": 150
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
062149 | nt_count_intersection_v1_1915831931_855 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $N$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 32$ and there exist positive integers $a \leq 6$, $b \leq 4$ satisfying $t = 2a + 5b$. Let $b$ be t... | 455 | 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(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(5),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_intersection_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 2.123 | 2026-02-08T15:43:11.435915Z | {
"verified": true,
"answer": 455,
"timestamp": "2026-02-08T15:43:13.558920Z"
} | 2cd6ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 2025
},
"timestamp": "2026-02-16T11:33:34.275Z",
"answer": 455
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
09c56c | lin_form_endings_v1_1440796553_1453 | Let $a = 60$ and $b = 48$. Let $k = 5$ and let $L$ be the least common multiple of $a$ and $b$. Compute the value of $5L + a + b$. | 1,308 | graphs = [
Graph(
let={
"a_coeff": Const(60),
"b_coeff": Const(48),
"k_val": Const(5),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"x": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
},
goal=Ref("x... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T14:00:48.872418Z | {
"verified": true,
"answer": 1308,
"timestamp": "2026-02-08T14:00:48.872996Z"
} | c8dacd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 256
},
"timestamp": "2026-02-16T05:12:02.239Z",
"answer": 1308
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
0cb5a4 | nt_sum_over_divisible_v1_238844314_140 | Let $n = 225$. Define $d$ to be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 225$. Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq 25281$ and $k$ is divisible by $d$. Compute the sum of all elements in $S$. Let $Q$ be the remainder when $39696$ times... | 46,949 | graphs = [
Graph(
let={
"_n": Const(225),
"upper": Const(25281),
"divisor": 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... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"B3"
] | 1 | 1.425 | 2026-02-08T13:08:15.660146Z | {
"verified": true,
"answer": 46949,
"timestamp": "2026-02-08T13:08:17.084753Z"
} | 6b29b6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 1603
},
"timestamp": "2026-02-15T10:08:58.883Z",
"answer": 46949
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6867f3 | comb_sum_binomial_row_v1_1520064083_5784 | Let $u_1 = 0$, and define $n_2 = u_1 + 1$. Let $$c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.$$ Define $u = 1 + c$, and let $n_1 = u + 1$. Let $$t = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.$$ Define $n = 10 + t$. Compute $2^n$. | 1,024 | graphs = [
Graph(
let={
"u1": Const(0),
"n2": Sum(Ref("u1"), Const(1)),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Sum(Const(1), Ref("c")),
"n1": Sum(Ref("u"), Co... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T07:38:01.225704Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T07:38:01.227001Z"
} | eaec00 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 625
},
"timestamp": "2026-02-24T08:14:55.374Z",
"answer": 1024
},
{
"id... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
589da2 | algebra_quadratic_discriminant_v1_1915831931_1437 | Let $ S $ be 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 $ m $ be the number of elements in $ S $. Let $ a = \sum_{k=1}^{2} k $, $ b = -4 $, and $ c = 9 $. Define $ r = b^m - 4ac $. Compute the remainder when... | 27,032 | graphs = [
Graph(
let={
"_m": Const(82845),
"_n": Const(96959),
"a": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"b": Const(-4),
"c": Const(9),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"),... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | ac053f | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.006 | 2026-02-08T16:08:49.829483Z | {
"verified": true,
"answer": 27032,
"timestamp": "2026-02-08T16:08:49.834993Z"
} | 7f73e9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1256
},
"timestamp": "2026-02-16T21:46:56.086Z",
"answer": 27032
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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