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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
eae7c4 | comb_count_surjections_v1_601307018_6665 | Let $k = 6$. Let $m = \sum_{k5=0}^{0} (-1)^{k5} \binom{0}{k5}$ and $f = \sum_{k2=\sum_{k3=0}^{3} (-1)^{k3} \binom{3}{k3}}^{0} (-1)^{k2} \binom{0}{k2}$. Let $n = 6f$, $R = 6$, and $v = \sum_{k1=0}^{6} (-1)^{k1} \binom{6}{k1}$. Let $S = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Fi... | 68,872 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(4),
"n3": Sum(Ref("a"), Ref("b")),
"v": Summation(var="k1", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n3"), k=Var("k1")))),
"n2": Const(0),
"f": Sum... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/BINOMIAL_ALTERNATING"
] | 0746fc | comb_count_surjections_v1 | null | 6 | 3 | [
"BINOMIAL_ALTERNATING",
"SUM_ARITHMETIC"
] | 2 | 0.005 | 2026-03-10T07:18:14.161247Z | {
"verified": true,
"answer": 68872,
"timestamp": "2026-03-10T07:18:14.166325Z"
} | 4fe8fd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 1133
},
"timestamp": "2026-04-19T04:59:39.242Z",
"answer": 68872
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
8c3c1f_l | nt_count_divisible_v1_458359167_5795 | Let $S$ be the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 3$ and $1 \leq j \leq 3$ such that $i + j = 4$. Let $d$ be the number of elements in $S$. Let $N$ be the set of all positive integers $n$ such that $1 \leq n \leq 70225$ and $$
\equiv \sum_{k=0}^{\binom{5}{0}} (-1)^k \binom{1}{k} \pmod{d}.... | 23,409 | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 47e85f | nt_count_divisible_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 3 | 5.225 | 2026-02-08T12:41:47.870008Z | {
"verified": false,
"answer": 23408,
"timestamp": "2026-02-08T12:41:53.094685Z"
} | 2a9b69 | 8c3c1f | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 2443
},
"timestamp": "2026-02-24T16:12:24.509Z",
"answer": 23408
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | |
a69653 | nt_sum_gcd_range_mod_v1_784195855_7493 | Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 162$. Let $k$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 576$. Define $M = 11351$ and let $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Let $\text{result}$ be the remainder w... | 144 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(162)))), expr=Mul(Var("x"), Var("y")))),
"k": CountOverSet(s... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1",
"B1"
] | 12acf0 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B1",
"COMB1"
] | 2 | 0.57 | 2026-02-08T09:20:42.286175Z | {
"verified": true,
"answer": 144,
"timestamp": "2026-02-08T09:20:42.856660Z"
} | f03eba | 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": 2908
},
"timestamp": "2026-02-14T03:25:29.557Z",
"answer": 144
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9cf0ca | alg_poly3_sum_v1_601307018_9205 | Let $T = \max\{ d \geq 1 : d \mid 5183 \text{ and } d^2 \leq 5183 \}$. Let $k = \left|\{ (x_1, x_2) : x_1 > 0,\, x_2 > 0,\, x_1 \text{ is odd},\, x_2 \text{ is odd},\, x_1 + x_2 = 4 \}\right|$. Compute the remainder when $$\sum_{a=1}^{17} \sum_{b=1}^{17} \sum_{c=1}^{17} \left( T \cdot c^3 - 222a b^2 + 87a^2 c - 53a^3 -... | 37,674 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(17)), Geq(Var("b"), Const(1)), Leq(Var("b"... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST",
"COMB1"
] | 2837fe | alg_poly3_sum_v1 | null | 4 | 0 | [
"B3_CLOSEST",
"COMB1"
] | 2 | 0.145 | 2026-03-10T09:36:00.029468Z | {
"verified": true,
"answer": 37674,
"timestamp": "2026-03-10T09:36:00.174404Z"
} | a11835 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 327,
"completion_tokens": 4493
},
"timestamp": "2026-04-19T10:50:19.062Z",
"answer": 37674
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
b1e474 | diophantine_product_count_v1_1440796553_1192 | Let $m = 126$ and define $n$ to be the sum of all positive integers at most $504$ that are divisible by $m$. Let $k$ be the largest positive divisor of $1611540$ that does not exceed $n$. Determine the value of the number of positive integers $x$ such that $1 \leq x \leq 309$, $x$ divides $k$, and $\frac{k}{x} \leq 309... | 28 | graphs = [
Graph(
let={
"_m": Const(126),
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(504)), Eq(Mod(value=Var("n"), modulus=Ref("_m")), Const(0))))),
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=An... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/MAX_DIVISOR"
] | 0e7b4f | diophantine_product_count_v1 | null | 5 | 0 | [
"MAX_DIVISOR",
"SUM_DIVISIBLE"
] | 2 | 0.015 | 2026-02-08T12:13:46.281789Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T12:13:46.296398Z"
} | d6ad18 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 4269
},
"timestamp": "2026-02-15T18:26:23.279Z",
"answer": 28
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
62c0de | comb_count_derangements_v1_601307018_1094 | Let $D_n$ denote the number of derangements of $n$ elements. For each non-negative integer $a$ with $0 \le a \le 72$, define the following modulo $73$:
- $M = a^{36} \bmod 73$,
- $R = (a^2 - 31) \bmod 73$,
- $S = R^{36} \bmod 73$,
- $T = (R^2 - 31) \bmod 73$,
- $K = T^{36} \bmod 73$,
- $L = (T^2 - 31) \bmod 73$,
- $P... | 60,161 | graphs = [
Graph(
let={
"_n": Const(73),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(72)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a")), Congruent(... | COMB | NT | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE"
] | 7c2be8 | comb_count_derangements_v1 | null | 8 | 0 | [
"POLY_ORBIT_LEGENDRE"
] | 1 | 0.007 | 2026-03-10T01:40:35.648346Z | {
"verified": true,
"answer": 60161,
"timestamp": "2026-03-10T01:40:35.654879Z"
} | a24ace | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 377,
"completion_tokens": 15240
},
"timestamp": "2026-04-18T15:16:45.105Z",
"answer": 60161
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": 3.52,
"mid": 5.88,
"hi": 8.98
} | ||
e896dd | modular_mod_compute_v1_1431428450_1211 | Let $a = -17424$. Define $m$ to be the number of positive integers $n$ with $1 \leq n \leq 4800$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $r$ be the remainder when $a$ is divided by $m$, and let $Q$ be the remainder when $44121 \cdot r$ is divided by $79864$. Find the value of $Q$. | 18,488 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": Const(-17424),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4800)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modul... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | modular_mod_compute_v1 | null | 4 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T13:58:09.332544Z | {
"verified": true,
"answer": 18488,
"timestamp": "2026-02-08T13:58:09.334049Z"
} | 1e459d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1595
},
"timestamp": "2026-02-15T22:16:34.258Z",
"answer": 18488
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9bfd1e | nt_max_prime_below_v1_1520064083_3816 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $N \leq n \leq 42025$. Let $R$ be the largest element of $T$. Compute the rem... | 43,363 | graphs = [
Graph(
let={
"upper": Const(42025),
"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 | 1.782 | 2026-02-08T05:55:22.789156Z | {
"verified": true,
"answer": 43363,
"timestamp": "2026-02-08T05:55:24.571219Z"
} | 23bc6b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 3246
},
"timestamp": "2026-02-12T16:23:56.190Z",
"answer": 43363
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
54ad23 | lin_form_endings_v1_2051736721_300 | Let $a = 40$ and $b = 32$. Compute the least common multiple of $a$ and $b$, and denote it by $L$. Let $k = 11542$ and $M = 99486$. Compute the remainder when $k \cdot L$ is divided by $M$. | 55,972 | graphs = [
Graph(
let={
"a_coeff": Const(40),
"b_coeff": Const(32),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(11542),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(99486),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T15:20:31.864268Z | {
"verified": true,
"answer": 55972,
"timestamp": "2026-02-08T15:20:31.865615Z"
} | d83952 | 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": 564
},
"timestamp": "2026-02-16T04:21:10.287Z",
"answer": 55972
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5f0bfa | modular_count_residue_v1_151522320_989 | Let $A$ be the set of all integers $n$ such that $1\le n\le 2293$ and the sum of the decimal digits of $n$ is congruent to $1$ modulo $2$. Let $D$ be the number of elements in $A$.
Let $B$ be the set of all integers $d$ such that $d\ge 2$ and $d$ divides $D$, and let $M$ be the smallest integer in $B$.
Let $r$ be the... | 3,666 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(80656),
"m": Const(22),
"r": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2))... | NT | null | COUNT | sympy | L3B | [
"L3B/MIN_PRIME_FACTOR/C4"
] | 0e1bde | modular_count_residue_v1 | null | 8 | 0 | [
"C4",
"L3B",
"MIN_PRIME_FACTOR"
] | 3 | 4.979 | 2026-02-08T03:42:07.390942Z | {
"verified": true,
"answer": 3666,
"timestamp": "2026-02-08T03:42:12.370240Z"
} | a132f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 7951
},
"timestamp": "2026-02-10T15:31:16.905Z",
"answer": 3666
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": -1.75,
"mid": 1.03,
"hi": 3.64
} | ||
2e0fa1 | antilemma_sum_equals_v1_784195855_5155 | Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 99$ and $1 \leq i \leq 99$, $1 \leq j \leq 99$. | 98 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(99)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(99)), right=IntegerRange(start=Const(1), end=Const(99))))),
},
... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.082 | 2026-02-08T07:42:28.654058Z | {
"verified": true,
"answer": 98,
"timestamp": "2026-02-08T07:42:28.736057Z"
} | b7e8dc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 263
},
"timestamp": "2026-02-24T08:20:05.354Z",
"answer": 98
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
2f1f32 | comb_count_surjections_v1_124444284_8173 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 12$. Let $k = 5$. Compute the value of $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 1,800 | graphs = [
Graph(
let={
"_n": Const(12),
"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")), Re... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T09:35:08.380255Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T09:35:08.383603Z"
} | 2948cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1032
},
"timestamp": "2026-02-24T11:29:07.042Z",
"answer": 1800
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
6a2edc | nt_count_divisible_and_v1_717093673_4097 | Let $d_1 = 10$ and $d_2$ be the sum of all even positive integers from $1$ to $6$, inclusive. Find the number of positive integers $n_1$ such that $1 \leq n_1 \leq 201000$, $n_1$ is divisible by $d_1$, and $n_1$ is divisible by $d_2$. | 3,350 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(201000),
"d1": Const(10),
"d2": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(2)), Const(0))))),
... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 7.719 | 2026-02-08T18:02:16.193031Z | {
"verified": true,
"answer": 3350,
"timestamp": "2026-02-08T18:02:23.912407Z"
} | 3a14e9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 213
},
"timestamp": "2026-02-16T12:03:39.107Z",
"answer": 1675
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
50c224 | alg_poly4_sum_v1_1218484723_3049 | Find the remainder when $$\sum_{\substack{a=1 \\ b=1}}^{85} \left( \min\{ x + y : x > 0, y > 0, xy = 38025 \} \cdot a^2 b^2 + 257a^4 + 17b^4 + 516a^3b + 132ab^3 \right)$$ is divided by $69759$. | 66,396 | graphs = [
Graph(
let={
"_n": Const(85),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(85)))), expr=Sum(Mul(MinOver... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_sum_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.028 | 2026-02-25T04:48:58.755852Z | {
"verified": true,
"answer": 66396,
"timestamp": "2026-02-25T04:48:58.784238Z"
} | d7976f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 12415
},
"timestamp": "2026-03-29T08:05:17.055Z",
"answer": 54558
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
124f30 | nt_lcm_compute_v1_1742523217_76 | Let $S$ be the set of all positive integers $t$ such that $21 \le t \le 8889$ and there exist positive integers $a \le 674$ and $b \le 89$ for which $t = 12a + 9b$. Let $a$ be the number of elements in $S$. Let $b = 1218$. Compute the least common multiple of $a$ and $b$, and then find the remainder when $69303$ times ... | 65,572 | 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=674)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_lcm_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T02:52:14.215885Z | {
"verified": true,
"answer": 65572,
"timestamp": "2026-02-08T02:52:14.217457Z"
} | 84ffcb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T17:18:07.233Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": 3.7,
"mid": 5.49,
"hi": 7.55
} | ||
7008db | comb_count_permutations_fixed_v1_124444284_8132 | Let $n$ be the number of positive integers less than or equal to $13$ that are relatively prime to $14$. Compute the value of $\binom{n}{2} \cdot !(n-2)$, where $!k$ denotes the number of derangements of $k$ elements. | 135 | graphs = [
Graph(
let={
"_n": Const(13),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k"))... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"C4"
] | 08d162 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"C4",
"COPRIME_PAIRS"
] | 2 | 0.009 | 2026-02-08T09:34:34.078065Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T09:34:34.087177Z"
} | 86f3d7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 533
},
"timestamp": "2026-02-15T20:44:29.738Z",
"answer": 135
},
{
"id": 11,
... | 2 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
78cb0a | geo_count_lattice_rect_v1_124444284_4305 | Let $a = 289$ and $b = 132$. Define a lattice point as a point in the plane with integer coordinates. Compute the number of lattice points in the rectangle defined by $0 \leq x \leq a$ and $0 \leq y \leq b$, including the boundary. Find the value of this quantity. | 38,570 | graphs = [
Graph(
let={
"a": Const(289),
"b": Const(132),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T05:54:32.457997Z | {
"verified": true,
"answer": 38570,
"timestamp": "2026-02-08T05:54:32.458645Z"
} | 9b99bd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 428
},
"timestamp": "2026-02-24T04:53:30.231Z",
"answer": 38570
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
d1ce50 | antilemma_sum_equals_v1_1918700295_1695 | Let $m = 172$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the number of ordered pairs $(i, j)$ with $1 \leq i \leq 84$ and $1 \leq j \leq 85$ such that $i + j = n$. | 84 | graphs = [
Graph(
let={
"_m": Const(172),
"_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 | GEOM | COMPUTE | sympy | LIN_FORM | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.031 | 2026-02-08T05:58:11.854079Z | {
"verified": true,
"answer": 84,
"timestamp": "2026-02-08T05:58:11.885225Z"
} | ddf0ff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1246
},
"timestamp": "2026-02-24T04:59:14.609Z",
"answer": 84
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
475fd0 | modular_mod_compute_v1_1742523217_2530 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 53$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 16$, and $t = 3a + 2b$. Let $a = |T|$, the number of elements in $T$. Let $r$ be the remainder when $a$ is divided by $39204$. Define $m = r + 2$. Compute the smallest... | 56 | 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=7)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:50:05.957271Z | {
"verified": true,
"answer": 56,
"timestamp": "2026-02-08T04:50:05.958908Z"
} | 467863 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 3319
},
"timestamp": "2026-02-11T22:05:57.368Z",
"answer": 112
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
7d5ecb | nt_count_divisors_in_range_v1_809748730_678 | Let $n = 83160$. Let $a = 80$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 853776$. Define $b$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let this number be $k$. Find the value of... | 267 | graphs = [
Graph(
let={
"n": Const(83160),
"a": Const(80),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(853776)))), e... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.02 | 2026-02-08T11:41:10.830865Z | {
"verified": true,
"answer": 267,
"timestamp": "2026-02-08T11:41:10.850471Z"
} | 139216 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 3443
},
"timestamp": "2026-02-14T17:31:48.713Z",
"answer": 267
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8ebfbb | sequence_count_fib_divisible_v1_1978505735_3555 | Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 12138256$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all pairs $(x, y) \in A$. Let $U$ be the set of positive integers $n$ such that $1 \leq n \leq s_{\text{min}}$, $8$ divides $n$, and $\gcd(n, 15) = 1$. Let $u = |U|$... | 51,578 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mu... | NT | null | COUNT | sympy | B3 | [
"B3/C5"
] | cde3b3 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"C5"
] | 2 | 0.023 | 2026-02-08T17:43:03.777939Z | {
"verified": true,
"answer": 51578,
"timestamp": "2026-02-08T17:43:03.800527Z"
} | c857bd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2487
},
"timestamp": "2026-02-18T07:23:52.552Z",
"answer": 51578
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c8bd0a | comb_count_derangements_v1_124444284_3404 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 514500$. Compute the number of derangements of $n$ elements, denoted $!n$. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=514500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T05:23:26.812897Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T05:23:26.815425Z"
} | 519023 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 2445
},
"timestamp": "2026-02-12T07:40:49.192Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
794ec3 | comb_count_surjections_v1_1918700295_1849 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k = 5$. Define $S = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the remainder when $44121 \cdot S$ is divided by 68872. | 32,336 | graphs = [
Graph(
let={
"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")), Const(14))))),
"k":... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T06:06:17.899311Z | {
"verified": true,
"answer": 32336,
"timestamp": "2026-02-08T06:06:17.902061Z"
} | 02bc8a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 2228
},
"timestamp": "2026-02-24T05:31:42.124Z",
"answer": 32336
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
98584b | antilemma_k3_v1_1742523217_5601 | Let $n = 26120$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Compute $x$. | 26,120 | graphs = [
Graph(
let={
"_n": Const(26120),
"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 | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T11:05:33.226617Z | {
"verified": true,
"answer": 26120,
"timestamp": "2026-02-08T11:05:33.227036Z"
} | 42a624 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 770
},
"timestamp": "2026-02-14T10:22:16.142Z",
"answer": 26120
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
31caea | nt_gcd_compute_v1_1918700295_369 | Let $a = 282780$ and $b = 636255$. Let $d = \gcd(a, b)$. Let $S$ be the set of all positive integers $d$ such that $1 \le d \le 5003$ and $d$ divides $25070033$. Compute the remainder when $$
(d \bmod 293) + \left( \max(S) \cdot (d \bmod 337) \right)
$$ is divided by $91244$. | 33,452 | graphs = [
Graph(
let={
"_n": Const(5003),
"a": Const(282780),
"b": Const(636255),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sum(Mod(value=Ref("result"), modulus=Const(293)), Mul(MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(G... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 9dada8 | nt_gcd_compute_v1 | two_moduli | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.003 | 2026-02-08T03:11:45.840851Z | {
"verified": true,
"answer": 33452,
"timestamp": "2026-02-08T03:11:45.843517Z"
} | f7cf13 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 6406
},
"timestamp": "2026-02-10T13:24:22.178Z",
"answer": 24636
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
e287fb | nt_sum_divisors_compute_v1_655260480_1406 | Let $n = 21904$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Let $d$ be the number of unordered pairs of coprime positive integers $(p, q)$ such that $p < q$ and $pq = 2037420$. Compute
$$
\sigma(n) + 2^{\sigma(n) \bmod d} \bmod 88160.
$$
Find the value of this expression. | 43,619 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(21904),
"result": SumDivisors(n=Ref("n")),
"Q": Sum(Ref("result"), Mod(value=Pow(Ref("_n"), Mod(value=Ref("result"), modulus=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 64a51e | nt_sum_divisors_compute_v1 | mod_exp | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:07:19.965858Z | {
"verified": true,
"answer": 43619,
"timestamp": "2026-02-08T16:07:19.967587Z"
} | 4763fd | 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": 2013
},
"timestamp": "2026-02-16T21:32:55.870Z",
"answer": 43619
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c9eb9a | nt_sum_divisors_mod_v1_1520064083_10132 | Let $t$ be a positive integer satisfying $9 \leq t \leq 260$. Suppose there exist positive integers $a$ and $b$ such that $1 \leq a \leq 30$, $1 \leq b \leq 28$, and $t = 4a + 5b$. Let $n$ be the number of such integers $t$.
Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Let $M = 10453$, and let $\sig... | 51,258 | graphs = [
Graph(
let={
"_n": Const(86837),
"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=30)), Geq(left=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.006 | 2026-02-08T11:13:31.051649Z | {
"verified": true,
"answer": 51258,
"timestamp": "2026-02-08T11:13:31.058014Z"
} | ec6f14 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 5851
},
"timestamp": "2026-02-14T11:04:59.550Z",
"answer": 51258
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
61b210 | nt_sum_divisors_compute_v1_1874849503_74 | Let $n = 21019$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Compute $\sigma(n)$. | 21,020 | graphs = [
Graph(
let={
"n": Const(21019),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"OMEGA_ZERO",
"WILSON"
] | 9579a9 | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"OMEGA_ZERO",
"WILSON"
] | 3 | 0.003 | 2026-02-08T12:47:36.432522Z | {
"verified": true,
"answer": 21020,
"timestamp": "2026-02-08T12:47:36.435809Z"
} | 672231 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2050
},
"timestamp": "2026-02-09T13:40:53.711Z",
"answer": 21020
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "V3",
"status": ... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
68aed1 | modular_min_linear_v1_717093673_254 | Let $a = 36733$, $b = 24721$, and $m = 64273$. Let $x_0$ be the smallest positive integer $x \leq m$ such that $ax \equiv b \pmod{m}$. Let $c$ be the largest prime number at most $1012$. Compute the remainder when $x_0 \bmod{251} + c \cdot (x_0 \bmod{397})$ is divided by $80245$. | 27,305 | graphs = [
Graph(
let={
"a": Const(36733),
"b": Const(24721),
"m": Const(64273),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Ref("b... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | modular_min_linear_v1 | two_moduli | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.891 | 2026-02-08T15:15:54.799542Z | {
"verified": true,
"answer": 27305,
"timestamp": "2026-02-08T15:15:57.690719Z"
} | 56cd35 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 4039
},
"timestamp": "2026-02-16T03:38:49.813Z",
"answer": 27305
},
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8ed648 | antilemma_k3_v1_168721529_1852 | Let $n = 19648$. Compute the sum $\sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the value of this sum. | 19,648 | graphs = [
Graph(
let={
"_n": Const(19648),
"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 | 2026-02-08T13:57:39.356906Z | {
"verified": true,
"answer": 19648,
"timestamp": "2026-02-08T13:57:39.357327Z"
} | 8fea88 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 531
},
"timestamp": "2026-02-09T22:30:46.202Z",
"answer": 19648
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
ff09d2 | nt_min_coprime_above_v1_809748730_1175 | Let $u$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 1692601$. Let $m = 476$ and $s = 2116$. Define $T$ as the set of all integers $n$ such that $s < n \le u$ and $\gcd(n, m) = 1$. Let $r$ be the smallest element of $T$. Compute the remainder when $44121 \cdot r$ ... | 24,586 | graphs = [
Graph(
let={
"_n": Const(44121),
"start": Const(2116),
"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(16... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.116 | 2026-02-08T12:13:26.049239Z | {
"verified": true,
"answer": 24586,
"timestamp": "2026-02-08T12:13:26.165056Z"
} | 3c48fd | 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": 1692
},
"timestamp": "2026-02-14T23:32:43.478Z",
"answer": 24586
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d7e071 | comb_sum_binomial_mod_v1_971394319_35 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4489$. Define $s$ to be the minimum value of $x + y$ over all such pairs in $S$. Compute the remainder when
$$
\sum_{k=35}^{116} \binom{s}{k}
$$
is divided by $11177$. Then multiply this remainder by $44121$ and compute the result mod... | 23,212 | graphs = [
Graph(
let={
"_n": Const(57809),
"sum": Summation(var="k", start=Const(35), end=Const(116), expr=Binom(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(... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_sum_binomial_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.046 | 2026-02-08T12:48:19.159870Z | {
"verified": true,
"answer": 23212,
"timestamp": "2026-02-08T12:48:19.205859Z"
} | 087328 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T16:28:32.910Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
fedddb | geo_visible_lattice_v1_1978505735_228 | A lattice point $(x, y)$ is said to be visible from the origin if $\gcd(x, y) = 1$. Let $Q$ be the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq 100$. Find the value of $Q$. | 6,087 | graphs = [
Graph(
let={
"n": Const(100),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.398 | 2026-02-08T15:14:08.386171Z | {
"verified": true,
"answer": 6087,
"timestamp": "2026-02-08T15:14:08.784239Z"
} | cc4ed2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 2508
},
"timestamp": "2026-02-24T20:12:54.262Z",
"answer": 6087
},
{
"i... | 1 | [] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||||
946711 | nt_count_divisible_v1_1080341949_89 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \le i \le 6$, $1 \le j \le 7$, and $i + j = 8$. Let $d$ be the number of elements in $S$. Compute the number of positive integers $n$ such that $1 \le n \le 32768$ and $n$ is divisible by $d$. | 5,461 | graphs = [
Graph(
let={
"upper": Const(32768),
"divisor": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | nt_count_divisible_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 1.089 | 2026-02-08T13:10:51.571587Z | {
"verified": true,
"answer": 5461,
"timestamp": "2026-02-08T13:10:52.660570Z"
} | 929ff3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 622
},
"timestamp": "2026-02-16T04:27:30.265Z",
"answer": 5461
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
3b95fb | comb_factorial_compute_v1_1520064083_4600 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 8820$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=8820)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T06:20:36.630060Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T06:20:36.631792Z"
} | f6e6a1 | 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": 2019
},
"timestamp": "2026-02-12T22:53:00.446Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
077cd2 | nt_count_gcd_equals_v1_349078426_1672 | Let $S$ be the set of integers $t$ such that $20 \leq t \leq 354$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 74$, and $t = 14a + 4b + 2$. Let $s = |S|$. Let $e$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = s$. Let $k = 415$ and $d... | 39,727 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("t"), co... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.532 | 2026-02-08T13:50:50.772960Z | {
"verified": true,
"answer": 39727,
"timestamp": "2026-02-08T13:50:51.305169Z"
} | 2a0c77 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 3481
},
"timestamp": "2026-02-15T20:52:16.702Z",
"answer": 39727
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
10661b | comb_bell_compute_v1_2051736721_504 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 40961$ and $\binom{40961}{j}$ is odd. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the remainder when $41022 \cdot B_n$ is divided by $77411$. | 68,757 | graphs = [
Graph(
let={
"_n": Const(77411),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(40961)), Eq(Mod(value=Binom(n=Const(40961), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T15:28:41.038844Z | {
"verified": true,
"answer": 68757,
"timestamp": "2026-02-08T15:28:41.040500Z"
} | b6d303 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 2277
},
"timestamp": "2026-02-24T20:57:14.456Z",
"answer": 68757
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
977628 | geo_count_lattice_rect_v1_1978505735_3849 | Let $a = 66$ and $b = 81$. Define $\mathcal{R}$ to be the rectangle with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. A lattice point is a point with integer coordinates. Compute the number of lattice points contained in $\mathcal{R}$, including its boundary. | 5,494 | graphs = [
Graph(
let={
"a": Const(66),
"b": Const(81),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T17:54:17.281489Z | {
"verified": true,
"answer": 5494,
"timestamp": "2026-02-08T17:54:17.282361Z"
} | e38533 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 509
},
"timestamp": "2026-02-24T23:08:03.590Z",
"answer": 5494
},
{
... | 1 | [] | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||||
4258d6 | antilemma_k3_v1_784195855_10233 | Let $x$ be the sum of $\varphi(d)$ over all positive divisors $d$ of $53312$. Compute the remainder when $4 - x$ is divided by $99056$. | 45,748 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=53312), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(4),
"Q": Mod(value=Sub(Ref("_c"), Ref("x")), modulus=Const(99056)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T17:31:06.138466Z | {
"verified": true,
"answer": 45748,
"timestamp": "2026-02-08T17:31:06.138885Z"
} | 866f1e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 440
},
"timestamp": "2026-02-18T03:19:02.147Z",
"answer": 45748
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e8a902 | nt_min_crt_v1_1520064083_3511 | Let $n$ be a positive integer such that $1 \leq n \leq 88$ and $n^3 \leq 681472$. Let $S$ be the set of all positive integers $j$ satisfying these conditions. Define $\text{upper}$ to be the number of elements in $S$. Compute the smallest positive integer $n$ such that $1 \leq n \leq \text{upper}$, $n \equiv 1 \pmod{8}... | 9 | graphs = [
Graph(
let={
"_n": Const(88),
"m": Const(8),
"k": Const(11),
"a": Const(1),
"b": Const(9),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j")... | NT | null | EXTREMUM | sympy | BINOMIAL_ALTERNATING | [
"C3"
] | 8a214c | nt_min_crt_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"C3"
] | 2 | 0.034 | 2026-02-08T05:43:32.217264Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T05:43:32.251737Z"
} | 767e94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1057
},
"timestamp": "2026-02-12T13:42:23.426Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
680332 | nt_count_phi_equals_v1_717093673_3934 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 99225$. Let $k$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Determine the number of positive integers $n$ such that $1 \le n \le 2809$ and $\phi(n) = k$, where $\phi$ denotes Euler's totient function. | 2 | graphs = [
Graph(
let={
"upper": Const(2809),
"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(99225)))), expr=Sum(Var("x"), Var("y")... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B3"
] | 1 | 2.715 | 2026-02-08T17:58:17.814744Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T17:58:20.529731Z"
} | fcf748 | 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": 5347
},
"timestamp": "2026-02-18T10:52:40.995Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ce77cd | sequence_fibonacci_compute_v1_865884756_5784 | Let $n$ be the largest prime number such that $2 \leq n \leq 25$. Define $F_n$ to be the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $a = |F_n| + 1$. Compute the value of $$F_n + \phi(a) + \tau(a),$$ where $\phi(a)$ is the number of positive integers less than ... | 40,289 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(25)), IsPrime(Var("n1"))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Ab... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T18:47:26.573436Z | {
"verified": true,
"answer": 40289,
"timestamp": "2026-02-08T18:47:26.575167Z"
} | 872186 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1175
},
"timestamp": "2026-02-18T19:26:31.744Z",
"answer": 40289
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
63c2b2 | algebra_vieta_sum_v1_238844314_916 | Let $P(x) = x^4 + 25x^3 + 227x^2 + c x + 1260$, where $c$ is the smallest integer greater than or equal to 2 that divides $537153695253474601$. Let $r_1, r_2, r_3, r_4$ be the roots of $P(x) = 0$. Compute the product $r_1 r_2 r_3 r_4$. | 1,260 | graphs = [
Graph(
let={
"_n": Const(4),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Ref(name='_n')), Mul(Const(value=25), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=227), Pow(base=Var(name='x'), exp... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.011 | 2026-02-08T13:44:02.481021Z | {
"verified": true,
"answer": 1260,
"timestamp": "2026-02-08T13:44:02.491770Z"
} | 3ddf18 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 659
},
"timestamp": "2026-02-16T04:57:13.852Z",
"answer": 1260
},
{
"id": 11,
... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
c9207d | comb_factorial_compute_v1_1978505735_8439 | Let $n$ be the largest integer $k$ such that $7^k \le 5385026$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(7),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(5385026)))),
"result": Factorial(Ref("n")),
},
goal=Ref("result"),
)
] | ALG | COMB | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_VAL"
] | 1 | 0.002 | 2026-02-08T20:49:48.980639Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T20:49:48.982700Z"
} | f5a3ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 747
},
"timestamp": "2026-02-19T01:14:56.084Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
066ae6 | antilemma_v8_lucas_1742523217_666 | Let $m = 1023$ and $n = 2$. Define $a = 4$ and $b = 15$, and let $n_1 = ab + 1$. Let $f$ be the remainder when the number of positive divisors of $n_1$ is divided by $n$. Let $u = \mu(2)^{2 + f}$, where $\mu$ denotes the M\"obius function. Let $x$ be the number of nonnegative integers $j$ such that $j \leq T$, where $T... | 1 | graphs = [
Graph(
let={
"_m": Const(1023),
"_n": Const(2),
"a": Const(4),
"b": Const(15),
"n1": Sum(Mul(Ref("a"), Ref("b")), Const(1)),
"f": Mod(value=NumDivisors(n=Ref("n1")), modulus=Ref("_n")),
"n": Const(2),
... | NT | COMB | COMPUTE | sympy | K14 | [
"COPRIME_PAIRS/V8",
"MOBIUS_SQUAREFREE",
"LIN_FORM/V8",
"DIVISOR_PARITY",
"V8"
] | f882b4 | antilemma_v8_lucas | null | 7 | 2 | [
"COPRIME_PAIRS",
"DIVISOR_PARITY",
"K14",
"LIN_FORM",
"MOBIUS_SQUAREFREE",
"V8"
] | 6 | 0.051 | 2026-02-08T03:09:55.208294Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T03:09:55.259243Z"
} | 2e38e0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 396,
"completion_tokens": 3602
},
"timestamp": "2026-02-09T21:02:12.583Z",
"answer": 1
},
{
"id":... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"sta... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
c64b19 | alg_poly_orbit_count_v1_1218484723_4689 | Define a function $f(x) = (3x^5 + 5x^4 + x^3 + 5x^2 - 3x - 4) \bmod 37$. Starting from a non-negative integer $a$, let $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, and $T = f(S)$. Find the number of $a$ with $0 \le a \le 15502$ such that $T = a$, but $N, M, R, S \ne a$. | 2,095 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(5))), Mul(Const(5), Pow(Var("a"), Const(4))), Pow(Var("a"), Const(3)), Mul(Const(5), Pow(Var("a"), Const(2))), Mul(Const(-3), Var("a")), Const(-4)), modulus=Const(37)),
"p2": Mod(value=Sum(Mul(Const(3), Pow... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 4 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.322 | 2026-02-25T06:21:54.264162Z | {
"verified": true,
"answer": 2095,
"timestamp": "2026-02-25T06:21:54.586488Z"
} | 866e1b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 11934
},
"timestamp": "2026-03-29T17:02:39.036Z",
"answer": 2095
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
bc4c41 | sequence_count_fib_divisible_v1_865884756_2303 | Compute the number of positive integers $n \leq 138$ such that the $n$-th Fibonacci number is divisible by 6. | 11 | graphs = [
Graph(
let={
"upper": Const(138),
"d": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
go... | NT | null | COUNT | sympy | LTE_DIFF | [
"V5"
] | 79df37 | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"LTE_DIFF",
"V5"
] | 2 | 0.121 | 2026-02-08T16:41:09.661556Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T16:41:09.782506Z"
} | 751e65 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 1388
},
"timestamp": "2026-02-17T09:50:59.185Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0ab5f9 | geo_visible_lattice_v1_1353956133_32 | Let $n = 190$. Compute the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$, where a point $(x, y)$ is visible if $\gcd(x, y) = 1$. | 21,951 | graphs = [
Graph(
let={
"n": Const(190),
"result": VisibleLatticePoints(n=Ref(name='n')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 1.727 | 2026-02-08T11:16:33.318109Z | {
"verified": true,
"answer": 21951,
"timestamp": "2026-02-08T11:16:35.044795Z"
} | 3e3cda | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T13:20:47.012Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
52c7b0 | nt_count_intersection_v1_1520064083_828 | Let $a = 11$. Define
$$
b = \frac{4}{8} \sum_{k=1}^{3} \sum_{\ell=1}^{2} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor.
$$
Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 50000$, $11$ divides $n$, and $\gcd(n, b) = 1$. Compute the number of elements in $S$. | 1,515 | graphs = [
Graph(
let={
"_n": Const(4),
"N": Const(50000),
"a": Const(11),
"b": Div(Mul(Ref("_n"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/K2"
] | 8580e7 | nt_count_intersection_v1 | null | 5 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 1.789 | 2026-02-08T03:37:29.438627Z | {
"verified": true,
"answer": 1515,
"timestamp": "2026-02-08T03:37:31.228000Z"
} | f076fa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1586
},
"timestamp": "2026-02-10T15:07:24.226Z",
"answer": 1515
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
80d4e5 | geo_count_lattice_triangle_v1_717093673_882 | Let the vertices of a triangle be $(0,0)$, $(121,144)$, and $(29,111)$. Let $A$ be twice the area of this triangle, and let $B$ be the number of lattice points on the boundary of the triangle, including the vertices. Compute $\frac{A + 2 - B}{2}$. | 4,627 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=121), Const(value=111)), Mul(Const(value=29), Sub(left=Const(value=0), right=Const(value=144))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=121)), b=Abs(arg=Const(value=144))), GCD(a=Abs(arg=Sub(left=Const(value=29), rig... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.003 | 2026-02-08T15:44:41.307349Z | {
"verified": true,
"answer": 4627,
"timestamp": "2026-02-08T15:44:41.310259Z"
} | 824db7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1025
},
"timestamp": "2026-02-16T12:09:34.284Z",
"answer": 4627
},
{... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
6c9d60 | algebra_quadratic_discriminant_v1_1520064083_5339 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $b$ be the number of ordered pairs $(i, j)$ with $i \in \{1, 2\}$ and $j \in \{1, 2, 3\}$ such that $i + j = 4$. Compute the value of $b^2 - 4 \cdot a \cdot (-84)$,... | 676 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"a": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=12)), Eq(left=GCD(a=V... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COPRIME_PAIRS"
] | e64e7a | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T06:44:35.023270Z | {
"verified": true,
"answer": 676,
"timestamp": "2026-02-08T06:44:35.035503Z"
} | 083dc0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 861
},
"timestamp": "2026-02-13T04:10:53.605Z",
"answer": 676
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
80fddd | antilemma_sum_equals_v1_2051736721_4992 | Let $d = 44121$. Let $c$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 2$ and $1 \leq j \leq 11$. Let $m$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = c$. Let $n$ be the number of ordered triples of positive odd integers $(x_{11}, x_{21}, x_3)$ such that... | 1,892 | graphs = [
Graph(
let={
"_d": Const(44121),
"_c": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(11)))),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condit... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1/COUNT_SUM_EQUALS",
"COMB1/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 48574a | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.012 | 2026-02-08T18:18:43.341791Z | {
"verified": true,
"answer": 1892,
"timestamp": "2026-02-08T18:18:43.353448Z"
} | 51b777 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1293
},
"timestamp": "2026-02-18T16:02:21.931Z",
"answer": 1892
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
022355 | nt_count_divisible_and_v1_1742523217_5481 | Let $d_1$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 360$ and $\gcd(p, q) = 1$. Let $S$ be the set of all positive integers $n \leq 15276$ such that $n \equiv r \pmod{d_1}$ and $n \equiv 0 \pmod{6}$, where $r$ is the sum of $\mu(d)$ over all positive divisor... | 1,273 | graphs = [
Graph(
let={
"upper": Const(15276),
"d1": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=360)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | COUNT | sympy | B3 | [
"B3/MOBIUS_COPRIME",
"COPRIME_PAIRS"
] | 57cc03 | nt_count_divisible_and_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"MOBIUS_COPRIME"
] | 3 | 0.689 | 2026-02-08T11:01:25.752999Z | {
"verified": true,
"answer": 1273,
"timestamp": "2026-02-08T11:01:26.442157Z"
} | c99d35 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 383
},
"timestamp": "2026-02-21T12:40:58.304Z",
"answer": 1273
}
] | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
bd3455 | comb_catalan_compute_v1_655260480_4484 | Define $S_1$ as the set of all integers $t$ such that there exist positive integers $a$ and $b$ satisfying $1 \leq a \leq 3$, $1 \leq b \leq 4$, $5 \leq t \leq 17$, and $t = 3a + 2b$. Let $n$ be the number of elements in $S_1$. Define the Catalan number $C_n = \frac{1}{n+1} \binom{2n}{n}$. Define $S_2$ as the set of al... | 35,202 | graphs = [
Graph(
let={
"_n": Const(93860),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | comb_catalan_compute_v1 | negation_mod | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T17:57:44.723955Z | {
"verified": true,
"answer": 35202,
"timestamp": "2026-02-08T17:57:44.729205Z"
} | 091ff1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 4901
},
"timestamp": "2026-02-18T10:27:03.773Z",
"answer": 35202
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
a64573 | antilemma_k2_v1_971394319_853 | Let $ n = 235 $. Compute the value of $ \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor $, where $ \phi(k) $ denotes Euler's totient function. | 27,730 | graphs = [
Graph(
let={
"_n": Const(235),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(235), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T13:20:08.755449Z | {
"verified": true,
"answer": 27730,
"timestamp": "2026-02-08T13:20:08.756160Z"
} | b72e6e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 659
},
"timestamp": "2026-02-15T14:09:07.656Z",
"answer": 27730
},
{... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
842ccd | comb_count_derangements_v1_1918700295_727 | Let $n$ be the smallest divisor of $11011$ that is at least $2$. Define $D_n$ to be the number of derangements of $n$ elements. Let $c = 24335$. Compute the value of $c \cdot D_n \bmod{96798}$. | 9,222 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(11011))))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(24335),
"Q": ... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T03:24:12.271109Z | {
"verified": true,
"answer": 9222,
"timestamp": "2026-02-08T03:24:12.272339Z"
} | 28a2c4 | 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": 7062
},
"timestamp": "2026-02-10T14:14:08.561Z",
"answer": 9222
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
b37f29 | nt_min_coprime_above_v1_655260480_1382 | Let $S$ be the set of integers $d \geq 2$ that divide 171371. Define $m$ to be the smallest element of $S$. Let $T$ be the set of integers $n$ such that $15129 < n \leq 15548$ and $\gcd(n, m) = 1$. Define $r$ to be the smallest element of $T$. Compute the remainder when $74098 \cdot r$ is divided by 66807. | 14,473 | graphs = [
Graph(
let={
"start": Const(15129),
"upper": Const(15548),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(171371))))),
"result": MinOverSet(set=SolutionsSet(var=Va... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.088 | 2026-02-08T16:06:12.403505Z | {
"verified": true,
"answer": 14473,
"timestamp": "2026-02-08T16:06:12.491830Z"
} | e28bf2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 3596
},
"timestamp": "2026-02-16T21:31:24.803Z",
"answer": 14473
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c5d908 | antilemma_k3_v1_2051736721_2606 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $21313$, where $\phi$ denotes Euler's totient function. | 21,313 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=21313), 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 | 2026-02-08T16:48:49.259186Z | {
"verified": true,
"answer": 21313,
"timestamp": "2026-02-08T16:48:49.259603Z"
} | 00b398 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 1814
},
"timestamp": "2026-02-17T12:02:14.798Z",
"answer": 21313
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4b8a33 | geo_count_lattice_rect_v1_458359167_4927 | Let $a = 64$ and $b = 231$. Define $L$ as the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $r = |L| \mod 11$. Compute the value of $B_r \mod 90040$, where $B_r$ denotes the $r$-th Bell number. Find this remainder. | 25,935 | graphs = [
Graph(
let={
"a": Const(64),
"b": Const(231),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))), modulus=Const(90040)),
},
goal=Ref("Q"),
... | GEOM | COMB | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 5 | 0 | null | null | 0.005 | 2026-02-08T12:07:40.120907Z | {
"verified": true,
"answer": 25935,
"timestamp": "2026-02-08T12:07:40.125689Z"
} | 6dfe16 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1652
},
"timestamp": "2026-02-24T15:16:11.671Z",
"answer": 25935
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
569947 | nt_sum_divisors_mod_v1_865884756_4278 | Let $d$ be a positive integer such that $1 \leq d \leq 180$ and $d$ divides $34380$. Let $n$ be the largest such $d$. Define $\sigma$ as the sum of all positive divisors of $n$. Let $r$ be the remainder when $\sigma$ is divided by $10559$. Compute the remainder when $44121 \cdot r$ is divided by $76568$. | 47,714 | graphs = [
Graph(
let={
"_n": Const(34380),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(180)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"M": Const(10559),
"sigma": SumDivisors(n=Ref("n")),
... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_sum_divisors_mod_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.005 | 2026-02-08T17:50:16.371318Z | {
"verified": true,
"answer": 47714,
"timestamp": "2026-02-08T17:50:16.375904Z"
} | 33df16 | 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": 1985
},
"timestamp": "2026-02-18T09:05:50.341Z",
"answer": 47714
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c855e6 | comb_count_derangements_v1_865884756_344 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 5250$, $\gcd(p, q) = 1$, and $p < q$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $537251$. Compute the Bell number of the remainder when the absolute value of the subfactorial of $n$ is... | 52 | graphs = [
Graph(
let={
"_n": Const(2),
"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=5250)), Eq(left=GCD(a=Var(name='p'), b=Var(name='... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | e00f22 | comb_count_derangements_v1 | bell_mod | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T15:19:18.363383Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T15:19:18.365113Z"
} | f8333b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1737
},
"timestamp": "2026-02-16T03:54:47.774Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e6369c | sequence_lucas_compute_v1_1439011603_3019 | Let $n = \sum_{k=1}^{6} k$. Compute the $n$-th Lucas number, then find the remainder when $96479$ times this number is divided by $55774$. | 4,618 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Lucas(arg=Ref(name='n')),
"_c": Const(96479),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(55774)),
},
... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_lucas_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T17:10:39.233308Z | {
"verified": true,
"answer": 4618,
"timestamp": "2026-02-08T17:10:39.234675Z"
} | edd4ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 1497
},
"timestamp": "2026-02-17T22:00:28.565Z",
"answer": 4618
},
{
... | 1 | [
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
316e68 | lte_diff_endings_v1_124444284_855 | Let $a = 25$, $b = 4$, $n = 48$, and $p = 3$. Let $v_p(x)$ denote the exponent of the highest power of $p$ that divides $x$. Compute $v_p(a^n - b^n) - v_p(a - b)$. Let $d$ be this difference. Compute the remainder when $19116 \cdot d$ is divided by 87455.
Find the value of $x$. | 19,116 | graphs = [
Graph(
let={
"a_val": Const(25),
"b_val": Const(4),
"n_val": Const(48),
"p_val": Const(3),
"a_pow": Pow(Ref("a_val"), Ref("n_val")),
"b_pow": Pow(Ref("b_val"), Ref("n_val")),
"pow_diff": Sub(Ref("a_pow"), Ref("b_p... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.002 | 2026-02-08T03:33:00.876890Z | {
"verified": true,
"answer": 19116,
"timestamp": "2026-02-08T03:33:00.878475Z"
} | c61b73 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 891
},
"timestamp": "2026-02-09T23:01:57.626Z",
"answer": 19116
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
9716d0 | lin_form_endings_v1_1440796553_394 | Let $a = 14$, $b = 35$, $A = 45$, and $B = 32$. Let $g = \gcd(a, b)$. Compute the value of $$\left(12334 \left\lfloor \frac{aA + bB - (a + b)}{g} \right\rfloor + 12334\right) \bmod 98440.$$ | 56,296 | graphs = [
Graph(
let={
"a_coeff": Const(14),
"b_coeff": Const(35),
"A_val": Const(45),
"B_val": Const(32),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:45:49.958636Z | {
"verified": true,
"answer": 56296,
"timestamp": "2026-02-08T11:45:49.960099Z"
} | 3dab08 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 901
},
"timestamp": "2026-02-14T18:23:05.929Z",
"answer": 56296
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c1e6e5 | geo_count_lattice_triangle_v1_124444284_674 | Let the area of a triangle with vertices at $(121, 300)$, $(88, 333)$, and $(0, 0)$ be computed using the shoelace formula. Let $\text{area}_{2x}$ be twice this area, so
$$
\text{area}_{2x} = \left| 121 \cdot 333 + 88 \cdot 0 + 0 \cdot 300 - (300 \cdot 88 + 333 \cdot 0 + 0 \cdot 121) \right|,
$$
which simplifies to $\l... | 6,930 | graphs = [
Graph(
let={
"_n": Const(24),
"area_2x": Abs(arg=Sum(Mul(Const(value=121), Const(value=333)), Mul(Const(value=88), Sub(left=Const(value=0), right=Summation(expr=Var(name='k'), var='k', start=Const(value=1), end=Ref(name='_n')))))),
"boundary": Sum(GCD(a=Abs(arg... | ALG | NT | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.007 | 2026-02-08T03:26:55.771438Z | {
"verified": true,
"answer": 6930,
"timestamp": "2026-02-08T03:26:55.778069Z"
} | be8a6a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 372,
"completion_tokens": 1136
},
"timestamp": "2026-02-09T20:31:57.143Z",
"answer": 6930
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
5ee2a1 | comb_binomial_compute_v1_153355830_702 | Let $n$ be the number of nonnegative integers $j$ such that $$\sum_{k=0}^{2} (-1)^k \binom{2}{k} \le j \le 1584$$ and $\binom{1584}{j}$ is odd. Let $r = \binom{n}{7}$. Compute the remainder when $44121 \cdot r$ is divided by $87515$. | 45,235 | graphs = [
Graph(
let={
"_n": Const(1584),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Const(0), end=Const(2), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(2), k=Var("k"))))), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"V8"
] | efe7d7 | comb_binomial_compute_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"V8"
] | 2 | 0.003 | 2026-02-08T04:08:21.643840Z | {
"verified": true,
"answer": 45235,
"timestamp": "2026-02-08T04:08:21.646707Z"
} | 00407c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 3283
},
"timestamp": "2026-02-23T23:33:59.909Z",
"answer": 45235
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
87b7b2 | sequence_count_fib_divisible_v1_601307018_4851 | Let $F_n$ denote the $n$-th Fibonacci number. Let $N$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers with $xy = 1236377$. Find the number of positive integers $n$ with $1 \le n \le N$ such that $7 \mid F_n$. | 98 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1236377)))), expr=Abs(arg=Sub(left=Var(name='x'), right=Var(name='y'... | NT | null | COUNT | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3_DIFF"
] | 1 | 0.007 | 2026-03-10T05:32:33.990260Z | {
"verified": true,
"answer": 98,
"timestamp": "2026-03-10T05:32:33.997220Z"
} | f06910 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 24947
},
"timestamp": "2026-03-29T13:40:32.706Z",
"answer": 98
},
{
"id... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "n... | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
ec338e | modular_count_residue_v1_677425708_3439 | Let $n_0 = 2$. Let $m$ be the number of prime numbers $n$ such that $n_0 \le n \le 61$. Let $r$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 13500$, $\gcd(p, q) = 1$, and $p < q$. Determine the number of positive integers $n \le 75625$ such that $n \equiv r \pmod{... | 4,202 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(75625),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(61)), IsPrime(Var("n"))))),
"r": CountOverSet(set=SolutionsSet(var=Var("p"), condition=A... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"COUNT_PRIMES"
] | 2a4bed | modular_count_residue_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"COUNT_PRIMES"
] | 2 | 3.636 | 2026-02-08T05:43:02.212310Z | {
"verified": true,
"answer": 4202,
"timestamp": "2026-02-08T05:43:05.848343Z"
} | f81e6d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 2364
},
"timestamp": "2026-02-12T14:01:36.137Z",
"answer": 4202
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b6e144 | comb_sum_binomial_row_v1_677425708_1684 | Let $ n $ be the number of positive integers $ p $ for which there exists a positive integer $ q $ such that $ pq = 13340250 $, $ \gcd(p, q) = 1 $, and $ p < q $. Let $ \mathcal{Q} $ be the remainder when $ 64516 - 2^n $ is divided by 69344. Find the value of $ \mathcal{Q} $. | 68,324 | graphs = [
Graph(
let={
"_n": Const(69344),
"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=13340250)), Eq(left=GCD(a=Var(name='p'), b=Va... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T04:22:25.549772Z | {
"verified": true,
"answer": 68324,
"timestamp": "2026-02-08T04:22:25.550872Z"
} | 6f1ffc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 2087
},
"timestamp": "2026-02-09T23:20:10.359Z",
"answer": 68324
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
d9c765 | algebra_vieta_sum_v1_1470522791_245 | Let $m = 82944$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$, and define $n = \min\{x + y \mid (x, y) \in S\}$. Let $T$ be the set of all positive integers $x$ satisfying the equation $x^4 + 14x^3 + n x^2 = 0$. Compute $35721$ minus the product of all elements of $T$. | 35,721 | graphs = [
Graph(
let={
"_m": Const(82944),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | algebra_vieta_sum_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.04 | 2026-02-08T12:55:04.661956Z | {
"verified": true,
"answer": 35721,
"timestamp": "2026-02-08T12:55:04.702202Z"
} | 5eff79 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 502
},
"timestamp": "2026-02-16T04:09:31.765Z",
"answer": 35245
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
191d9e | comb_count_partitions_v1_1125832087_1927 | Let $n = 38$ and $\text{result} = p(n)$, the number of integer partitions of $n$. Let $P$ be the set of all prime numbers $n$ such that $2 \le n \le 12$, and let $m$ be the largest element of $P$. Define $Q = B_r$, where $r = |\text{result}| \bmod m$ and $B_r$ denotes the $r$-th Bell number.
Compute $Q$. | 1 | graphs = [
Graph(
let={
"_n": Const(12),
"n": Const(38),
"result": Partition(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")),... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | comb_count_partitions_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T04:14:47.002622Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T04:14:47.005448Z"
} | 75b6de | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1907
},
"timestamp": "2026-02-10T15:55:56.150Z",
"answer": 1
},
{
"id"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
c10320 | nt_count_gcd_equals_v1_124444284_3964 | Let $U = 17711$. Let $T$ be the set of integers $t$ with $10 \leq t \leq 74$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 11$, $1 \leq b \leq 5$, and $t = 4a + 6b$. Let $k = |T|$. Compute the number of positive integers $n \leq U$ such that $\gcd(n, k) = 1$. | 17,140 | graphs = [
Graph(
let={
"upper": Const(17711),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 1.9 | 2026-02-08T05:41:29.704592Z | {
"verified": true,
"answer": 17140,
"timestamp": "2026-02-08T05:41:31.604343Z"
} | 783b99 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 2557
},
"timestamp": "2026-02-12T12:56:10.967Z",
"answer": 17140
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
577e77 | geo_count_lattice_triangle_v1_784195855_7288 | Consider the triangle with vertices at $(0,0)$, $(128, 233)$, and $(64, 0)$. Let $A$ be twice the area of this triangle.
Let $I$ be the number of interior lattice points of the triangle, and let $B$ be the number of boundary lattice points. Use the following expressions:
- $A = |128 \cdot 233 + 64 \cdot (-196)|$,
- $... | 8,638 | graphs = [
Graph(
let={
"_m": Const(233),
"_n": Const(196),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=233)), Mul(Const(value=64), Sub(left=Const(value=0), right=Ref(name='_n'))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const... | ALG | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"B1"
] | 43d79a | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B1",
"COUNT_SUM_EQUALS"
] | 2 | 0.007 | 2026-02-08T09:11:30.759230Z | {
"verified": true,
"answer": 8638,
"timestamp": "2026-02-08T09:11:30.766696Z"
} | 3f9c9d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 1979
},
"timestamp": "2026-02-14T01:22:12.217Z",
"answer": 8638
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"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": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
28dadd | sequence_count_fib_divisible_v1_601307018_3904 | Let $F_n$ denote the $n$-th Fibonacci number. Let $d$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 544$. Let $M$ be the largest positive integer $d_1$ such that $d_1^2 \leq 617795$ and $d_1 \mid 617795$. Find the number of positive integers $n$ with $1 \leq n \l... | 2,419 | graphs = [
Graph(
let={
"_n": Const(544),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Divides(divisor=Var("d1"), dividend=Const(617795)), Leq(Mul(Var("d1"), Var("d1")), Const(617795))))),
"d": MinOverSet(set=MapOverSet(set=S... | NT | null | COUNT | sympy | B3_CLOSEST | [
"B3_CLOSEST",
"B3_DIFF"
] | e18306 | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"B3_CLOSEST",
"B3_DIFF"
] | 2 | 0.01 | 2026-03-10T04:30:51.744614Z | {
"verified": true,
"answer": 2419,
"timestamp": "2026-03-10T04:30:51.754373Z"
} | 0c4617 | 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": "2026-03-29T10:21:09.444Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status"... | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
caddc7 | nt_count_divisors_in_range_v1_1918700295_3987 | Let $n = 25200$, $a = 63$, and $b = 5050$. Let $A$ be the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$.
Let $B$ be the number of positive integers $m \leq 29581$ such that $m \equiv \left\lfloor \frac{m}{2} \right\rfloor \pmod{7}$.
Compute $B - A$. | 4,169 | graphs = [
Graph(
let={
"n": Const(25200),
"a": Const(63),
"b": Const(5050),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
"Q":... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | fba717 | nt_count_divisors_in_range_v1 | negation_mod | 5 | 0 | [
"L3C"
] | 1 | 0.046 | 2026-02-08T09:04:55.357281Z | {
"verified": true,
"answer": 4169,
"timestamp": "2026-02-08T09:04:55.403607Z"
} | 3aa5f6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 2929
},
"timestamp": "2026-02-14T00:03:15.048Z",
"answer": 4169
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8a5f1d | diophantine_fbi2_min_v1_153355830_1957 | Let $d$ be an integer satisfying $2 \leq d \leq 26$ such that $d$ divides $16$ and $\frac{16}{d} \geq 5$. Determine the value of the smallest such $d$. | 2 | graphs = [
Graph(
let={
"k": Const(16),
"a": Const(1),
"b": Const(4),
"upper": Const(26),
"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... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.051 | 2026-02-08T06:49:13.755683Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T06:49:13.807132Z"
} | ff0ef4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 296
},
"timestamp": "2026-02-15T17:47:06.212Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
c9ff17 | comb_count_partitions_v1_865884756_4101 | Let $n$ be the number of integers $t$ such that $14 \le t \le 106$ and there exist positive integers $a$ and $b$ with $1 \le a \le 7$, $1 \le b \le 8$, and $t = 6a + 8b$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $50861 \cdot p(n)$ is divided by $70936$. | 66,723 | 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=7)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:44:28.771713Z | {
"verified": true,
"answer": 66723,
"timestamp": "2026-02-08T17:44:28.773619Z"
} | d0b2e0 | 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": 3798
},
"timestamp": "2026-02-18T06:56:20.596Z",
"answer": 66723
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
889bb7 | algebra_poly_eval_v1_717093673_9 | Let $x$ and $y$ be positive integers such that $x + y = 6$. Define $m$ to be the maximum value of $xy$ over all such pairs. Compute $3m^2 + 4m + 7$. | 286 | graphs = [
Graph(
let={
"_n": Const(2),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 3 | 0 | [
"B1",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.175 | 2026-02-08T15:08:45.168778Z | {
"verified": true,
"answer": 286,
"timestamp": "2026-02-08T15:08:45.343396Z"
} | 520b0e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 309
},
"timestamp": "2026-02-16T05:16:13.338Z",
"answer": 286
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
ed006a | diophantine_fbi2_count_v1_1742523217_4853 | Let $k = 240$. Find the number of positive integers $d$ such that $4 \leq d \leq 84$, $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 85$. Let this number be $r$. Compute $30276 - r$. | 30,263 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(84)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Ref("_n")), Leq(Div(R... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.013 | 2026-02-08T09:19:07.273721Z | {
"verified": true,
"answer": 30263,
"timestamp": "2026-02-08T09:19:07.287030Z"
} | 25e262 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 2175
},
"timestamp": "2026-02-14T02:43:19.807Z",
"answer": 30263
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
cb9c4f | comb_count_partitions_v1_717093673_3827 | Let $m = 40$. Let $d_{\text{max}}$ be the largest positive integer $d$ such that $d \leq m$ and $d$ divides 1880. Define $n$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = d_{\text{max}}$ and $1 \leq i, j \leq 39$. Compute the number of integer partitions of $n$. | 31,185 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(1880))))),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), V... | NT | COMB | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/COUNT_SUM_EQUALS"
] | 1bc6d3 | comb_count_partitions_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"MAX_DIVISOR"
] | 2 | 0.01 | 2026-02-08T17:53:42.138009Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T17:53:42.148057Z"
} | 6c1ebd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1045
},
"timestamp": "2026-02-18T10:09:22.399Z",
"answer": 31185
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ba3a6e | nt_num_divisors_compute_v1_458359167_1783 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 82$. Let $d$ be the number of positive divisors of $n$. Compute the remainder when $50123 \cdot d$ is divided by $93678$. | 6,568 | graphs = [
Graph(
let={
"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")), Const(82))))),
"res... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T04:50:38.313513Z | {
"verified": true,
"answer": 6568,
"timestamp": "2026-02-08T04:50:38.315643Z"
} | 78515f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 568
},
"timestamp": "2026-02-11T21:57:05.430Z",
"answer": 42
},
{
"id": 11,
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
fbe8f6 | comb_factorial_compute_v1_898971024_465 | Let $ N = 24578 $. Define $ n $ to be the number of nonnegative integers $ j \leq N $ such that $ \binom{N}{j} $ is odd. Compute the value of $ n! $. | 40,320 | graphs = [
Graph(
let={
"_n": Const(24578),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(24578)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T15:27:55.908248Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T15:27:55.910166Z"
} | 63b3bc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 545
},
"timestamp": "2026-02-24T21:05:25.106Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
161fd7 | comb_count_permutations_fixed_v1_124444284_1016 | Let $n = \sum_{k=1}^{3} k$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 135 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), ... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | ac053f | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.003 | 2026-02-08T03:39:09.350611Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T03:39:09.353319Z"
} | 16bc2e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1099
},
"timestamp": "2026-02-10T01:23:06.055Z",
"answer": 135
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
a3913f_l | nt_count_divisible_v1_1520064083_3741 | Let $A$ be the number of positive integers $n \leq 33856$ that are divisible by $8$. Let $B$ be the number of positive integers $j \leq 16$ such that $j^3 \leq 4096$. Compute the value of $$ A + \left(2^{A \bmod B} \bmod 50721\right). $$ | 4,233 | NT | ALG | COUNT | sympy | C3 | [
"C3"
] | 537280 | nt_count_divisible_v1 | mod_exp | 3 | 0 | [
"C3"
] | 1 | 1.111 | 2026-02-08T05:50:18.606899Z | {
"verified": false,
"answer": 4488,
"timestamp": "2026-02-08T05:50:19.718190Z"
} | f7092c | a3913f | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 486
},
"timestamp": "2026-02-12T16:16:50.640Z",
"answer": 4488
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | |
bf85c7 | modular_mod_compute_v1_2080023795_186 | Let $n = 803$. Define $a = -85849$ and $m = 2011$. Let $r$ be the remainder when $a$ is divided by $m$, so $r \equiv a \pmod{m}$ and $0 \le r < m$. Let $D$ be the set of all positive integers $d$ such that $d \le n$ and $d$ divides 649627. Let $M$ be the maximum element of $D$. Compute the remainder when $M \cdot r$ is... | 8,576 | graphs = [
Graph(
let={
"_n": Const(803),
"a": Const(-85849),
"m": Const(2011),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": Mod(value=Mul(MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 17466c | modular_mod_compute_v1 | affine_mod | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.003 | 2026-02-08T11:35:19.680132Z | {
"verified": true,
"answer": 8576,
"timestamp": "2026-02-08T11:35:19.683042Z"
} | f4e451 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1703
},
"timestamp": "2026-02-08T20:50:23.613Z",
"answer": 8576
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.3,
"mid": -2.05,
"hi": 1.82
} | ||
68201d | antilemma_k3_v1_809748730_143 | Let $x = \sum_{d \mid 80757} \phi(d)$, where the sum is over all positive divisors $d$ of $80757$. Compute the remainder when $x^2 + 24x + 3000$ is divided by $54075$. | 26,217 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=80757), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Const(24), Ref("x")), Const(3000)), modulus=Const(54075)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T11:21:13.411905Z | {
"verified": true,
"answer": 26217,
"timestamp": "2026-02-08T11:21:13.412598Z"
} | 3a73e4 | 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": 2532
},
"timestamp": "2026-02-14T12:29:34.240Z",
"answer": 26217
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
faa994 | alg_poly4_sum_v1_1218484723_1605 | Compute the remainder when $$\sum_{\substack{a=1 \\ b=1}}^{216} \left( 97b^4 + 256a^4 + 512a^3b + \left( \min_{\substack{a_1=1 \\ b_1=1}}^{11} \left\{ 50b_1^2 + 18a_1^2 + 60a_1b_1 \right\} \right) ab^3 + 384a^2b^2 \right)$$ is divided by $67489$. | 14,566 | graphs = [
Graph(
let={
"_n": Const(216),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(216)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")))), expr=Sum(Mul(Const... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | alg_poly4_sum_v1 | null | 6 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.112 | 2026-02-25T03:19:16.912449Z | {
"verified": true,
"answer": 14566,
"timestamp": "2026-02-25T03:19:17.024280Z"
} | c74dca | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T07:29:30.410Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": 4.43,
"mid": 6.62,
"hi": 9.7
} | ||
5fc6a4 | antilemma_sum_equals_v1_1353956133_705 | Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 86$ and $1 \leq i, j \leq 84$. | 83 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(86)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(84)), right=IntegerRange(start=Const(1), end=Const(84))))),
},
... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.062 | 2026-02-08T11:48:07.789935Z | {
"verified": true,
"answer": 83,
"timestamp": "2026-02-08T11:48:07.852021Z"
} | ed257a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 245
},
"timestamp": "2026-02-24T14:46:31.038Z",
"answer": 83
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
2e5e7e | modular_sum_quadratic_residues_v1_1520064083_5121 | Let $p$ be the smallest divisor of $49681111313$ that is at least $2$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. For each such pair, compute $x + y$, and let $s$ be the minimum value among these sums. Compute $\frac{p(p-1)}{s}$. | 4,658 | 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(49681111313))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), MinOverSet(set=MapOverSet(set=Sol... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B3"
] | 6c6c26 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T06:38:24.947613Z | {
"verified": true,
"answer": 4658,
"timestamp": "2026-02-08T06:38:24.950003Z"
} | b80790 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1376
},
"timestamp": "2026-02-13T02:53:42.964Z",
"answer": 4658
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e46a37 | comb_count_derangements_v1_1978505735_3138 | Let $m = 16$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. For each such pair, compute $x + y$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all such pairs. Let $n$ be the largest prime number less than or equal to $s_{\text{min}}$. Define $D(n)$ to be the number ... | 45,528 | graphs = [
Graph(
let={
"_m": Const(16),
"_n": Const(62038),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositiv... | NT | COMB | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | comb_count_derangements_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T17:23:07.256384Z | {
"verified": true,
"answer": 45528,
"timestamp": "2026-02-08T17:23:07.260186Z"
} | ce9ab4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1090
},
"timestamp": "2026-02-18T02:10:45.930Z",
"answer": 45528
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bbce10 | algebra_quadratic_discriminant_v1_677425708_1719 | Let $a = 1$, $b = 15$, and $c$ be the number of ordered pairs $(x, y)$ where $x$ is an integer from 1 to 6, inclusive, and $y$ is an integer from 1 to 9, inclusive. Define $\text{result} = b^2 - 4ac$. Compute the remainder when $36375 \cdot \text{result}$ is divided by 92189.
Find the value of $Q$. | 50,808 | graphs = [
Graph(
let={
"_n": Const(92189),
"a": Const(1),
"b": Const(15),
"c": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(9)))),
"result": Sub(Pow(Ref("b"), Const... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:23:09.907470Z | {
"verified": true,
"answer": 50808,
"timestamp": "2026-02-08T04:23:09.908680Z"
} | 4e3987 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 757
},
"timestamp": "2026-02-09T23:51:10.751Z",
"answer": 50808
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
891eb5 | algebra_vieta_sum_v1_677425708_3988 | Let $S$ be the set of all positive integers $x$ such that
$$
2x^4 - 36x^3 + c x^2 - 648x + 648 = 0,
$$
where $c$ is the number of ordered pairs $(x_1, x_2)$ of positive odd integers satisfying $x_1 + x_2 = 468$. Compute the sum of all elements in $S$. | 18 | graphs = [
Graph(
let={
"_n": Const(2),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Const(2), Pow(Var("x"), Const(4))), Mul(Const(-36), Pow(Var("x"), Const(3))), Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(I... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"COMB1"
] | 567f58 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"COMB1",
"MIN_PRIME_FACTOR"
] | 2 | 0.022 | 2026-02-08T06:07:35.160579Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T06:07:35.183062Z"
} | 5a62bd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 642
},
"timestamp": "2026-02-18T23:32:13.153Z",
"answer": 470
},
{
"id": 11,
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
dd514e | antilemma_k2_v1_1978505735_6550 | Let $n = 175$. Compute the value of $$\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 175} \phi(d) \right\rfloor,$$ where $\phi$ denotes Euler's totient function. Find the remainder when $233$ minus this value is divided by $72863$. | 57,696 | graphs = [
Graph(
let={
"_n": Const(175),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=175), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
"Q": Mod(value=Sub(Const(233), Ref("x")), ... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.003 | 2026-02-08T19:38:57.348441Z | {
"verified": true,
"answer": 57696,
"timestamp": "2026-02-08T19:38:57.351146Z"
} | 5aafc8 | 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": 1650
},
"timestamp": "2026-02-18T23:08:59.153Z",
"answer": 57696
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
07ba22 | modular_sum_quadratic_residues_v1_655260480_5053 | Let $p = 257$. Define $r = \frac{p(p-1)}{4}$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ such that $d$ divides $537251$. Compute the Bell number $B_n$, where $n$ is the remainder when $|r|$ is divided by $d_{\text{min}}$. Find the value of $B_n$. | 5 | graphs = [
Graph(
let={
"_n": Const(2),
"p": Const(257),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")),... | NT | COMB | SUM | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | modular_sum_quadratic_residues_v1 | bell_mod | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.011 | 2026-02-08T18:15:50.549178Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T18:15:50.560116Z"
} | 84b45b | 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": 814
},
"timestamp": "2026-02-18T15:39:44.912Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0d749c | lin_form_endings_v1_124444284_9599 | Let $a = 10$ and $b = 15$. Let $d$ be the greatest common divisor of $a$ and $b$. Let $k = 22$ and let $g = \gcd(k, d)$. Define $s = \left\lfloor \frac{k}{g} \right\rfloor$. Multiply $s$ by $16810$, and let $x$ be the remainder when this product is divided by $84772$. Compute $x$. | 30,732 | graphs = [
Graph(
let={
"a_coeff": Const(10),
"b_coeff": Const(15),
"k_val": Const(22),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(16... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:34:46.707515Z | {
"verified": true,
"answer": 30732,
"timestamp": "2026-02-08T12:34:46.708538Z"
} | 7e71a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 324
},
"timestamp": "2026-02-15T02:27:42.886Z",
"answer": 30732
},
{... | 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": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
e16ecb | algebra_poly_eval_v1_784195855_6875 | Let $A$ be the set of all prime numbers $n$ such that $2 \leq n \leq 23$. Let $B$ be the set of all integers $t$ such that $5 \leq t \leq 14$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $c = 77077$ and let $D$ be the set of all integers $d \geq 2$ that divide $... | 43,252 | graphs = [
Graph(
let={
"_c": Const(77077),
"_m": Const(2),
"_n": Const(71831),
"x": Const(11),
"result": Sum(Mul(Const(8), Pow(Ref("x"), Const(3))), Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COUNT_PRIMES",
"LIN_FORM"
] | e109d5 | algebra_poly_eval_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.012 | 2026-02-08T08:56:15.844229Z | {
"verified": true,
"answer": 43252,
"timestamp": "2026-02-08T08:56:15.855900Z"
} | 59ffbf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2093
},
"timestamp": "2026-02-13T23:00:13.468Z",
"answer": 43252
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
82fedb | nt_count_divisors_in_range_v1_898971024_1973 | Let $n = 27720$. Define $a$ to be the number of ordered pairs $(p, q)$ of positive integers such that $p \cdot q = 52920$, $\gcd(p, q) = 1$, and $p < q$. Let $b = 27730$. Let $T$ be the set of all positive divisors $d$ of $n$ such that $a \leq d \leq b$. Compute the number of elements in $T$, multiply it by $23293$, an... | 84,911 | graphs = [
Graph(
let={
"n": Const(27720),
"a": 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=52920)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.24 | 2026-02-08T16:27:57.360047Z | {
"verified": true,
"answer": 84911,
"timestamp": "2026-02-08T16:27:57.599758Z"
} | 201bcb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 2127
},
"timestamp": "2026-02-17T04:22:12.511Z",
"answer": 84911
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
181d93 | comb_count_partitions_v1_349078426_1950 | Let $T$ be the set of all integers $t$ such that $12 \leq t \leq 519$ and there exist positive integers $a \leq 42$, $b \leq 45$ satisfying $t = 7a + 5b$. Let $m = |T|$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = m$. Define $n$ to be the minimum value of $x + y$ over al... | 75,175 | 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=42)), Geq(left=Var(name='b'), right=Const(value... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_count_partitions_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T14:02:00.065487Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T14:02:00.070344Z"
} | 1e8158 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T19:38:15.464Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
bde221 | comb_count_permutations_fixed_v1_2051736721_4111 | Let $n = 9$. Let $S$ be the set of all positive integers $k$ such that $1 \le k \le 90$ and $20$ divides $F_k$, where $F_k$ denotes the $k$-th Fibonacci number. Let $k = \sum_{i=1}^{|S|} \varphi(i) \left\lfloor \frac{3}{i} \right\rfloor$, where $\varphi$ is Euler's totient function. Compute $\binom{n}{k} \cdot !(n - k)... | 10,648 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(3)), IsPrime(Var("n1"))))),
"n": Const(9),
"k": Summation(var="k1", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("n2"), condi... | NT | COMB | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/K2",
"MAX_PRIME_BELOW/K2"
] | ca8e2e | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K2",
"MAX_PRIME_BELOW"
] | 3 | 0.005 | 2026-02-08T17:44:39.167043Z | {
"verified": true,
"answer": 10648,
"timestamp": "2026-02-08T17:44:39.171664Z"
} | 87e6d3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1547
},
"timestamp": "2026-02-18T07:56:47.762Z",
"answer": 10648
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b0964c | comb_count_derangements_v1_784195855_7130 | Let $n$ be the largest prime number such that $2 \leq n \leq 8$. Define $\text{result}$ to be the number of derangements of an $n$-element set. Let $Q$ be the remainder when $78418 \cdot \text{result}$ is divided by $93255$.
Compute $Q$. | 2,427 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(78418),
"Q": Mod(va... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T09:06:21.662207Z | {
"verified": true,
"answer": 2427,
"timestamp": "2026-02-08T09:06:21.663624Z"
} | b65944 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1598
},
"timestamp": "2026-02-14T00:16:10.527Z",
"answer": 2427
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_S... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} |
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