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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
627362_n | modular_modexp_compute_v1_601307018_3621 | A rectangular garden with area $684$ square meters is to be designed with integer side lengths. The landscaper chooses dimensions that minimize the difference between length and width; let $a$ be this minimal difference. Separately, a solar panel array of area $49284$ square meters is planned with integer dimensions th... | 74,561 | NT | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF",
"B3"
] | 69b567 | modular_modexp_compute_v1 | null | 5 | null | [
"B3",
"B3_DIFF"
] | 2 | 0.003 | 2026-03-10T04:14:52.518620Z | null | deb2a5 | 627362 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 7255
},
"timestamp": "2026-03-29T17:50:16.836Z",
"answer": 369
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
... | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
af8ea7 | nt_count_divisors_in_range_v1_784195855_6507 | Let $n = 15120$. Determine the number of positive divisors $d$ of $n$ such that $1 \leq d \leq 1893$. Denote this number by $r$. Let $s$ be the number of positive integers $k$ with $1 \leq k \leq 21756$ that are divisible by $444$. Compute $r^2 + s \cdot r + 5$. | 8,911 | graphs = [
Graph(
let={
"n": Const(15120),
"a": Const(1),
"b": Const(1893),
"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"))))),
"_c":... | NT | null | COUNT | sympy | C2 | [
"C2"
] | ae61b9 | nt_count_divisors_in_range_v1 | quadratic_mod | 4 | 0 | [
"C2"
] | 1 | 0.188 | 2026-02-08T08:42:29.420773Z | {
"verified": true,
"answer": 8911,
"timestamp": "2026-02-08T08:42:29.609174Z"
} | 36b9d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 2071
},
"timestamp": "2026-02-13T20:36:31.916Z",
"answer": 8911
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
04f2a0 | modular_sum_quadratic_residues_v1_898971024_1912 | Let $n$ be an integer such that $n \geq 2$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 89401$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $p$ be the largest prime number that is less than or equal to the minimum element of $T$. Compute $\frac{p(p-1)}{4}... | 87,764 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(ar... | NT | null | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T16:25:01.762003Z | {
"verified": true,
"answer": 87764,
"timestamp": "2026-02-08T16:25:01.765056Z"
} | 82ac97 | 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": 1379
},
"timestamp": "2026-02-17T02:48:12.018Z",
"answer": 87764
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_l... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
014588 | geo_visible_lattice_v1_1978505735_1443 | Let $n = 120$. Define a lattice point $(x, y)$ to be visible from the origin if $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$. Compute the remainder when $44121 \cdot R$ is divided by $89519$. | 84,173 | graphs = [
Graph(
let={
"n": Const(120),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(89519)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.66 | 2026-02-08T16:09:04.228658Z | {
"verified": true,
"answer": 84173,
"timestamp": "2026-02-08T16:09:04.889153Z"
} | db65dd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 9169
},
"timestamp": "2026-02-24T20:04:05.237Z",
"answer": 84173
},
{
... | 1 | [] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||||
3550ab | modular_mod_compute_v1_124444284_8930 | Let $a = -10946$ and $m = 2024$. Define $r$ to be the remainder when $a$ is divided by $m$, so $r \equiv a \pmod{m}$ and $0 \le r < m$. Let $c$ be the number of positive integers $n$ such that $1 \le n \le 72376$ and $7$ divides the $n$-th Fibonacci number. Compute the remainder when $c \cdot r$ is divided by $88462$. | 45,942 | graphs = [
Graph(
let={
"a": Const(-10946),
"m": Const(2024),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(72376)), Divides(divisor=Const(7), divid... | ALG | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 52ef24 | modular_mod_compute_v1 | affine_mod | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T11:58:58.210479Z | {
"verified": true,
"answer": 45942,
"timestamp": "2026-02-08T11:58:58.212254Z"
} | fdb926 | 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": 2137
},
"timestamp": "2026-02-14T22:05:35.387Z",
"answer": 45942
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b12bae | diophantine_fbi2_min_v1_2051736721_38 | Let $d$ be a positive integer. Define $S$ as the set of all integers $d$ such that $6 \leq d \leq 42$, $d$ divides $32$, and $\frac{32}{d} \geq 4$. Let $r$ be the minimum element of $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. Define $s = \sum_{(x,y) \in T} (x + y)$. C... | 264 | graphs = [
Graph(
let={
"_n": Const(99770),
"k": Const(32),
"upper": Const(42),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"B3"
] | 385411 | diophantine_fbi2_min_v1 | mod_exp | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.111 | 2026-02-08T15:10:06.782298Z | {
"verified": true,
"answer": 264,
"timestamp": "2026-02-08T15:10:06.893289Z"
} | d3bc82 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 383
},
"timestamp": "2026-02-16T05:19:05.416Z",
"answer": 264
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
be984a | nt_count_divisible_v1_1439011603_1761 | Let $n = 9$. Consider the set of all integers $t$ with $15 \leq t \leq 315$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 18$ and $1 \leq b \leq 23$, such that $t = 6a + 9b$. Let $c$ be the number of such integers $t$. Let $d$ be the largest divisor of $c$ that is at most $n$. Determine the v... | 4,669 | graphs = [
Graph(
let={
"_n": Const(9),
"upper": Const(42025),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Ex... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_DIVISOR"
] | 8c55ae | nt_count_divisible_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 1.892 | 2026-02-08T16:15:14.496260Z | {
"verified": true,
"answer": 4669,
"timestamp": "2026-02-08T16:15:16.388333Z"
} | 8f3288 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 2575
},
"timestamp": "2026-02-17T00:36:55.618Z",
"answer": 4669
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
290852 | comb_binomial_compute_v1_1125832087_408 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 15$ and $1 \leq i, j \leq 14$. Compute $\binom{n}{8}$. | 3,003 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(15)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(14)), right=IntegerRange(start=Const(1), end=Const(14))))),
"k": ... | ALG | COMB | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_binomial_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T03:02:56.771757Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T03:02:56.782556Z"
} | 565756 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 687
},
"timestamp": "2026-02-10T12:34:45.001Z",
"answer": 3003
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
bc2ae4 | sequence_count_fib_divisible_v1_153355830_2783 | Let $u$ be the number of integers $t$ such that $24 \le t \le 2424$ and there exist integers $a$ and $b$ with $1 \le a \le 216$, $1 \le b \le 32$, and $t = 9a + 15b$. Determine the number of positive integers $n$ such that $1 \le n \le u$ and $18$ divides the $n$-th Fibonacci number. Let $c$ be this count. Find the rem... | 44,366 | graphs = [
Graph(
let={
"_n": Const(78467),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=216)), Geq(l... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.066 | 2026-02-08T07:21:39.612715Z | {
"verified": true,
"answer": 44366,
"timestamp": "2026-02-08T07:21:39.678306Z"
} | be164a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 3276
},
"timestamp": "2026-02-13T10:05:17.105Z",
"answer": 44366
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
959ffb | comb_count_partitions_v1_1978505735_5265 | Let $n$ be the number of integers $t$ such that $24 \leq t \leq 154$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 7$, and $t = 14a + 10b$. Let $r$ be the number of integer partitions of $n$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisi... | 1,224 | 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=6)), Geq(left=Var(name='b'), right=Const(value=1... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:52:51.224397Z | {
"verified": true,
"answer": 1224,
"timestamp": "2026-02-08T18:52:51.226596Z"
} | bca645 | 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": 4300
},
"timestamp": "2026-02-18T20:24:00.243Z",
"answer": 1224
},
{... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9fffc6 | modular_sum_quadratic_residues_v1_601307018_9989 | Let $k = \left|\{ (a_1, b_1) \mid a_1, b_1 \in \mathbb{Z}^+,\ 1 \le a_1 \le b_1 \le 40,\ 32a_1^2 - 64a_1b_1 + 32b_1^2 = 800 \}\right|$. Let $p$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le k$ and $1 \le b \le 35$ such that $10a^2 - 18ab + 25b^2 \le 4394$. Compute $\frac{p(p - 1)}{4}$. | 31,064 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"p": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=An... | NT | null | SUM | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/QF_PSD_COUNT_LEQ"
] | b29ba8 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_ORBIT"
] | 2 | 0.006 | 2026-03-10T10:26:16.031236Z | {
"verified": true,
"answer": 31064,
"timestamp": "2026-03-10T10:26:16.036966Z"
} | 0d034a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 4137
},
"timestamp": "2026-04-19T12:43:24.993Z",
"answer": 31064
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
1a4dc0_l | comb_count_derangements_v1_1520064083_3779 | Let $d$ be the smallest integer $d \geq 2$ such that $d$ divides the number of positive integers $n \leq N$ for which the sum of the decimal digits of $n$ is odd, where $N$ is the number of integers $t$ in the range $15 \leq t \leq 6021$ that can be expressed as $t = 6a + 9b$ for positive integers $a \leq 705$ and $b \... | 2 | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/L3B/MIN_PRIME_FACTOR"
] | e8389b | comb_count_derangements_v1 | null | 7 | 0 | [
"L3B",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.003 | 2026-02-08T05:51:56.727741Z | {
"verified": false,
"answer": 1854,
"timestamp": "2026-02-08T05:51:56.730556Z"
} | 39d363 | 1a4dc0 | 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": 163,
"completion_tokens": 4498
},
"timestamp": "2026-02-12T16:22:43.936Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | |
368168 | nt_count_with_divisor_count_v1_784195855_1307 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $\nu$ be the number of elements in $P$. Let $\delta$ be the largest prime number $n$ such that $\nu \leq n \leq 16$. Determine the number of positive integers $n$ with $1... | 59,047 | 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=54)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COUNT | sympy | B3 | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 1.308 | 2026-02-08T04:57:45.104301Z | {
"verified": true,
"answer": 59047,
"timestamp": "2026-02-08T04:57:46.412277Z"
} | 6b7dbd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 1739
},
"timestamp": "2026-02-11T22:34:06.759Z",
"answer": 59047
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_la... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
563344 | comb_factorial_compute_v1_784195855_3303 | Let $n$ be the number of integers $j$ with $0 \le j \le 16898$ such that $\binom{16898}{j}$ is odd. Define $P = n!$. Let $m = 55543$. Compute the remainder when $m \cdot P$ is divided by $84745$. | 22,390 | graphs = [
Graph(
let={
"_n": Const(55543),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16898)), Eq(Mod(value=Binom(n=Const(16898), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T06:19:56.706041Z | {
"verified": true,
"answer": 22390,
"timestamp": "2026-02-08T06:19:56.707102Z"
} | dfc171 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2481
},
"timestamp": "2026-02-24T06:05:01.522Z",
"answer": 22390
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
ca3f88 | diophantine_fbi2_count_v1_1520064083_1587 | Let $k = 360$. Let $r$ be the number of integers $d$ such that $5 \leq d \leq 124$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 123$. Let $s$ be the smallest integer $d \geq 2$ that divides $104927$. Compute $r \bmod 307 + 1009 \cdot (r \bmod s)$. | 17,170 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(360),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(124)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Ref("_n")), Leq(Div(... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | diophantine_fbi2_count_v1 | two_moduli | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.015 | 2026-02-08T04:07:44.163265Z | {
"verified": true,
"answer": 17170,
"timestamp": "2026-02-08T04:07:44.177981Z"
} | d11d06 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 4350
},
"timestamp": "2026-02-10T15:26:20.944Z",
"answer": 17170
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
dd9ea5 | comb_sum_binomial_mod_v1_124444284_667 | Let $P$ be the set of all prime numbers $n$ such that $2 \leq n \leq 64$. Let $M$ be the maximum element of $P$. Compute the remainder when $$\sum_{k=12}^{44} \binom{M}{k}$$ is divided by $11717$. | 10,867 | graphs = [
Graph(
let={
"_n": Const(12),
"sum": Summation(var="k", start=Ref("_n"), end=Const(44), expr=Binom(n=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(64)), IsPrime(Var("n"))))), k=Var("k"))),
"result": Mod(val... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_mod_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T03:26:36.317181Z | {
"verified": true,
"answer": 10867,
"timestamp": "2026-02-08T03:26:36.321577Z"
} | 87bf76 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 19271
},
"timestamp": "2026-02-23T19:48:26.646Z",
"answer": 10867
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
1cd039 | comb_sum_binomial_row_v1_124444284_3210 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 24$. Let $m = |A|$. Let $B$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 49$. Let $s$ be the minimum value of $x + y$ over all $(x, y) \in B$. Let... | 18,472 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": 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=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3/MAX_PRIME_BELOW"
] | 8998b4 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.005 | 2026-02-08T05:17:23.828543Z | {
"verified": true,
"answer": 18472,
"timestamp": "2026-02-08T05:17:23.833685Z"
} | a84bc2 | 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": 2025
},
"timestamp": "2026-02-12T05:53:59.831Z",
"answer": 18472
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c74e57 | antilemma_k3_v1_1918700295_2231 | Let $n = 83058$. Compute the remainder when $61640$ multiplied by $\sum_{d \mid n} \phi(d)$ is divided by $65963$. | 42,838 | graphs = [
Graph(
let={
"_n": Const(83058),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(61640), Ref("x")), modulus=Const(65963)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T07:45:59.243752Z | {
"verified": true,
"answer": 42838,
"timestamp": "2026-02-08T07:45:59.244283Z"
} | fd73b6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 2019
},
"timestamp": "2026-02-13T12:06:19.411Z",
"answer": 42838
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
6324f9 | comb_binomial_compute_v1_784195855_7178 | Let $u$ be the number of positive integers $n$ such that $1 \leq n \leq 72$ and $16$ divides the $n$-th Fibonacci number. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = u$. Let $k$ be the maximum value of $xy$ over all such pairs. Compute $\binom{16}{k}$. | 11,440 | graphs = [
Graph(
let={
"n": Const(16),
"k": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("n"), condit... | ALG | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/B1"
] | e7f15f | comb_binomial_compute_v1 | null | 7 | 0 | [
"B1",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.002 | 2026-02-08T09:08:09.673230Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T09:08:09.674953Z"
} | c06256 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 2569
},
"timestamp": "2026-02-14T00:51:12.184Z",
"answer": 11440
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c85e8d | comb_count_partitions_v1_1419126231_169 | Let $n = \sum_{k=\binom{15}{15} - 1}^{3} 3^k$. Compute the number of integer partitions of $n$, denoted $p(n)$. | 37,338 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Summation(var="k", start=Sub(Binom(n=Const(15), k=Const(15)), Const(1)), end=Const(3), expr=Pow(Ref("_n"), Var("k"))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_partitions_v1 | null | 3 | 0 | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 2 | 0.002 | 2026-02-25T09:44:56.096311Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-25T09:44:56.098794Z"
} | f25bcd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 665
},
"timestamp": "2026-03-30T07:21:03.341Z",
"answer": 37338
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
2f5ad1 | nt_count_divisible_v1_1520064083_7385 | Let $d$ be the smallest divisor of $143143$ that is at least $2$. Let $N$ be the number of positive integers $n \leq 33856$ such that $n$ is divisible by $d$. Compute $N$. | 4,836 | graphs = [
Graph(
let={
"upper": Const(33856),
"divisor": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(143143))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_divisible_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.466 | 2026-02-08T09:00:28.917872Z | {
"verified": true,
"answer": 4836,
"timestamp": "2026-02-08T09:00:30.383781Z"
} | 47cd7a | 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": 503
},
"timestamp": "2026-02-13T23:28:26.983Z",
"answer": 4836
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"stat... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
f05199 | antilemma_sum_equals_v1_1978505735_1113 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 100$, $1 \leq i \leq 99$, and $1 \leq j \leq 99$. Let $c$ be the number of integers $t$ with $7 \leq t \leq 5565$ for which there exist positive integers $a \leq 1285$ and $b \leq 599$ such that $t = 2a + 5b$. Compute the value of $... | 17,237 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(100),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(99)), right=Integer... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | a464cd | antilemma_sum_equals_v1 | quadratic_mod | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.093 | 2026-02-08T15:49:58.010989Z | {
"verified": true,
"answer": 17237,
"timestamp": "2026-02-08T15:49:58.104400Z"
} | d727ec | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 2990
},
"timestamp": "2026-02-24T18:48:42.306Z",
"answer": 17239
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},... | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||
36798d | nt_count_divisible_and_v1_153355830_2489 | Let $d_1 = \sum_{k=1}^4 k$ and $d_2 = 15$. Determine the number of positive integers $n$ at most $141960$ that are divisible by both $d_1$ and $d_2$. Let $c$ be the number of integers $t$ with $7 \leq t \leq 5495$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 2075$ and $1 \leq b \leq 269$, su... | 19,548 | graphs = [
Graph(
let={
"_n": Const(95351),
"upper": Const(141960),
"d1": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"d2": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 1b831e | nt_count_divisible_and_v1 | affine_mod | 3 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 4.781 | 2026-02-08T07:09:09.196806Z | {
"verified": true,
"answer": 19548,
"timestamp": "2026-02-08T07:09:13.977882Z"
} | 6c939a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 3904
},
"timestamp": "2026-02-13T08:26:38.825Z",
"answer": 19548
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
689783 | algebra_poly_eval_v1_1439011603_1573 | Let $d_0=15$ and $m=7$. Let $N$ be the number of ordered pairs $(u,v)$ with $u$ and $v$ integers such that $1\le u\le 7$ and $1\le v\le 11$.
Consider all ordered pairs $(x,y)$ of positive integers such that $xy=1459264$. Among all such pairs, let $s$ be the minimum possible value of $x+y$.
Consider all integers $n$ s... | 43,283 | graphs = [
Graph(
let={
"_d": Const(15),
"_m": Const(7),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(11)))),
"b": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/MIN_PRIME_FACTOR",
"B3/C5/MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | f0d776 | algebra_poly_eval_v1 | null | 7 | 0 | [
"B3",
"C5",
"COUNT_CARTESIAN",
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 5 | 0.013 | 2026-02-08T16:10:25.411664Z | {
"verified": true,
"answer": 43283,
"timestamp": "2026-02-08T16:10:25.424864Z"
} | 3bd23d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 1598
},
"timestamp": "2026-02-16T22:08:34.092Z",
"answer": 43283
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_late... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c670f8 | nt_min_crt_v1_1978505735_6511 | Let $m = 3$ and $k = 7$. Find the smallest positive integer $n$ such that $n \leq 21$, $n \equiv 0 \pmod{3}$, and $n \equiv 4 \pmod{7}$. Let this integer be $r$. Let $C$ be the number of positive integers $n_1$ with $1 \leq n_1 \leq 5880$ such that $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{7}$. Compute... | 1,740 | graphs = [
Graph(
let={
"m": Const(3),
"k": Const(7),
"a": Const(0),
"b": Const(4),
"upper": Const(21),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | b81e9a | nt_min_crt_v1 | quadratic_mod | 5 | 0 | [
"L3C"
] | 1 | 0.007 | 2026-02-08T19:38:38.258302Z | {
"verified": true,
"answer": 1740,
"timestamp": "2026-02-08T19:38:38.265613Z"
} | 08b2a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1588
},
"timestamp": "2026-02-18T23:05:52.704Z",
"answer": 1740
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
10541a | sequence_count_fib_divisible_v1_458359167_3548 | Let $u$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 9$ and $1 \leq j \leq 157$ such that $\gcd(i, j) = 1$. Let $d = 13$. Determine the number of positive integers $n \leq u$ such that the $n$-th Fibonacci number is divisible by $13$. | 131 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=IntegerRange(start=Const(1), end=Const(157))))),
... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"COUNT_COPRIME_GRID"
] | 20ec03 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID",
"MOBIUS_COPRIME"
] | 2 | 0.059 | 2026-02-08T08:24:24.179605Z | {
"verified": true,
"answer": 131,
"timestamp": "2026-02-08T08:24:24.238195Z"
} | ddc30a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 1956
},
"timestamp": "2026-02-13T18:39:33.220Z",
"answer": 131
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9c4c0c | antilemma_sum_factor_cartesian_v1_677425708_1979 | Let $S$ be the set of all ordered pairs $(i, j)$ with $1 \leq i \leq 26$ and $1 \leq j \leq 20$. Define $d = \sum_{d' \mid \gcd(13,17)} \mu(d')$, where $\mu$ denotes the M\"obius function. If $d = 0$, then interpret the sum as evaluating to 0. Let $T$ be the set of all products $i \cdot j$ where $(i, j) \in S$. Compute... | 73,710 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=SumOverDivisors(n=GCD(a=Const(value=13), b=Const(value=17)), var='d', expr=MoebiusMu(n=Var(name='d')))), domain=CartesianProduct(left=IntegerRange(start=Const(1)... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | deaa80 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"ONE_PHI_1",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.001 | 2026-02-08T04:41:08.600030Z | {
"verified": true,
"answer": 73710,
"timestamp": "2026-02-08T04:41:08.600969Z"
} | 11deab | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 592
},
"timestamp": "2026-02-18T12:46:02.223Z",
"answer": 73710
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
368330 | alg_poly_orbit_hensel_v1_1218484723_1286 | Let $a$ be a non-negative integer with $0 \le a \le 11905262$. Define $N = (a^2 - 2075) \bmod 7921$ and $M = (N^2 - 2075) \bmod 7921$. Find the number of such $a$ for which $M = a$ and $N \ne a$. | 3,006 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-2075)), modulus=Const(7921)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-2075)), modulus=Const(7921)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), C... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.027 | 2026-02-25T03:02:25.175482Z | {
"verified": true,
"answer": 3006,
"timestamp": "2026-02-25T03:02:25.202456Z"
} | a3634b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 25644
},
"timestamp": "2026-03-10T06:26:17.714Z",
"answer": 2
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.79,
"mid": 5.69,
"hi": 7.81
} | ||
94bb70 | modular_mod_compute_v1_1742523217_81 | Let $a = -88804$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1827904$. Define $m$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Compute the remainder when $a$ is divided by $m$. | 428 | graphs = [
Graph(
let={
"a": Const(-88804),
"m": 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(1827904)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T02:52:15.532503Z | {
"verified": true,
"answer": 428,
"timestamp": "2026-02-08T02:52:15.533547Z"
} | 55a8f2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 953
},
"timestamp": "2026-02-09T13:40:50.753Z",
"answer": 428
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -0.86,
"mid": 0.99,
"hi": 2.63
} | ||
268270 | comb_binomial_compute_v1_238844314_578 | Let $n = 13$. Let $k$ be the smallest divisor of 847 that is at least 2. Define $r = \binom{n}{k}$. Let $A$ be the sum of the cubes of the positions (starting from 1) of each digit in the decimal representation of $r$, weighted by the corresponding digit. Specifically, if the decimal representation of $r$ has digits $d... | 46,745 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(13),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(847))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(46... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.004 | 2026-02-08T13:24:54.191611Z | {
"verified": true,
"answer": 46745,
"timestamp": "2026-02-08T13:24:54.195498Z"
} | 6a7535 | 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": 1026
},
"timestamp": "2026-02-15T15:14:43.042Z",
"answer": 46745
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
016b1d | modular_count_residue_v1_1918700295_2706 | Let $ m $ be the smallest positive integer $ n $ such that the largest power of $ 2 $ dividing $ n! $ is at least $ 3 $. Let $ r = \sum_{k=1}^{2} k $. Let $ \text{result} $ be the number of positive integers $ n $ in the range $ 1 \leq n \leq 79524 $ such that $ n \equiv r \pmod{m} $. Determine the value of $ \text{res... | 19,881 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(79524),
"m": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(2)), Const(3)), domain='Z_{>0}')),
"r": Summation(var="k", start=Const(1), end=Ref("_... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"V5"
] | 7fdb37 | modular_count_residue_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC",
"V5"
] | 2 | 3.13 | 2026-02-08T08:10:08.278440Z | {
"verified": true,
"answer": 19881,
"timestamp": "2026-02-08T08:10:11.408357Z"
} | f2818e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 744
},
"timestamp": "2026-02-20T10:54:55.223Z",
"answer": 19881
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"stat... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
f7d113 | algebra_vieta_sum_v1_124444284_9400 | Let $S$ be the set of all integers $x$ such that
$$
x^3 - 18x^2 + c x - 162 = 0,
$$
where $c$ is the number of positive integers $n \leq 247$ such that $\gcd(n, 20) = 1$.
Compute the sum of all elements of $S$. Multiply this sum by 88157, and find the remainder when the result is divided by 51521. | 41,196 | graphs = [
Graph(
let={
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(3)), Mul(Const(-18), Pow(Var("x"), Const(2))), Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(247)), Eq(GCD(a=Var("n"), b=C... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.008 | 2026-02-08T12:26:27.920837Z | {
"verified": true,
"answer": 41196,
"timestamp": "2026-02-08T12:26:27.928756Z"
} | 4b8702 | 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": 1017
},
"timestamp": "2026-02-15T01:36:43.952Z",
"answer": 41196
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3517dc_n | alg_sum_ap_v1_601307018_4232 | A baker prepares a sequence of cakes, starting with 30 decorations on the first cake. Each subsequent cake has 9 more decorations than the previous one, continuing for 123 cakes total (from $k = 0$ to $k = 122$). The total number of decorations used is the sum $\sum_{k=0}^{122} (9k + 30)$. Compute the remainder when th... | 6 | ALG | null | COMPUTE | sympy | K13 | [
"K13/LIN_FORM"
] | e3c3ba | alg_sum_ap_v1 | null | 2 | null | [
"K13",
"LIN_FORM"
] | 2 | 0.045 | 2026-03-10T04:51:35.294860Z | null | 04cbcc | 3517dc | narrative | 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": 346
},
"timestamp": "2026-03-29T18:29:53.491Z",
"answer": 6
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MA... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
798edd | sequence_count_fib_divisible_v1_784195855_8296 | Let $n_0 = 6889$. Let $u$ be the largest prime number less than or equal to 175. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq u$ and the $n$-th Fibonacci number is divisible by 7. Let $r$ be the number of elements in $S$. Define $Q = n_0 + \sum_{i=0}^{d-1} d_i (i+1)^2$, where $d$ is the numb... | 6,898 | graphs = [
Graph(
let={
"_n": Const(6889),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(175)), IsPrime(Var("n"))))),
"d": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.011 | 2026-02-08T15:59:57.469174Z | {
"verified": true,
"answer": 6898,
"timestamp": "2026-02-08T15:59:57.479987Z"
} | cc5298 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 1562
},
"timestamp": "2026-02-16T19:02:04.895Z",
"answer": 6898
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e61990 | modular_min_linear_v1_124444284_519 | Let $a = \sum_{d \mid 2311} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $m$ be the number of positive integers $n \leq 12367$ such that $\gcd(n, 14) = 1$. Let $x$ be the smallest positive integer $x \leq m$ such that $a x \equiv 792 \pmod{m}$. Compute $18225 - x$. | 15,651 | graphs = [
Graph(
let={
"_m": Const(12367),
"_n": Const(14),
"a": SumOverDivisors(n=Const(value=2311), var='d', expr=EulerPhi(n=Var(name='d'))),
"b": Const(792),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1))... | NT | null | EXTREMUM | sympy | C4 | [
"C4",
"K3"
] | b90d1a | modular_min_linear_v1 | null | 7 | 0 | [
"C4",
"K3"
] | 2 | 0.263 | 2026-02-08T03:20:27.431103Z | {
"verified": true,
"answer": 15651,
"timestamp": "2026-02-08T03:20:27.693762Z"
} | d30960 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 3103
},
"timestamp": "2026-02-09T18:47:27.789Z",
"answer": 15651
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma":... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
56dc8f | comb_count_partitions_v1_1918700295_4248 | Let $n = 41$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the Bell number of $|p(n)| \mod 11$. | 1 | graphs = [
Graph(
let={
"n": Const(41),
"result": Partition(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"C3"
] | 8a214c | comb_count_partitions_v1 | null | 5 | 0 | [
"C3",
"MIN_PRIME_FACTOR"
] | 2 | 0.066 | 2026-02-08T09:15:39.879475Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T09:15:39.945270Z"
} | f15a44 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 2635
},
"timestamp": "2026-02-24T10:57:00.086Z",
"answer": 6
},
{
"id... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
617dad | geo_count_lattice_rect_v1_784195855_8890 | Let $a = 80$ and $b = 76$. Define $L$ to be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Find the value of $L$. | 6,237 | graphs = [
Graph(
let={
"a": Const(80),
"b": Const(76),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0 | 2026-02-08T16:24:13.262054Z | {
"verified": true,
"answer": 6237,
"timestamp": "2026-02-08T16:24:13.262432Z"
} | c41ae5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 231
},
"timestamp": "2026-02-24T20:49:55.354Z",
"answer": 6237
},
{
"i... | 2 | [] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||||
9c79ae | lin_form_endings_v1_1470522791_1203 | Let $a = 75$ and $b = 60$. Let $d$ be the greatest common divisor of $a$ and $b$. Let $k = 14$, and let $g = \gcd(k, d)$. Define $m = \left\lfloor \frac{k}{g} \right\rfloor$. Compute the remainder when $5847 \cdot m$ is divided by $88320$. | 81,858 | graphs = [
Graph(
let={
"a_coeff": Const(75),
"b_coeff": Const(60),
"k_val": Const(14),
"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(58... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:30:44.895912Z | {
"verified": true,
"answer": 81858,
"timestamp": "2026-02-08T13:30:44.896735Z"
} | 1895eb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 473
},
"timestamp": "2026-02-15T16:57:46.729Z",
"answer": 81858
},
{... | 1 | [
{
"lemma": "C2",
"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": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
90a94c | antilemma_k3_v1_1918700295_2901 | Let $n = 10241$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 10,241 | graphs = [
Graph(
let={
"_n": Const(10241),
"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 | 2026-02-08T08:18:33.427523Z | {
"verified": true,
"answer": 10241,
"timestamp": "2026-02-08T08:18:33.427918Z"
} | f645c7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 613
},
"timestamp": "2026-02-15T20:00:43.075Z",
"answer": 7991
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
2f5fae | antilemma_sum_equals_v1_865884756_7153 | Let $D=55$. Let $m$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le 53$ and $1\le j\le 53$ such that $i+j=D$.
Let $n$ be the number of ordered pairs $(x_1,x_2)$ of positive odd integers such that $x_1+x_2=m$.
Let $x$ be the number of ordered pairs $(i_1,j_1)$ of integers with $1\le i_1\le 24$ and $... | 80,400 | graphs = [
Graph(
let={
"_d": Const(55),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_d")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(53)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1/COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | e13eb0 | antilemma_sum_equals_v1 | two_stage_modexp | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.017 | 2026-02-08T19:38:34.273855Z | {
"verified": true,
"answer": 80400,
"timestamp": "2026-02-08T19:38:34.290872Z"
} | 7c524d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 2882
},
"timestamp": "2026-02-18T23:02:10.488Z",
"answer": 80400
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
0e4319 | modular_inverse_v1_124444284_6046 | Let $a$ be the number of integers $t$ with $16 \leq t \leq 1470$ for which there exist positive integers $a'$ and $b'$ such that $t = 10a' + 4b' + 2$, $1 \leq a' \leq 16$, and $1 \leq b' \leq 327$. Let $m$ be the number of positive integers $k$ at most $32402$ that are divisible by $34$. Determine the smallest positive... | 541 | 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=16)), Geq(left=Var(name='b'), right=Const(value=... | ALG | NT | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM",
"C2"
] | c556ae | modular_inverse_v1 | null | 6 | 0 | [
"C2",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.09 | 2026-02-08T08:05:55.352010Z | {
"verified": true,
"answer": 541,
"timestamp": "2026-02-08T08:05:55.442472Z"
} | 7f9a7f | 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": 4881
},
"timestamp": "2026-02-13T14:45:08.850Z",
"answer": 541
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
23ec87 | comb_count_partitions_v1_655260480_3945 | Let $T$ be the set of all integers $t$ such that there exist positive integers $a \leq 3$ and $b \leq 3$ satisfying $t = 3a + 2b$ and $5 \leq t \leq 15$. Let $n$ be the sum of the integers from $1$ to the number of elements in $T$. Let $P(n)$ denote the number of integer partitions of $n$. Compute the value of $$\sum_{... | 16,753 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(16384),
"n": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/SUM_ARITHMETIC"
] | 5a2696 | comb_count_partitions_v1 | null | 7 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.005 | 2026-02-08T17:38:10.216090Z | {
"verified": true,
"answer": 16753,
"timestamp": "2026-02-08T17:38:10.221294Z"
} | 8e994b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1232
},
"timestamp": "2026-02-18T05:09:47.493Z",
"answer": 16753
},
... | 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": "SUM_ARITHMETI... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
45d675 | comb_count_permutations_fixed_v1_784195855_5794 | Let $n = 7$ and let $k = \sum_{k=1}^{2} k$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 315 | graphs = [
Graph(
let={
"n": Const(7),
"k": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Ref("result"),
},
go... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.003 | 2026-02-08T08:06:54.687729Z | {
"verified": true,
"answer": 315,
"timestamp": "2026-02-08T08:06:54.690943Z"
} | e65ede | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 502
},
"timestamp": "2026-02-24T08:55:40.653Z",
"answer": 315
},
{
"id"... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
d120ac | nt_num_divisors_compute_v1_655260480_680 | Let $x$ and $y$ be positive integers such that $xy = 1936$. Define $n$ to be the minimum value of $x + y$ over all such pairs.
Let $d(n)$ denote the number of positive divisors of $n$. Compute the remainder when $44121 \cdot d(n)$ is divided by $65756$. | 24,188 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1936)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T15:31:59.408559Z | {
"verified": true,
"answer": 24188,
"timestamp": "2026-02-08T15:31:59.411990Z"
} | d368eb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1081
},
"timestamp": "2026-02-16T08:30:23.503Z",
"answer": 24188
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a2ef21 | antilemma_k3_v1_1520064083_2448 | Let $n = 34124$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient function. Compute the remainder when $17038 \cdot x$ is divided by $81471$. | 27,656 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=34124), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(17038), Ref("x")), modulus=Const(81471)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:44:45.296436Z | {
"verified": true,
"answer": 27656,
"timestamp": "2026-02-08T04:44:45.296906Z"
} | 0e0276 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1133
},
"timestamp": "2026-02-11T21:51:10.317Z",
"answer": 27656
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
fca0e5 | comb_count_permutations_fixed_v1_153355830_1407 | Let $n = 7$ and $k = 1$. Define the quantity
$$
\binom{n}{k} \cdot !(n - k),
$$
where $!m$ denotes the number of derangements of $m$ elements. Compute this quantity. | 1,855 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(1),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.007 | 2026-02-08T06:22:48.261000Z | {
"verified": true,
"answer": 1855,
"timestamp": "2026-02-08T06:22:48.267518Z"
} | 8b4081 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 477
},
"timestamp": "2026-02-24T06:12:33.568Z",
"answer": 1855
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
9271dc | lin_form_endings_v1_717093673_4084 | Let $a = 25$, $b = 15$, $A = 50$, and $B = 42$. Compute $\gcd(a, b)$, and let
$$
n = \left\lfloor \frac{aA + bB - (a + b)}{\gcd(a, b)} \right\rfloor + 1.
$$
Let $x = (11122 \cdot n) \bmod 83925$. Find the value of $x$. | 75,618 | graphs = [
Graph(
let={
"a_coeff": Const(25),
"b_coeff": Const(15),
"A_val": Const(50),
"B_val": Const(42),
"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 | 2026-02-08T18:02:03.847609Z | {
"verified": true,
"answer": 75618,
"timestamp": "2026-02-08T18:02:03.848995Z"
} | a4f9be | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 736
},
"timestamp": "2026-02-18T12:22:40.422Z",
"answer": 75618
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
53ae12 | lin_form_endings_v1_1742523217_2407 | Let $a = 98$ and $b = 28$. Compute the remainder when $12502 \left\lfloor \frac{28}{\gcd(a,b)} \right\rfloor$ is divided by $95127$. | 25,004 | graphs = [
Graph(
let={
"a_coeff": Const(98),
"b_coeff": Const(28),
"_inner_result": Floor(Div(Const(28), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(12502),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T04:44:40.099855Z | {
"verified": true,
"answer": 25004,
"timestamp": "2026-02-08T04:44:40.100208Z"
} | 229b77 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 332
},
"timestamp": "2026-02-11T21:47:02.101Z",
"answer": 25004
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"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": -10,
"mid": -7.73,
"hi": -5.46
} | ||
851583 | antilemma_sum_primes_v1_1742523217_4365 | Let $m = 4$. Define $n$ to be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 216$. Let $S$ be the set of all prime numbers $n$ satisfying $n \geq n$ and $n \leq m$. Compute the sum of all elements in $S$. | 5 | graphs = [
Graph(
let={
"_m": Const(4),
"_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=216)), Eq(left=GCD(a=Var(name='p'), b=Var(name='... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_PRIMES",
"SUM_PRIMES"
] | 020700 | antilemma_sum_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"SUM_PRIMES"
] | 2 | 0.002 | 2026-02-08T07:13:52.972553Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T07:13:52.974585Z"
} | 7fe644 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 442
},
"timestamp": "2026-02-20T01:16:25.335Z",
"answer": 5
}
] | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
988585_n | alg_sum_powers_v1_1218484723_2035 | An encrypted message uses a key derived from a large number: $25060027$. The decryption modulus $M$ is the largest factor of this number not exceeding $5003$. The message length is tied to the minimal perimeter of a rectangle with area $772641$ and positive integer sides; let $P = x + y$ be this minimal sum. The messag... | 4,726 | ALG | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/B3"
] | 51e324 | alg_sum_powers_v1 | null | 5 | null | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.07 | 2026-02-25T03:43:49.386095Z | null | 8b545c | 988585 | narrative | 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": 17490
},
"timestamp": "2026-03-30T17:41:51.310Z",
"answer": 4726
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
261a4a | nt_min_crt_v1_1526740231_31 | Let $m = 7$, $k = 8$, $a = 6$, $b = 3$, and $u = 56$. Determine the value of the smallest positive integer $n$ such that $1 \leq n \leq u$, $n \equiv a \pmod{m}$, and $n \equiv b \pmod{k}$. | 27 | graphs = [
Graph(
let={
"m": Const(7),
"k": Const(8),
"a": Const(6),
"b": Const(3),
"upper": Const(56),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | NT | null | EXTREMUM | sympy | V1 | [
"V1/C2"
] | ebdb30 | nt_min_crt_v1 | null | 4 | 0 | [
"C2",
"V1"
] | 2 | 0.04 | 2026-02-08T11:18:46.269239Z | {
"verified": true,
"answer": 27,
"timestamp": "2026-02-08T11:18:46.308814Z"
} | 38d20a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 685
},
"timestamp": "2026-02-14T11:50:33.864Z",
"answer": 27
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "ok... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
24330b | modular_sum_quadratic_residues_v1_1918700295_381 | Let $p = 233$ and define $r = \frac{p(p-1)}{4}$. Let $Q = B_k$, where $B_k$ is the $k$th Bell number and $k = |r| \bmod 11$. Compute $Q$. | 203 | graphs = [
Graph(
let={
"p": Const(233),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | COMB | null | SUM | sympy | MAX_VAL | [
"MAX_VAL",
"K13"
] | ceec8c | modular_sum_quadratic_residues_v1 | bell_mod | 4 | 0 | [
"K13",
"MAX_VAL"
] | 2 | 0.012 | 2026-02-08T03:11:57.239819Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T03:11:57.251450Z"
} | 1d230d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 559
},
"timestamp": "2026-02-10T13:24:24.292Z",
"answer": 203
},
{
"id"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
e8a437 | nt_max_prime_below_v1_1125832087_997 | Let $c$ be the number of positive integers $n$ with $1 \leq n \leq 2$ such that the sum of the digits of $n$ is odd. Determine the largest prime number $n$ such that $c \leq n \leq 59536$. | 59,513 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(59536),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=DigitSu... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | nt_max_prime_below_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 1.345 | 2026-02-08T03:25:05.002531Z | {
"verified": true,
"answer": 59513,
"timestamp": "2026-02-08T03:25:06.347558Z"
} | 0c6d54 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 4016
},
"timestamp": "2026-02-10T13:33:19.486Z",
"answer": 59513
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
45c14f | diophantine_product_count_v1_1742523217_49 | Let $n_1 = 1$. Define $h = \Omega(n_1)$, where $\Omega(n)$ is the number of prime factors of $n$ counted with multiplicity. Let $n = 2077 + h$, and define $f = \lambda(n)$, where $\lambda(n)$ is the Liouville function, equal to $(-1)^{\Omega(n)}$. Let $k = 120 \cdot f$. Determine the number of positive integers $x$ suc... | 14 | graphs = [
Graph(
let={
"n1": Const(1),
"h": BigOmega(n=Ref(name='n1')),
"n": Sum(Const(2077), Ref("h")),
"f": LiouvilleLambda(n=Ref(name='n')),
"k": Mul(Const(120), Ref("f")),
"upper": Const(60),
"result": CountOverSet(set=... | NT | null | COUNT | sympy | BIG_OMEGA_ZERO | [
"BIG_OMEGA_ZERO",
"LIOUVILLE_ONE"
] | 464f18 | diophantine_product_count_v1 | null | 5 | 2 | [
"BIG_OMEGA_ZERO",
"LIOUVILLE_ONE"
] | 2 | 0.006 | 2026-02-08T02:51:25.434427Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T02:51:25.440267Z"
} | f8e076 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 1819
},
"timestamp": "2026-02-09T13:08:04.034Z",
"answer": 14
},
{
"id"... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
426067 | comb_count_permutations_fixed_v1_238844314_1046 | Let $n_2 = 11$. Define $v = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = 0$ and define $t = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = (6 + v) \cdot t$. Let $k = 0$ and define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the remai... | 28,189 | graphs = [
Graph(
let={
"n2": Const(11),
"v": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"t": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), ... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T13:51:59.143032Z | {
"verified": true,
"answer": 28189,
"timestamp": "2026-02-08T13:51:59.144917Z"
} | 6a0b19 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 849
},
"timestamp": "2026-02-24T19:15:34.606Z",
"answer": 28189
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
75b817 | nt_max_prime_below_v1_865884756_1918 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Determine the value of the largest prime number $n$ such that $m \leq n \leq 14161$. | 14,159 | graphs = [
Graph(
let={
"upper": Const(14161),
"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 | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.417 | 2026-02-08T16:23:32.048991Z | {
"verified": true,
"answer": 14159,
"timestamp": "2026-02-08T16:23:32.465999Z"
} | f8f2a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1491
},
"timestamp": "2026-02-17T03:19:04.683Z",
"answer": 14159
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b331e3 | alg_poly_orbit_count_v1_601307018_2914 | Define a function $f(x) = (x^3 + 4x) \bmod 73$. For a non-negative integer $a$, let $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$, and $K = f(T)$. Find the number of integers $a$ with $0 \le a \le 12555$ such that $K = a$, but $N \ne a$, $M \ne a$, $R \ne a$, $S \ne a$, and $T \ne a$. | 1,032 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(4), Var("a"))), modulus=Const(73)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(4), Ref("p1"))), modulus=Const(73)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(4), Ref(... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.044 | 2026-03-10T03:31:59.843670Z | {
"verified": true,
"answer": 1032,
"timestamp": "2026-03-10T03:31:59.887448Z"
} | b3caf8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T06:57:37.710Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
9e6e05 | geo_count_lattice_rect_v1_655260480_2374 | Let $a = 90$ and $b = 269$. Let $L$ be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Compute the remainder when $999 - L$ is divided by $93467$. | 69,896 | graphs = [
Graph(
let={
"a": Const(90),
"b": Const(269),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Sub(Const(999), Ref("result")), modulus=Const(93467)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T16:41:26.692870Z | {
"verified": true,
"answer": 69896,
"timestamp": "2026-02-08T16:41:26.695166Z"
} | 44d6d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 538
},
"timestamp": "2026-02-17T09:32:49.664Z",
"answer": 69896
},
{... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
a92869 | geo_count_lattice_rect_v1_717093673_1875 | Let $a = 463$ and $b = 176$. Define $R$ as the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$.
Let $Q = (89648 \cdot R) \bmod 78389$.
Find the value of $Q$. | 2,508 | graphs = [
Graph(
let={
"a": Const(463),
"b": Const(176),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(89648),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(78389)),
},
goal=Ref("Q"),
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T16:22:43.582478Z | {
"verified": true,
"answer": 2508,
"timestamp": "2026-02-08T16:22:43.584427Z"
} | ca37b0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1093
},
"timestamp": "2026-02-24T20:42:13.119Z",
"answer": 2508
},
{
"... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
dbdba1 | lin_form_endings_v1_784195855_10250 | Let $a = 49$, $b = 14$, $A = 24$, and $B = 46$. Let $g = \gcd(a, b)$. Define $N = (aA + bB) - (a + b)$. Let $k = \left\lfloor \frac{N}{g} \right\rfloor + 1$. Compute the remainder when $9350 \cdot k$ is divided by $50860$. | 16,640 | graphs = [
Graph(
let={
"a_coeff": Const(49),
"b_coeff": Const(14),
"A_val": Const(24),
"B_val": Const(46),
"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 | 2026-02-08T17:31:54.297616Z | {
"verified": true,
"answer": 16640,
"timestamp": "2026-02-08T17:31:54.298985Z"
} | 1cde64 | 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": 3455
},
"timestamp": "2026-02-18T03:22:26.067Z",
"answer": 16640
},
... | 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
} | ||
e0d5f4 | antilemma_sum_equals_v1_153355830_891 | Let $n = 49$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 49$, $1 \le i \le 48$, and $1 \le j \le 49$. Let $Q$ be the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|x| + 2$. Find the value of $Q$. | 75 | graphs = [
Graph(
let={
"_n": Const(49),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(48)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.109 | 2026-02-08T04:14:59.736705Z | {
"verified": true,
"answer": 75,
"timestamp": "2026-02-08T04:14:59.845832Z"
} | 8dd0b4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 5325
},
"timestamp": "2026-02-24T00:08:27.446Z",
"answer": 75
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
8b1628 | nt_num_divisors_compute_v1_124444284_2827 | Let $n$ be the sum of the first $71$ positive integers. Determine the number of positive divisors of $n$. | 18 | graphs = [
Graph(
let={
"_n": Const(71),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T05:02:22.891306Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T05:02:22.892677Z"
} | 700d0d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 398
},
"timestamp": "2026-02-11T22:12:26.665Z",
"answer": 24
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
42438a | nt_sum_gcd_range_mod_v1_548369836_263 | Let $N$ be the number of integers $t$ with $5 \leq t \leq 3006$ for which there exist positive integers $a \leq 1137$ and $b \leq 244$ such that $t = 2a + 3b$. Let $k = 144$ and let
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Find the remainder when $\text{sum}$ is divided by $11173$. | 9,749 | 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=1137)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_PHI_1"
] | e67fb6 | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"LIN_FORM",
"ONE_PHI_1"
] | 2 | 0.133 | 2026-02-08T02:49:44.747976Z | {
"verified": true,
"answer": 9749,
"timestamp": "2026-02-08T02:49:44.881083Z"
} | 6119ab | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 5234
},
"timestamp": "2026-02-09T21:42:27.255Z",
"answer": 9749
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lem... | {
"lo": 2.06,
"mid": 5.24,
"hi": 8.53
} | ||
eaa509 | antilemma_sum_equals_v1_48377204_1267 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 28$ and $1 \leq i, j \leq 27$. Compute $x$. | 27 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(28)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(27)), right=IntegerRange(start=Const(1), end=Const(27))))),
},
... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.146 | 2026-02-08T16:00:18.554402Z | {
"verified": true,
"answer": 27,
"timestamp": "2026-02-08T16:00:18.700692Z"
} | f99d39 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 356
},
"timestamp": "2026-02-24T19:22:29.009Z",
"answer": 27
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
f86fd1 | nt_count_divisors_in_range_v1_784195855_3338 | Let $n = 332640$. Let $b$ be the number of positive integers at most 23783 that are relatively prime to 20. Determine the value of $Q$, defined as the number of positive divisors $d$ of $n$ such that $49 \le d \le b$. Then compute
$$
\sum_{k=1}^Q \tau(k),
$$
where $\tau(k)$ denotes the number of positive divisors of $k... | 687 | graphs = [
Graph(
let={
"n": Const(332640),
"a": Const(49),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(23783)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.234 | 2026-02-08T06:21:49.469817Z | {
"verified": true,
"answer": 687,
"timestamp": "2026-02-08T06:21:49.703535Z"
} | b7e600 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 5037
},
"timestamp": "2026-02-12T23:24:36.251Z",
"answer": 687
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d0b9b0 | nt_count_squarefree_v1_1456120455_15 | Let $n$ be a positive integer such that $1 \leq n \leq 32768$. Define a quantity based on the condition that the square of the M\"obius function evaluated at $n$ equals Euler's totient function evaluated at 1. Note that $\mu(n)^2 = 1$ if $n$ is squarefree, and 0 otherwise, and $\varphi(1) = 1$. Thus, the condition $\mu... | 19,920 | graphs = [
Graph(
let={
"upper": Const(32768),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mul(MoebiusMu(n=Var(name='n')), MoebiusMu(n=Var(name='n'))), EulerPhi(n=Const(1)))))),
},
goal=R... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_squarefree_v1 | null | 5 | 0 | [
"ONE_PHI_1"
] | 1 | 12.136 | 2026-02-08T02:48:34.202371Z | {
"verified": true,
"answer": 19920,
"timestamp": "2026-02-08T02:48:46.338645Z"
} | 0c9d5b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 6549
},
"timestamp": "2026-02-10T00:43:03.788Z",
"answer": 19921
},... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
... | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
0c3920 | nt_count_digit_sum_v1_677425708_4036 | Let $t$ be an integer such that $9 \leq t \leq 10013$. A positive integer $t$ is called \emph{expressible} if there exist integers $a$ and $b$ with $1 \leq a \leq 253$ and $1 \leq b \leq 4121$ such that $t = 7a + 2b$. Let $u$ be the number of expressible integers $t$ in the given range.
Let $s$ be the largest prime nu... | 44,556 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=253)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.388 | 2026-02-08T06:24:29.158646Z | {
"verified": true,
"answer": 44556,
"timestamp": "2026-02-08T06:24:29.546659Z"
} | 479900 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 6276
},
"timestamp": "2026-02-12T23:48:53.432Z",
"answer": 44556
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d66c46 | modular_modexp_compute_v1_1978505735_4178 | Let $n$ be the largest prime number less than or equal to 1298. Compute the remainder when $3^n$ is divided by 16290. | 12,123 | graphs = [
Graph(
let={
"_n": Const(1298),
"a": Const(3),
"e": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"m": Const(16290),
"result": ModExp(base=Ref("a"), exp=R... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_modexp_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T18:03:53.226999Z | {
"verified": true,
"answer": 12123,
"timestamp": "2026-02-08T18:03:53.231333Z"
} | d1a320 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 3392
},
"timestamp": "2026-02-18T13:43:23.794Z",
"answer": 12123
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cc6dfd | diophantine_product_count_v1_717093673_1239 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $S$ be the set of all positive integers $x_1$ such that $1 \le x_1 \le 41$, $x_1$ divides $k$, and $\frac{k}{x_1} \le 41$. Compute the remainder when $44121$ times the number of elements in $S$ is d... | 55,164 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(4... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.023 | 2026-02-08T15:58:23.444798Z | {
"verified": true,
"answer": 55164,
"timestamp": "2026-02-08T15:58:23.467993Z"
} | cac555 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1567
},
"timestamp": "2026-02-16T17:17:58.719Z",
"answer": 55164
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d5f98d | diophantine_fbi2_count_v1_677425708_3972 | Let $S$ be the set of all positive integers $n$ with $1 \le n \le 289$ such that $n \equiv \lfloor n/2 \rfloor \pmod{5}$. Let $u = |S|$. Let $r$ be the number of positive integers $d$ such that $3 \le d \le u$, $d$ divides $60$, and $2 \le 60/d \le 56$. Compute the remainder when $49682 \cdot r$ is divided by $82373$. | 35,273 | graphs = [
Graph(
let={
"k": Const(60),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(289)), Congruent(a=Var(name='n'), ... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.006 | 2026-02-08T06:07:34.396974Z | {
"verified": true,
"answer": 35273,
"timestamp": "2026-02-08T06:07:34.403271Z"
} | 23f9fd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 994
},
"timestamp": "2026-02-12T19:34:18.318Z",
"answer": 35273
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
dcf5c9 | nt_count_coprime_and_v1_865884756_6300 | Let $n = 64708$ and let $u = 10524$. Let $k_1 = 7$. Let $S$ be the set of all positive divisors $d$ of $1800$ such that $d \geq 2$. Let $m$ be the minimum element of $S$. Let $T$ be the set of all prime numbers $n$ such that $m \leq n \leq 12$. Let $k_2$ be the maximum element of $T$. Define $A$ as the set of all posit... | 32,657 | graphs = [
Graph(
let={
"_n": Const(64708),
"upper": Const(10524),
"k1": Const(7),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var(... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 1.093 | 2026-02-08T19:08:14.433136Z | {
"verified": true,
"answer": 32657,
"timestamp": "2026-02-08T19:08:15.526425Z"
} | 84c7c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1714
},
"timestamp": "2026-02-18T21:17:46.397Z",
"answer": 32657
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
827739 | comb_count_partitions_v1_1978505735_7756 | Let $m = 2$, and let $\_n$ be the largest prime number $p$ such that $m \leq p \leq 42$. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = \_n$, $1 \leq i \leq 39$, and $1 \leq j \leq 39$. Compute the number of integer partitions of $n$. | 26,015 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_m")), Leq(Var("n1"), Const(42)), IsPrime(Var("n1"))))),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Su... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COUNT_SUM_EQUALS"
] | 06c6d1 | comb_count_partitions_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"MAX_PRIME_BELOW"
] | 2 | 0.008 | 2026-02-08T20:25:38.660817Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T20:25:38.668752Z"
} | 7a5d6d | 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": 1111
},
"timestamp": "2026-02-19T00:33:19.951Z",
"answer": 26015
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
976227 | sequence_fibonacci_compute_v1_971394319_241 | Let $F_{20}$ be the 20th Fibonacci number. Let $d$ be the smallest divisor of $2431$ that is at least $2$. Compute the Bell number $B_{F_{20} \bmod d}$, that is, the number of partitions of a set with $F_{20} \bmod d$ elements. | 1 | graphs = [
Graph(
let={
"n": Const(20),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2431))))))),
... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | sequence_fibonacci_compute_v1 | bell_mod | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T12:54:40.626459Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T12:54:40.627729Z"
} | 58e3ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 958
},
"timestamp": "2026-02-15T08:02:57.156Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
2a3427 | comb_sum_binomial_row_v1_1874849503_866 | Let $N = 75623$. Define $T$ as the set of all integers $t$ such that $10 \leq t \leq 36$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 2$, and $t = 4a + 6b$. Let $n$ be the number of elements in $T$. Define $P$ as the set of all positive integers $p$ such that there exists a posit... | 61,358 | graphs = [
Graph(
let={
"_n": Const(75623),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Va... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T13:22:57.547163Z | {
"verified": true,
"answer": 61358,
"timestamp": "2026-02-08T13:22:57.549461Z"
} | 0524d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 5406
},
"timestamp": "2026-02-09T21:57:29.981Z",
"answer": 61358
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"stat... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
ab25eb | modular_min_modexp_v1_655260480_1712 | Let $a = 2$ and let $b$ be the largest prime number $n$ such that $2 \leq n \leq 141$. Let $m$ be the largest positive divisor of $34933$ that is at most $181$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq 180$ and $2^x \equiv b \pmod{m}$. | 162 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(141)), IsPrime(Var("n"))))),
"m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var(... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"MAX_PRIME_BELOW",
"MAX_DIVISOR"
] | beffb0 | modular_min_modexp_v1 | null | 7 | 0 | [
"LIN_FORM",
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 3 | 0.058 | 2026-02-08T16:18:22.222362Z | {
"verified": true,
"answer": 162,
"timestamp": "2026-02-08T16:18:22.280035Z"
} | f6413d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 4173
},
"timestamp": "2026-02-17T01:14:10.658Z",
"answer": 162
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ece113 | antilemma_sum_equals_v1_784195855_5875 | Let $n$ be the number of ordered pairs $(i, j)$ where $i$ is an integer from 1 to 3 and $j$ is an integer from 1 to 9. Determine the value of $x$, the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 26$, $j \leq 27$, and $i + j = n$. | 26 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(9)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.018 | 2026-02-08T08:09:58.559776Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T08:09:58.578144Z"
} | 1ca2d1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 671
},
"timestamp": "2026-02-24T08:57:14.035Z",
"answer": 26
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
b9ab0e | nt_count_divisible_and_v1_865884756_3292 | Let $d_2$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 81$. Determine the number of positive integers $n$ such that $1 \leq n \leq 51696$, $n$ is divisible by $12$, and $n$ is divisible by $d_2$. | 1,436 | graphs = [
Graph(
let={
"upper": Const(51696),
"d1": Const(12),
"d2": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(81)))),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 1.658 | 2026-02-08T17:15:08.087438Z | {
"verified": true,
"answer": 1436,
"timestamp": "2026-02-08T17:15:09.745373Z"
} | 3686fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 664
},
"timestamp": "2026-02-17T23:31:20.517Z",
"answer": 1436
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
61e2c3 | nt_sum_over_divisible_v1_397696148_442 | Let $N = 62110$. Define $u$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 13122$. Define $d$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers satisfying $x + y = 10$. Let $s$ be the sum of all positive integers $n$ such that $1 \leq n ... | 19,945 | graphs = [
Graph(
let={
"_n": Const(62110),
"upper": 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... | NT | null | SUM | sympy | COMB1 | [
"COMB1",
"B1"
] | 12acf0 | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"B1",
"COMB1"
] | 2 | 0.425 | 2026-02-08T11:29:58.275242Z | {
"verified": true,
"answer": 19945,
"timestamp": "2026-02-08T11:29:58.700439Z"
} | 8faf32 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 3193
},
"timestamp": "2026-02-14T15:12:10.925Z",
"answer": 19945
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
183e37 | lin_form_endings_v1_458359167_1426 | Let $a = 21$, $b = 49$, $A = 55$, and $B = 39$. Let $g = \gcd(a, b)$. Define $n = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1$. Let $k = 13146$. Compute the remainder when $k \cdot n$ is divided by $96401$. | 48,376 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(49),
"A_val": Const(55),
"B_val": Const(39),
"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 | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:36:42.960142Z | {
"verified": true,
"answer": 48376,
"timestamp": "2026-02-08T04:36:42.961517Z"
} | 059f52 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 694
},
"timestamp": "2026-02-10T17:20:35.763Z",
"answer": 48376
},
{
"... | 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": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
0e816b | lin_form_endings_v1_1742523217_1019 | Let $a = 35$, $b = 21$, and $k = 189$. Let $d = \gcd(a, b)$ and $g = \gcd(k, d)$. Define $m = \left\lfloor \frac{k}{g} \right\rfloor$. Compute the remainder when $6817 \cdot m$ is divided by $78430$. | 27,199 | graphs = [
Graph(
let={
"a_coeff": Const(35),
"b_coeff": Const(21),
"k_val": Const(189),
"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(6... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:23:30.053832Z | {
"verified": true,
"answer": 27199,
"timestamp": "2026-02-08T03:23:30.054475Z"
} | e38aab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 746
},
"timestamp": "2026-02-10T02:09:57.122Z",
"answer": 27199
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"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": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
b8d592 | comb_sum_binomial_row_v1_168721529_1266 | Let $n = 5$. Let $S$ be the set of all positive integers $j$ such that $1 \leq j \leq 12$ and $j^n \leq 248832$. Let $N$ be the number of elements in $S$. Compute $2^N$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(12)), Leq(Pow(Var("j"), Ref("_n")), Const(248832))), domain='positive_integers')),
"result": Pow(Const(2), Ref("n")),
... | NT | null | SUM | sympy | C3 | [
"C3"
] | 8a214c | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"C3"
] | 1 | 0.002 | 2026-02-08T13:33:22.523098Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T13:33:22.524897Z"
} | 80658c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 814
},
"timestamp": "2026-02-09T15:05:54.173Z",
"answer": 4096
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.65,
"mid": -2.15,
"hi": 1.88
} | ||
a7ca43 | nt_num_divisors_compute_v1_53965629_92 | Let $n = 512$. Compute the number of positive divisors of $n$. Multiply this number by $28923$, and find the remainder when the product is divided by $98987$. | 91,256 | graphs = [
Graph(
let={
"n": Const(512),
"result": NumDivisors(n=Ref("n")),
"_c": Const(28923),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(98987)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"LTE_DIFF"
] | 1 | 0.008 | 2026-02-08T11:16:38.708606Z | {
"verified": true,
"answer": 91256,
"timestamp": "2026-02-08T11:16:38.717000Z"
} | ab067e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 315
},
"timestamp": "2026-02-09T12:07:53.152Z",
"answer": 91256
},
{
"i... | 2 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
42dbd6 | sequence_count_fib_divisible_v1_1353956133_335 | Let $d$ be the number of integers $t$ such that $10 \leq t \leq 30$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 6a + 4b$. Let $n$ be a positive integer such that $1 \leq n \leq 649$ and $d$ divides the $n$th Fibonacci number. Compute the number of such integers $n$. | 54 | graphs = [
Graph(
let={
"upper": Const(649),
"d": 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=V... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM",
"ONE_PHI_1"
] | 2 | 0.103 | 2026-02-08T11:25:08.401226Z | {
"verified": true,
"answer": 54,
"timestamp": "2026-02-08T11:25:08.504595Z"
} | d6e2b4 | 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": 1768
},
"timestamp": "2026-02-14T13:38:54.965Z",
"answer": 54
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b692c0 | nt_sum_divisors_mod_v1_397696148_850 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 32400$. Let $\sigma$ be the sum of the positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10729$. | 1,170 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10729)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T11:46:50.997937Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T11:46:50.999266Z"
} | 467fc5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 382
},
"timestamp": "2026-02-16T03:28:10.492Z",
"answer": 303
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
82873f | antilemma_k3_v1_677425708_1830 | Let $n = 21902$. Compute $\sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ of $n$ and $\phi$ is Euler's totient function. Let $x$ be the absolute value of this sum plus $2$. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $x$. | 8,436 | graphs = [
Graph(
let={
"_n": Const(21902),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T04:29:16.422600Z | {
"verified": true,
"answer": 8436,
"timestamp": "2026-02-08T04:29:16.423413Z"
} | 6dd7ba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 3134
},
"timestamp": "2026-02-10T01:40:26.665Z",
"answer": 16872
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
589e5d | comb_count_derangements_v1_1439011603_838 | Let $m = 66424$. Define a pair of positive integers $(p, q)$ to be good if $p \cdot q = 370440$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such good pairs. Let $!n$ denote the subfactorial of $n$, which is the number of derangements of $n$ elements. Let $Q$ be the remainder when $44121 \cdot (!n)$ is divi... | 37,545 | graphs = [
Graph(
let={
"_n": Const(66424),
"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=370440)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T15:46:36.599071Z | {
"verified": true,
"answer": 37545,
"timestamp": "2026-02-08T15:46:36.603245Z"
} | 8e3469 | 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": 2346
},
"timestamp": "2026-02-16T12:42:31.339Z",
"answer": 37545
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f3b81d | geo_visible_lattice_v1_677425708_843 | Compute the remainder when $33862$ times the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq 196$ is divided by $51539$. | 47,060 | graphs = [
Graph(
let={
"n": Const(196),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(33862), Ref("result")), modulus=Const(51539)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.814 | 2026-02-08T03:49:13.066157Z | {
"verified": true,
"answer": 47060,
"timestamp": "2026-02-08T03:49:13.880084Z"
} | f70112 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 21236
},
"timestamp": "2026-02-23T22:58:23.380Z",
"answer": 26399
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
02136d | nt_gcd_compute_v1_1248542787_522 | Let $p = 2$ and let $f = \Omega(p)$, where $\Omega(n)$ denotes the number of prime factors of $n$ counted with multiplicity. Define $n = 97f$. Let $m = \sum_{d \mid n} \mu(d)$, where $\mu$ is the M\"obius function. Let $a = 290580 + m$ and $b = 639276$. Compute $\gcd(a, b)$. | 58,116 | graphs = [
Graph(
let={
"p": Const(2),
"f": BigOmega(n=Ref(name='p')),
"n": Mul(Const(97), Ref("f")),
"m": SumOverDivisors(n=Ref(name='n'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"a": Sum(Const(290580), Ref("m")),
"b": Const(639276)... | NT | null | COMPUTE | sympy | BIG_OMEGA_ONE | [
"BIG_OMEGA_ONE",
"MOBIUS_SUM"
] | a0b0aa | nt_gcd_compute_v1 | null | 4 | 2 | [
"BIG_OMEGA_ONE",
"MOBIUS_SUM"
] | 2 | 0.003 | 2026-02-08T03:11:32.703677Z | {
"verified": true,
"answer": 58116,
"timestamp": "2026-02-08T03:11:32.706585Z"
} | b045f4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 477
},
"timestamp": "2026-02-09T05:05:22.364Z",
"answer": 58116
},
{
"i... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"stat... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
d8796e | antilemma_sum_equals_v1_655260480_3316 | Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 100$, $1 \leq j \leq 100$, and $i + j = 102$. Find the value of this number. | 99 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(102)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(100)), right=IntegerRange(start=Const(1), end=Const(100))))),
},
... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.003 | 2026-02-08T17:19:25.339066Z | {
"verified": true,
"answer": 99,
"timestamp": "2026-02-08T17:19:25.341696Z"
} | 2d40de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 548
},
"timestamp": "2026-02-17T23:41:07.461Z",
"answer": 99
},
{
... | 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",
... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
189e1b | comb_count_surjections_v1_548369836_355 | Let $T$ be the set of all integers $t$ such that $15 \leq t \leq 42$ and $t = 9a + 6b$ for some integers $a \in \{1, 2\}$ and $b \in \{1, 2, 3, 4\}$. Let $\ell$ be the number of elements in $T$. Let $S$ be the set of all ordered pairs $(i, j)$ with $1 \leq i \leq 6$ and $1 \leq j \leq 6$ such that $i + j = \ell$. Let $... | 120 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.013 | 2026-02-08T02:52:59.626986Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-02-08T02:52:59.639621Z"
} | 6050ed | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 309,
"completion_tokens": 845
},
"timestamp": "2026-02-08T20:22:38.053Z",
"answer": 120
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.98
} | ||
dfc618 | comb_count_derangements_v1_677425708_1365 | Let $a = 2$ and $b = 4$, and define $n_2 = a + b$. Let $m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = 0$ and $e = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Define $n = (7 + m) \cdot e$. Let $\text{result}$ be the subfactorial of $n$. Find the value of $\text{result}$. | 1,854 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(4),
"n2": Sum(Ref("a"), Ref("b")),
"m": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"e": Summat... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_derangements_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T04:07:29.835293Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T04:07:29.836287Z"
} | 51c1b6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 883
},
"timestamp": "2026-02-09T19:03:21.170Z",
"answer": 1854
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
e63c8c | alg_poly4_sum_v1_601307018_10201 | Let $T = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 30,\, 10a_1^2 - 18a_1b_1 + 25b_1^2 \le 4033 \}\right|$. Compute the remainder when
$$
\sum_{\substack{1 \le a \le T \\ 1 \le b \le 323}} \left( 257a^4 + 780a^3b + 918a^2b^2 + 540ab^3 + 162b^4 \right)
$$
is divided by $81048$. | 19,314 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=An... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_sum_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.267 | 2026-03-10T10:43:12.027724Z | {
"verified": true,
"answer": 19314,
"timestamp": "2026-03-10T10:43:12.295033Z"
} | 2d67da | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 9851
},
"timestamp": "2026-04-19T13:11:27.333Z",
"answer": 19314
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
6eac2f | comb_count_derangements_v1_601307018_4874 | Let $D_n$ denote the number of derangements of $n$ elements. Let $c = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, $n = 7c$, $M = 7$, $R = D_n$, $u = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, $S = u$, and $e = \sum_{k=0}^{S} (-1)^k \binom{S}{k}$. Compute $R$. | 1,854 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(5),
"n3": Sum(Ref("a"), Ref("b")),
"u": Summation(var="k", start=Sub(Binom(n=Const(17), k=Const(0)), Const(1)), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"n... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | comb_count_derangements_v1 | null | 4 | 3 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 0.003 | 2026-03-10T05:36:16.404426Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-03-10T05:36:16.407358Z"
} | fe289b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1242
},
"timestamp": "2026-03-29T13:44:11.409Z",
"answer": 1854
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
c37dd3 | lte_diff_endings_v1_153355830_642 | Let $a = 67$, $b = 11$, $p = 2$, $K = 7$, and $N = 939927$. Compute the value of
$$
\left\lfloor \frac{N}{p^{K - v_p(a - b)}} \right\rfloor,
$$
where $v_p(n)$ denotes the largest integer $k$ such that $p^k$ divides $n$. Compute the value of this expression. | 58,745 | graphs = [
Graph(
let={
"a_val": Const(67),
"b_val": Const(11),
"p_val": Const(2),
"K_val": Const(7),
"N_val": Const(939927),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_va... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 4 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T04:06:04.138954Z | {
"verified": true,
"answer": 58745,
"timestamp": "2026-02-08T04:06:04.139455Z"
} | 9467f0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 545
},
"timestamp": "2026-02-18T08:03:57.334Z",
"answer": 58745
}
] | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
210df8 | nt_sum_totient_over_divisors_v1_1520064083_405 | Let $n$ be the number of positive integers at most $6108$ whose digit sum is odd. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 3,055 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6108)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"result": SumOverDivisors(n=Ref(name='n'), var='d... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"L3B"
] | 1 | 0.003 | 2026-02-08T03:20:56.827165Z | {
"verified": true,
"answer": 3055,
"timestamp": "2026-02-08T03:20:56.830033Z"
} | a24b82 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1681
},
"timestamp": "2026-02-10T13:53:11.839Z",
"answer": 3055
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
0be5e3 | comb_count_derangements_v1_124444284_9537 | Let $n = \sum_{d\mid 7} \phi(d)$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(7),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | K3 | [
"K3"
] | 54c41e | comb_count_derangements_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T12:33:39.523919Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T12:33:39.524720Z"
} | 49271b | 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": 1269
},
"timestamp": "2026-02-15T02:21:56.488Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ba4eb6 | sequence_count_fib_divisible_v1_1742523217_3215 | Let $t$ be an integer. Define $S$ as the set of all integers $t$ such that $27 \le t \le 2097$ and there exist positive integers $a$ and $b$ with $1 \le a \le 33$, $1 \le b \le 234$, and $t = 21a + 6b$. Let $u$ be the number of elements in $S$.\\
Let $T$ be the set of all positive integers $n$ such that $1 \le n \le u... | 7,192 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=33)), Geq(left=Var(name='b'), right=Const(va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.03 | 2026-02-08T05:43:19.057370Z | {
"verified": true,
"answer": 7192,
"timestamp": "2026-02-08T05:43:19.087179Z"
} | ea1341 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 5643
},
"timestamp": "2026-02-12T13:32:08.879Z",
"answer": 7192
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
071178 | antilemma_k3_v1_153355830_1978 | Let $x = \sum_{d \mid 35290} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the value of $x + \phi(|x| + 1) + \tau(|x| + 1)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 70,582 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=35290), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Const(1)))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO",
"K3"
] | feee28 | antilemma_k3_v1 | null | 5 | 0 | [
"IDENTITY_POW_ZERO",
"K3"
] | 2 | 0.001 | 2026-02-08T06:50:28.735032Z | {
"verified": true,
"answer": 70582,
"timestamp": "2026-02-08T06:50:28.735885Z"
} | 9bfcea | 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": 1656
},
"timestamp": "2026-02-13T05:19:32.806Z",
"answer": 70582
},
... | 1 | [
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
78c66d | nt_sum_over_divisible_v1_1978505735_63 | Let $d$ be the largest prime number less than or equal to $116$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 11111$ and $n_1 \equiv 0 \pmod{d}$. Let $s$ be the sum of all elements in $S$. Compute the remainder when $44121 \cdot s$ is divided by $78350$. | 29,973 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(11111),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(116)), IsPrime(Var("n"))))),
"result": SumOverSet(set=SolutionsSet(var=Var("n1"),... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.353 | 2026-02-08T15:10:41.306489Z | {
"verified": true,
"answer": 29973,
"timestamp": "2026-02-08T15:10:41.659610Z"
} | c2832e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 3063
},
"timestamp": "2026-02-16T00:51:37.331Z",
"answer": 29973
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7a1743 | nt_count_coprime_v1_151522320_619 | Let $T$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ satisfying $1 \leq a \leq 7$, $1 \leq b \leq 10$, $7 \leq t \leq 61$, and $t = 3a + 4b$. Let $k$ denote the number of elements in $T$.\\
Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 44444$ and $\gcd(n,... | 38,095 | graphs = [
Graph(
let={
"upper": Const(44444),
"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=7)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 9.875 | 2026-02-08T03:25:41.778509Z | {
"verified": true,
"answer": 38095,
"timestamp": "2026-02-08T03:25:51.653600Z"
} | 23cea9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 2645
},
"timestamp": "2026-02-10T13:27:42.335Z",
"answer": 38095
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} |
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