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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
544cca | nt_count_divisible_and_v1_1742523217_2810 | Let $T$ be the set of all positive integers $t$ such that $t = 9a + 6b$ for some positive integers $a \leq 2$ and $b \leq 3$, and $15 \leq t \leq 36$. Let $d_1 = |T|$ and $d_2 = 10$. Let $N$ be the number of positive integers $n \leq 114360$ that are divisible by both $d_1$ and $d_2$. Compute the remainder when $88 - N... | 78,383 | graphs = [
Graph(
let={
"_n": Const(88),
"upper": Const(114360),
"d1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 6.154 | 2026-02-08T05:23:49.639594Z | {
"verified": true,
"answer": 78383,
"timestamp": "2026-02-08T05:23:55.793432Z"
} | ceb602 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 853
},
"timestamp": "2026-02-12T08:21:36.046Z",
"answer": 78383
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
896f8a | nt_count_divisors_in_range_v1_124444284_8644 | Let $n = 55440$, $a = 23$, and let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6370576$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 91 | graphs = [
Graph(
let={
"n": Const(55440),
"a": Const(23),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6370576)))), ... | NT | null | COUNT | sympy | V1 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B3",
"V1"
] | 2 | 0.094 | 2026-02-08T11:51:18.635595Z | {
"verified": true,
"answer": 91,
"timestamp": "2026-02-08T11:51:18.729762Z"
} | 26823e | 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": 2265
},
"timestamp": "2026-02-14T19:44:29.776Z",
"answer": 91
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1637d4 | comb_sum_binomial_row_v1_717093673_770 | Let $n$ be the largest prime number less than or equal to $14$. Compute the remainder when $44121 \cdot 2^n$ is divided by $56599$. | 54,617 | graphs = [
Graph(
let={
"_n": Const(14),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Pow(Const(2), Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T15:40:54.548686Z | {
"verified": true,
"answer": 54617,
"timestamp": "2026-02-08T15:40:54.550590Z"
} | c9cbad | 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": 1090
},
"timestamp": "2026-02-16T11:43:23.752Z",
"answer": 54617
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
95fe53 | nt_max_prime_below_v1_865884756_271 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $L = |P|$. Let $T$ be the set of all prime numbers $n$ such that $L \leq n \leq 42436$. Determine the value of the largest element in $T$. | 42,433 | graphs = [
Graph(
let={
"upper": Const(42436),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.269 | 2026-02-08T15:17:26.979349Z | {
"verified": true,
"answer": 42433,
"timestamp": "2026-02-08T15:17:29.248430Z"
} | a6a613 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 4570
},
"timestamp": "2026-02-10T06:24:43.044Z",
"answer": 42433
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
87ce9c | diophantine_product_count_v1_677425708_3406 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 16402500$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = n$. Determine the number of positive integers $x$ such that $1 \leq x \leq 16... | 88,242 | graphs = [
Graph(
let={
"_m": 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(16402500)))), expr=Sum(Var("x"), Var("y... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | diophantine_product_count_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.013 | 2026-02-08T05:41:24.689563Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T05:41:24.702803Z"
} | 240143 | 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": 3317
},
"timestamp": "2026-02-12T13:54:01.961Z",
"answer": 88242
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
554652 | comb_factorial_compute_v1_1218484723_2889 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 15$ such that
$$
17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 5640192.
$$
Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(68),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Eq(Sum(Mul(Const(102), Pow(Var("a"), Const(2)), Po... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_factorial_compute_v1 | null | 3 | 0 | [
"POLY4_COUNT"
] | 1 | 0.003 | 2026-02-25T04:39:22.812269Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T04:39:22.814791Z"
} | f4adce | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1104
},
"timestamp": "2026-03-29T07:09:22.953Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
3e837c | antilemma_cartesian_v1_1978505735_683 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 16$ and $1 \leq b \leq 18$. Find the remainder when $44121 \cdot x$ is divided by $91942$. | 18,852 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(18)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(91942)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T15:32:37.734130Z | {
"verified": true,
"answer": 18852,
"timestamp": "2026-02-08T15:32:37.735277Z"
} | c0845e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 633
},
"timestamp": "2026-02-24T17:57:33.245Z",
"answer": 18852
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
148f33 | diophantine_fbi2_count_v1_1520064083_4945 | Let $k = 120$ and $n = 81$. Let $r$ be the number of integers $d$ such that $5 \leq d \leq n$, $d$ divides $k$, and $3 \leq k/d \leq 79$. Let $d_{\min}$ be the smallest integer $d \geq 2$ that divides $1665595754747521$. Compute the value of $$r \mod 293 + 1009 \cdot (r \mod d_{\min}).$$ | 10,100 | graphs = [
Graph(
let={
"_n": Const(81),
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(R... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | diophantine_fbi2_count_v1 | two_moduli | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.007 | 2026-02-08T06:31:38.894284Z | {
"verified": true,
"answer": 10100,
"timestamp": "2026-02-08T06:31:38.901742Z"
} | 691c2c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 5097
},
"timestamp": "2026-02-13T01:04:05.457Z",
"answer": 10100
},
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
b7cd3c | comb_count_derangements_v1_1915831931_3114 | Let $m = 32771$. Let $T$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq 32771$ and $\binom{m}{j} \equiv 1 \pmod{d}$, where $d$ is the number of positive integers $p$ for which there exists an integer $q > p$ such that $pq = 18$ and $\gcd(p, q) = 1$. Let $n$ be the largest prime number less than or ... | 1,854 | graphs = [
Graph(
let={
"_m": Const(32771),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32771... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8/MAX_PRIME_BELOW"
] | 62a93c | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"V8"
] | 3 | 0.006 | 2026-02-08T17:22:12.648646Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T17:22:12.654642Z"
} | 79473f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1958
},
"timestamp": "2026-02-18T01:10:54.191Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ba9b3 | nt_sum_totient_over_divisors_v1_124444284_4218 | Let $n = 19013$. Define $r = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $T$ be the set of all integers $t$ such that $23 \leq t \leq 35$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b + 18$. Let $k$ be the number of elements in $T$. Com... | 52 | graphs = [
Graph(
let={
"n": Const(19013),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), conditi... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"LIN_FORM"
] | 1ae498 | nt_sum_totient_over_divisors_v1 | bell_mod | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.017 | 2026-02-08T05:51:39.782737Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T05:51:39.800184Z"
} | 5d7b07 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1137
},
"timestamp": "2026-02-12T15:32:25.672Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
29755a | comb_count_derangements_v1_151522320_1452 | Let $n$ be the smallest divisor of $847$ that is greater than or equal to $2$. Compute the subfactorial of $n$, denoted $!n$. | 1,854 | graphs = [
Graph(
let={
"_n": Const(847),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T04:01:46.809724Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T04:01:46.811156Z"
} | b6a56c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 660
},
"timestamp": "2026-02-10T15:12:49.579Z",
"answer": 1854
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
204223 | comb_count_partitions_v1_1915831931_2897 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 38$, $1 \leq j \leq 38$, and $i + j = 39$. Let $p(n)$ denote the number of integer partitions of $n$. Compute $p(n)$. | 26,015 | graphs = [
Graph(
let={
"_n": Const(39),
"n": 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(38)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_partitions_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T17:13:38.826416Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T17:13:38.836759Z"
} | fa9f38 | 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": 869
},
"timestamp": "2026-02-17T22:35:12.844Z",
"answer": 26015
},
{... | 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": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
1208ca | modular_count_residue_v1_153355830_1320 | Let $u = 60000$. Define $T$ to be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 24$. Let $m$ be the number of elements in $T$. Define $S$ to be the set of all positive integers $n$ such that $1 \leq n \leq u$ and $n \equiv 5 \pmod{m}$. Let $r$ be the number of elements in $S$... | 54,422 | graphs = [
Graph(
let={
"upper": Const(60000),
"m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2"... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_count_residue_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 2.027 | 2026-02-08T06:19:00.033465Z | {
"verified": true,
"answer": 54422,
"timestamp": "2026-02-08T06:19:02.060538Z"
} | df1c6b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1033
},
"timestamp": "2026-02-12T23:01:09.176Z",
"answer": 54422
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8cf93e | sequence_lucas_compute_v1_865884756_2267 | Let $S$ be the set of all positive integers $t$ such that $16 \leq t \leq 70$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 4$, and $t = 6a + 10b$. Let $n$ be the number of elements in $S$.
Compute the $n$-th Lucas number.
Find the value of this number. | 15,127 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:39:52.077373Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T16:39:52.079368Z"
} | 0f7392 | 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": 1319
},
"timestamp": "2026-02-17T09:50:53.379Z",
"answer": 15127
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
784cfb | nt_count_coprime_and_v1_865884756_6542 | Let $T$ be the set of all integers $t$ with $8 \leq t \leq 72$ such that there exist positive integers $a$, $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 9$, and $t = 3a + 5b$.
Let $k_1$ be the number of positive integers $n$ such that $1 \leq n \leq |T|$, $3$ divides $n$, and $\gcd(n, 14) = 1$.
Let $k_2 = 16$.
Let $r$... | 1,712 | graphs = [
Graph(
let={
"_n": Const(14),
"upper": Const(44016),
"k1": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/C5"
] | 683493 | nt_count_coprime_and_v1 | null | 6 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 4.218 | 2026-02-08T19:17:13.929921Z | {
"verified": true,
"answer": 1712,
"timestamp": "2026-02-08T19:17:18.147517Z"
} | 2e85c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 3832
},
"timestamp": "2026-02-18T21:50:27.675Z",
"answer": 1712
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
389118 | comb_binomial_compute_v1_655260480_4196 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 2$ and $1 \leq j \leq 9$ such that $\gcd(i, j) = 1$. Compute the remainder when $44121 \cdot \binom{n}{6}$ is divided by $99614$. | 8,743 | graphs = [
Graph(
let={
"_n": Const(99614),
"n": 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(2)), right=IntegerRange(start=Const(1), en... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | comb_binomial_compute_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.002 | 2026-02-08T17:48:04.463101Z | {
"verified": true,
"answer": 8743,
"timestamp": "2026-02-08T17:48:04.465436Z"
} | 534192 | 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": 865
},
"timestamp": "2026-02-18T08:41:33.475Z",
"answer": 8743
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2393aa | lin_form_endings_v1_1520064083_8730 | Let $T$ be the set of all integers $t$ such that $100 \leq t \leq 2340$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 35$, $1 \leq b \leq 9$, and
$$
t = 56a + 42b + 2.
$$
Let $r$ be the number of elements in $T$.
Compute the remainder when $16845 \cdot r$ is divided by $54883$. | 31,474 | graphs = [
Graph(
let={
"_inner_result": 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=35)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T10:20:44.603061Z | {
"verified": true,
"answer": 31474,
"timestamp": "2026-02-08T10:20:44.606056Z"
} | 835ef8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 8046
},
"timestamp": "2026-02-24T11:57:16.659Z",
"answer": 31474
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
c0799e | nt_count_divisible_v1_168721529_1048 | Let $N$ be the number of positive integers $n$ such that $n \leq 41616$ and $n$ is divisible by 12. Let $S$ be the set of positive integers $j$ such that $j \leq 337$ and $j^4 \leq 12897917761$. Compute the value of $$N \bmod 293 + 1009 \cdot (N \bmod |S|).$$ | 99,127 | graphs = [
Graph(
let={
"upper": Const(41616),
"divisor": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"_c": C... | NT | null | COUNT | sympy | C3 | [
"C3"
] | 015077 | nt_count_divisible_v1 | two_moduli | 3 | 0 | [
"C3"
] | 1 | 1.539 | 2026-02-08T13:26:00.895097Z | {
"verified": true,
"answer": 99127,
"timestamp": "2026-02-08T13:26:02.434246Z"
} | 3c7387 | 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": 1585
},
"timestamp": "2026-02-09T13:11:48.203Z",
"answer": 99127
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
6f0335 | nt_lcm_compute_v1_1978505735_1757 | Let $a = 1821$ and $b = 949$. Define $L = \mathrm{lcm}(a, b)$. Let
$$
P = \max\{ n \mid 2 \le n \le 98 \text{ and } n \text{ is prime} \}.
$$
Compute
$$
Q = \left( 353702 \cdot (L \bmod P) + 329703 \cdot \left( (L^2 + 1) \bmod 101 \right) + 215534 \cdot \left( (L + 9) \bmod 103 \right) \right) \bmod 1009091.
$$
Find th... | 70,375 | graphs = [
Graph(
let={
"a": Const(1821),
"b": Const(949),
"result": LCM(a=Ref("a"), b=Ref("b")),
"_c": Const(9),
"Q": Mod(value=Sum(Mul(Const(353702), Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), conditi... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 045f57 | nt_lcm_compute_v1 | crt_mix_3 | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T16:23:27.792998Z | {
"verified": true,
"answer": 70375,
"timestamp": "2026-02-08T16:23:27.796909Z"
} | c5e9e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1957
},
"timestamp": "2026-02-17T02:22:54.407Z",
"answer": 70375
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b1b6df | modular_product_range_v1_865884756_261 | Let $m = 16$ and $n = 83475$. Define $\text{prod}$ to be the product $\prod_{i=m}^{86} i$. Let $r$ be the remainder when $\text{prod}$ is divided by $10667$. Let $c$ be the largest prime number between $2$ and $42$, inclusive. Compute the remainder when
\[
353702 \cdot (|r| \bmod 97) + 329703 \cdot \left(|r|^2 + 1 \bmo... | 64,493 | graphs = [
Graph(
let={
"_m": Const(16),
"_n": Const(83475),
"prod": MathProduct(expr=Var("i"), var="i", start=Ref("_m"), end=Const(86)),
"result": Mod(value=Ref("prod"), modulus=Const(10667)),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condit... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"MAX_DIVISOR"
] | 8bb558 | modular_product_range_v1 | crt_mix_3 | 4 | 0 | [
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 2 | 0.013 | 2026-02-08T15:17:23.459607Z | {
"verified": true,
"answer": 64493,
"timestamp": "2026-02-08T15:17:23.473005Z"
} | 1c45a2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 4946
},
"timestamp": "2026-02-16T02:59:37.937Z",
"answer": 64493
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d2273a | sequence_fibonacci_compute_v1_717093673_1343 | Let $m = 6$. Consider the set of ordered pairs $(k, j)$ where $k$ ranges from 1 to 6 and $j$ ranges from 1 to 9. For each such $k$, define the value $\varphi(k) \left\lfloor \frac{m}{k} \right\rfloor$, where $\varphi$ denotes Euler's totient function. Let $n$ be $\frac{6}{54}$ times the sum of these values over all suc... | 13,292 | graphs = [
Graph(
let={
"_m": Const(6),
"n": Div(Mul(Const(6), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Con... | NT | null | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"K2"
] | d64c9f | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.003 | 2026-02-08T16:00:41.012768Z | {
"verified": true,
"answer": 13292,
"timestamp": "2026-02-08T16:00:41.016076Z"
} | 12f9f3 | 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": 1590
},
"timestamp": "2026-02-16T18:55:21.776Z",
"answer": 13292
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6bfd76 | sequence_count_fib_divisible_v1_865884756_4058 | Compute the number of positive integers $n$ at most $691$ such that $15$ divides the $n$th Fibonacci number. | 34 | graphs = [
Graph(
let={
"upper": Const(691),
"d": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | LIN_FORM | [
"COMB1/COMB1",
"B3"
] | 07dce9 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"COMB1",
"LIN_FORM"
] | 3 | 0.175 | 2026-02-08T17:43:36.824789Z | {
"verified": true,
"answer": 34,
"timestamp": "2026-02-08T17:43:37.000034Z"
} | e16e3f | 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": 1654
},
"timestamp": "2026-02-18T06:51:53.575Z",
"answer": 34
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
095ae0 | diophantine_sum_product_min_v1_784195855_8521 | Let $m = 4163$. Define $P$ to be $12$ plus the number of nonnegative integers $j \leq m$ for which the binomial coefficient $\binom{4163}{j}$ is odd. Let $S = 16$. Find the smallest positive integer $x$ such that $1 \leq x \leq 1 + 2 + 3 + 4 + 5$ and $x(S - x) = P$. Multiply this $x$ by 39926 and compute the result.
F... | 79,852 | graphs = [
Graph(
let={
"_m": Const(4163),
"_n": Const(5),
"S": Const(16),
"P": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Const(4163), k=Var("j")), modulus=Const(2)), C... | ALG | COMB | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"V8"
] | 912956 | diophantine_sum_product_min_v1 | null | 7 | 0 | [
"SUM_ARITHMETIC",
"V8"
] | 2 | 0.005 | 2026-02-08T16:08:39.393744Z | {
"verified": true,
"answer": 79852,
"timestamp": "2026-02-08T16:08:39.398973Z"
} | e120c7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 780
},
"timestamp": "2026-02-24T20:03:43.922Z",
"answer": 79852
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
16bd78 | comb_count_derangements_v1_655260480_1828 | Let $m = 95913$ and $n = 7$. Let $j$ range over the positive integers from 1 to $n$, inclusive, such that $j^4$ does not exceed the number of positive integers $n_1$ from 1 to 4803 inclusive for which the sum of the decimal digits of $n_1$ is even. Let $\nu$ be the number of such $j$.
Let $r$ be the number of derangem... | 80,494 | graphs = [
Graph(
let={
"_m": Const(95913),
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(4)), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n... | COMB | null | COUNT | sympy | L3B | [
"L3B/C3"
] | 16113d | comb_count_derangements_v1 | null | 4 | 0 | [
"C3",
"L3B"
] | 2 | 0.003 | 2026-02-08T16:26:13.206032Z | {
"verified": true,
"answer": 80494,
"timestamp": "2026-02-08T16:26:13.208583Z"
} | 2a1f38 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 3502
},
"timestamp": "2026-02-24T20:57:17.964Z",
"answer": 80494
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
98ed67 | modular_count_residue_v1_458359167_1174 | Let $ r = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor $, where $ \phi $ denotes Euler's totient function. Let $ m = 18 $ and $ N = 71824 $. Compute the number of positive integers $ n $ such that $ 1 \leq n \leq N $ and $ n \equiv r \pmod{m} $. | 3,990 | graphs = [
Graph(
let={
"upper": Const(71824),
"m": Const(18),
"r": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | modular_count_residue_v1 | null | 5 | 0 | [
"K2"
] | 1 | 4.347 | 2026-02-08T04:26:17.845856Z | {
"verified": true,
"answer": 3990,
"timestamp": "2026-02-08T04:26:22.192988Z"
} | 913ade | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 873
},
"timestamp": "2026-02-10T16:52:45.136Z",
"answer": 3990
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
7f41f7 | nt_euler_phi_compute_v1_1918700295_126 | Let $g = 11$, $m = 7$, and $n_2 = 10$. Define $a = g \cdot m$ and $b = g \cdot n_2$. Let $e = \sum_{d \mid \gcd(a,b)} \mu(d)$. Let $n_1 = 20$ and $c = \left( \sum_{d \mid n_1} \phi(d) \right) - n_1$. Define $n = 78400 + c$ and let $\phi(n)$ be the value of Euler's totient function at $n$. Compute the remainder when $(4... | 15,442 | graphs = [
Graph(
let={
"g": Const(11),
"m": Const(7),
"n2": Const(10),
"a": Mul(Ref("g"), Ref("m")),
"b": Mul(Ref("g"), Ref("n2")),
"e": SumOverDivisors(n=GCD(a=Ref(name='a'), b=Ref(name='b')), var='d', expr=MoebiusMu(n=Var(name='d')))... | NT | null | COMPUTE | sympy | EULER_TOTIENT_SUM | [
"EULER_TOTIENT_SUM",
"MOBIUS_COPRIME"
] | 0bcbf0 | nt_euler_phi_compute_v1 | null | 5 | 2 | [
"EULER_TOTIENT_SUM",
"MOBIUS_COPRIME"
] | 2 | 0.001 | 2026-02-08T03:00:42.101157Z | {
"verified": true,
"answer": 15442,
"timestamp": "2026-02-08T03:00:42.102129Z"
} | e9b2c0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 5174
},
"timestamp": "2026-02-08T23:02:50.457Z",
"answer": 15442
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"stat... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
e8aa04 | nt_count_divisors_in_range_v1_1520064083_7690 | Let $n = 110880$. Define $a$ as the number of positive integers $n'$ with $1 \leq n' \leq 131$ such that $\gcd(n', 30) = 1$. Let $b = 10083$. Let $d$ range over the positive divisors of $n$. Define $\mathcal{S}$ as the set of all such divisors $d$ satisfying $a \leq d \leq b$. Let $Q = \sum_{k=1}^{|\mathcal{S}|} \phi(k... | 3,716 | graphs = [
Graph(
let={
"_n": Const(131),
"n": Const(110880),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(30)), Const(1))))),
"b": Const(10083),
"resul... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.092 | 2026-02-08T09:14:39.447384Z | {
"verified": true,
"answer": 3716,
"timestamp": "2026-02-08T09:14:39.539602Z"
} | 48820a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 3745
},
"timestamp": "2026-02-14T02:09:06.481Z",
"answer": 3716
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dea6c9 | nt_sum_over_divisible_v1_153355830_2179 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 56169$ and $n \equiv \sum_{k=0}^{5} (-1)^k \binom{5}{k} \pmod{167}$. Let $r$ be the sum of all elements in $S$. Compute the remainder when $42811 \cdot r$ is divided by $94632$. | 43,368 | graphs = [
Graph(
let={
"upper": Const(56169),
"divisor": Const(167),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Summation(var="k", start=Const(0),... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 1.802 | 2026-02-08T06:57:34.120518Z | {
"verified": true,
"answer": 43368,
"timestamp": "2026-02-08T06:57:35.922961Z"
} | 9ce9c1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T07:27:39.399Z",
"answer": 43368
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
ffa31c | nt_min_with_divisor_count_v1_2051736721_2320 | Let $n = 8$. Let $S$ be the set of all ordered pairs $(k, \_j)$ of positive integers with $1 \le k \le 3$ and $1 \le \_j \le 5$. Let $T$ be the set of all values of $k$ as $(k, \_j)$ ranges over $S$. Define
$$
div\_count = \frac{n \cdot \left(\sum T\right)}{40}.
$$
Let $U$ be the set of all positive integers $n$ such t... | 12 | graphs = [
Graph(
let={
"_n": Const(8),
"upper": Const(13689),
"div_count": Div(Mul(Ref("_n"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3))... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME",
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 3 | 9.64 | 2026-02-08T16:34:24.072301Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T16:34:33.711933Z"
} | f42352 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1255
},
"timestamp": "2026-02-17T08:32:35.992Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "... | {
"lo": -7.08,
"mid": -0.32,
"hi": 6.26
} | ||
ceabdb | geo_count_lattice_rect_v1_784195855_7844 | Let $a = 66$ and $b = 122$. Define a lattice point as a point in the plane with integer coordinates. Consider the rectangle consisting of all points $(x, y)$ such that $0 \le x \le a$ and $0 \le y \le b$. Compute the number of lattice points in this rectangle. | 8,241 | graphs = [
Graph(
let={
"a": Const(66),
"b": Const(122),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T09:33:22.651962Z | {
"verified": true,
"answer": 8241,
"timestamp": "2026-02-08T09:33:22.653067Z"
} | aa5d7b | 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": 305
},
"timestamp": "2026-02-24T11:30:26.327Z",
"answer": 8241
},
{
"id... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
ced87c | comb_catalan_compute_v1_151522320_706 | Let $N$ be the number of integers $t$ such that $11 \leq t \leq 6126$ and $t = 4a + 7b$ for some positive integers $a$ and $b$ with $1 \leq a \leq 1150$ and $1 \leq b \leq 218$. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = N$. Let $R = C_{10}$, where $C_n$ denotes ... | 82,610 | 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=1150)), Geq(left=Var(name='b'), right=Const(val... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 3b3567 | comb_catalan_compute_v1 | affine_mod | 5 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T03:27:52.517707Z | {
"verified": true,
"answer": 82610,
"timestamp": "2026-02-08T03:27:52.521803Z"
} | 0d262e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 2232
},
"timestamp": "2026-02-23T22:21:16.814Z",
"answer": 65814
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": ... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
4ec995 | comb_catalan_compute_v1_655260480_4283 | Let $n = 10$. Define $\text{result} = C_n$, where $C_n$ is the $n$-th Catalan number. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 16928$. Let $Q$ be the remainder when $c - \text{result}$ is divided by $94418$. Determine the value of $Q$. | 86,086 | graphs = [
Graph(
let={
"_n": Const(16928),
"n": Const(10),
"result": Catalan(Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | comb_catalan_compute_v1 | negation_mod | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T17:51:57.994553Z | {
"verified": true,
"answer": 86086,
"timestamp": "2026-02-08T17:51:57.997046Z"
} | 681f7b | 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": 883
},
"timestamp": "2026-02-18T08:49:14.589Z",
"answer": 86086
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
01a6f2 | modular_mod_compute_v1_1520064083_7589 | Let $a = \sum_{k=1}^{6} k$. Let $m = 27889$. Define $r$ to be the remainder when $a$ is divided by $m$, so $r = a \bmod m$. Let $Q = \sum_{n=1}^{r} \phi(n)$, where $\phi(n)$ denotes Euler's totient function. Compute $Q$. | 140 | graphs = [
Graph(
let={
"a": Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")),
"m": Const(27889),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": Summation(var="n", start=Const(1), end=Abs(arg=Ref(name='result')), expr=EulerPhi(n=Var("n"))... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_mod_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T09:10:40.534688Z | {
"verified": true,
"answer": 140,
"timestamp": "2026-02-08T09:10:40.536169Z"
} | a3fc51 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 824
},
"timestamp": "2026-02-14T01:29:45.959Z",
"answer": 140
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
50586e | alg_poly4_sum_v1_1218484723_1205 | Find the remainder when
$$
\sum_{\substack{1 \le a \le 146 \\ 1 \le b \le 146}} \left( \min\{ d \ge 2 : d \mid 4634945206559 \} \cdot a^{4} + 337 b^{4} - 700 a^{3} b - 700 a b^{3} + \left| \{1,2,\ldots,6\} \times \{1,2,\ldots,337\} \right| \cdot a^{2} b^{2} \right)
$$
is divided by $72199$. | 61,297 | graphs = [
Graph(
let={
"_n": Const(146),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(146)))), expr=Sum(Mul(MinOv... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COUNT_CARTESIAN"
] | fea473 | alg_poly4_sum_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN",
"MIN_PRIME_FACTOR"
] | 2 | 0.065 | 2026-02-25T02:59:02.184886Z | {
"verified": true,
"answer": 61297,
"timestamp": "2026-02-25T02:59:02.249955Z"
} | d8bbbe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T06:07:29.217Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
... | {
"lo": 3.79,
"mid": 5.69,
"hi": 7.81
} | ||
804964 | alg_qf_psd_min_v1_1218484723_6485 | For positive integers $a, b$ with $1 \le a, b \le 200$, define $E(a, b) = 11798 \cdot a^k + 20126 \cdot b^2 - 18044ab$, where $k$ is the number of ordered pairs $(a1, b1)$ with $1 \le a1, b1 \le 15$ satisfying
$$
82b1^4 + 540a1^2b1^2 + 216a1^3b1 + 162a1^4 + 312a1b1^3 = 1683712.
$$
Find the minimum value of $E(a, b)$ ov... | 13,880 | graphs = [
Graph(
let={
"_n": Const(200),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(200)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")))), expr=Sum(Mul(Const(11798), P... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"POLY4_COUNT"
] | 1 | 0.07 | 2026-02-25T08:03:08.090446Z | {
"verified": true,
"answer": 13880,
"timestamp": "2026-02-25T08:03:08.160336Z"
} | 19afdb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 13131
},
"timestamp": "2026-03-30T01:55:34.359Z",
"answer": 13880
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
5a1aaa | algebra_vieta_sum_v1_865884756_5740 | Let $N$ be the number of integers $n$ with $1\le n\le 57024$ such that
$$n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}.$$
Consider the quartic equation
$$2x^4+2x^3-216x^2-72x+N=0.$$
Let $P$ be the product of all integer roots $x$ of this equation. Compute $P$. | 2,592 | graphs = [
Graph(
let={
"_n": Const(2),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Ref(name='_n'), Pow(base=Var(name='x'), exp=Const(value=4))), Mul(Const(value=2), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=-216), Pow(ba... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"L3C"
] | 73f8b0 | algebra_vieta_sum_v1 | null | 8 | 0 | [
"L3C",
"MIN_PRIME_FACTOR"
] | 2 | 0.062 | 2026-02-08T18:46:04.609067Z | {
"verified": true,
"answer": 2592,
"timestamp": "2026-02-08T18:46:04.671122Z"
} | ce63e6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1894
},
"timestamp": "2026-02-18T19:25:05.633Z",
"answer": 2592
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e68076 | antilemma_sum_equals_v1_1125832087_411 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 51$, $1 \leq i \leq 50$, and $1 \leq j \leq 51$. Compute $x^2 + 20x + 6724$. | 10,224 | graphs = [
Graph(
let={
"_n": Const(51),
"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(50)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.007 | 2026-02-08T03:02:56.988659Z | {
"verified": true,
"answer": 10224,
"timestamp": "2026-02-08T03:02:56.995523Z"
} | c24bd1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1091
},
"timestamp": "2026-02-10T12:34:48.956Z",
"answer": 10224
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
2bf0b9 | comb_count_surjections_v1_865884756_7131 | Let $n = 4$ and $k = 4$. Define $s$ to be the number of ways to partition a set of $n$ elements into exactly $k$ nonempty subsets, multiplied by $k!$. Compute the value of $37 - s$. | 13 | graphs = [
Graph(
let={
"n": Const(4),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Sub(Const(37), Ref("result")),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | 8ec7d9 | comb_count_surjections_v1 | negation_mod | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.022 | 2026-02-08T19:38:02.341176Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T19:38:02.363156Z"
} | 2d95e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 524
},
"timestamp": "2026-02-18T22:53:19.637Z",
"answer": 13
},
{
... | 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": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
afe758 | comb_count_surjections_v1_124444284_2641 | Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3\}$. Let $k = 2$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the smallest positive integer such that the $Q$-th Fibonacci number is divisible by $|\t... | 48 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(3)))),
"k": Const(2),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
... | COMB | NT | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_surjections_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:52:05.933674Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T04:52:05.934907Z"
} | f3d382 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 3984
},
"timestamp": "2026-02-24T02:08:56.059Z",
"answer": 48
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
559110 | lte_diff_endings_v1_168721529_1904 | Let $a = 325$, $b = 1$, $p = 3$, and $n = 378$. Compute $a^n - b^n$ and determine the largest integer $k$ such that $p^k$ divides this difference. Multiply $k$ by $11457$ and find the remainder when the result is divided by $82301$. Compute this remainder. | 80,199 | graphs = [
Graph(
let={
"a_val": Const(325),
"b_val": Const(1),
"p_val": Const(3),
"n_val": Const(378),
"a_pow": Pow(Ref("a_val"), Ref("n_val")),
"b_pow": Pow(Ref("b_val"), Ref("n_val")),
"pow_diff": Sub(Ref("a_pow"), Ref("b... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T13:58:44.650233Z | {
"verified": true,
"answer": 80199,
"timestamp": "2026-02-08T13:58:44.651508Z"
} | 11fd17 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1370
},
"timestamp": "2026-02-09T23:15:02.913Z",
"answer": 80199
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
53c4f1 | nt_lcm_compute_v1_397696148_1293 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1183744$. For each such pair, compute $x + y$, and let $a$ be the smallest value of $x + y$ over all such pairs. Let $b = 714$. Compute $\operatorname{lcm}(a, b)$. | 45,696 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1183744)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(714)... | NT | null | COMPUTE | sympy | LIN_FORM | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.02 | 2026-02-08T12:29:44.633880Z | {
"verified": true,
"answer": 45696,
"timestamp": "2026-02-08T12:29:44.653775Z"
} | 0d6e88 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1764
},
"timestamp": "2026-02-15T01:27:42.557Z",
"answer": 45696
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
519c45 | modular_modexp_compute_v1_601307018_1789 | Let $a$ be the largest prime number $n$ in the range $2 \le n \le 30$. Let $L = \left|\left\{ n_1 \in \mathbb{Z}^+ : 1 \le n_1 \le 224,\ n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{7} \right\}\right|$. Let $e$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = L$.... | 16,321 | graphs = [
Graph(
let={
"_m": Const(224),
"_n": Const(30),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"L3C/B1"
] | 5af77e | modular_modexp_compute_v1 | null | 6 | 0 | [
"B1",
"L3C",
"MAX_PRIME_BELOW"
] | 3 | 0.004 | 2026-03-10T02:32:21.924541Z | {
"verified": true,
"answer": 16321,
"timestamp": "2026-03-10T02:32:21.928688Z"
} | acdb9f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 2635
},
"timestamp": "2026-03-29T03:24:20.481Z",
"answer": 16321
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"sta... | {
"lo": -2.48,
"mid": 1.07,
"hi": 4.5
} | ||
cd0ede | comb_binomial_compute_v1_784195855_4065 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 15$, $1 \leq j \leq 16$, and $i + j = 16$. Compute $\binom{n}{8}$. | 6,435 | graphs = [
Graph(
let={
"_n": Const(16),
"n": 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(15)), right=IntegerRange(start=Const(1), end=Con... | ALG | COMB | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_binomial_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T06:47:52.457904Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T06:47:52.467607Z"
} | c8dc84 | 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": 565
},
"timestamp": "2026-02-24T07:05:31.902Z",
"answer": 6435
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
63437c_n | alg_qf_psd_min_v1_1218484723_3057 | A vending machine accepts tokens worth $2$ or $5$ points. A valid score is any total $t$ between $7$ and $312$ that can be made using at least one token of each type, with no more than $31$ of the $2$-point tokens and $50$ of the $5$-point tokens. Let $B$ be the number of valid scores. A robot plays a game where it sel... | 85,068 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_qf_psd_min_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.13 | 2026-02-25T04:49:15.950714Z | null | 7ef31c | 63437c | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 26574
},
"timestamp": "2026-03-30T19:29:15.783Z",
"answer": 85068
},
{
... | 2 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
0ebe6d | nt_count_divisible_v1_124444284_8203 | Let $p$ be the largest prime number less than or equal to 21. Let $N = 42849$. Find the number of positive integers $n$ such that $1 \leq n \leq N$ and $n$ is divisible by $p$. | 2,255 | graphs = [
Graph(
let={
"_n": Const(21),
"upper": Const(42849),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), co... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_divisible_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.357 | 2026-02-08T09:36:03.245939Z | {
"verified": true,
"answer": 2255,
"timestamp": "2026-02-08T09:36:05.603238Z"
} | e00331 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 347
},
"timestamp": "2026-02-15T20:46:52.031Z",
"answer": 2255
},
{
"id": 11,
... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
2a63ba | nt_count_intersection_v1_151522320_797 | Let $N = 5000$. Define $S$ as the set of all integers $n$ such that $1 \leq n \leq N$, $7$ divides $n$, and $\gcd(n, 18) = 1$. Let $a$ be the number of elements in $S$. Let $b$ be the number of positive integers $n \leq 60552$ such that $7$ divides the $n$-th Fibonacci number. Compute the value of $2^{|a|} \bmod 99991$... | 56,398 | graphs = [
Graph(
let={
"N": Const(5000),
"a": Const(7),
"b": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Re... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 03e0f1 | nt_count_intersection_v1 | two_stage_modexp | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.361 | 2026-02-08T03:32:19.976797Z | {
"verified": true,
"answer": 56398,
"timestamp": "2026-02-08T03:32:20.337509Z"
} | 70d69d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 7505
},
"timestamp": "2026-02-23T20:46:39.408Z",
"answer": 56398
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
ae641d | modular_mod_compute_v1_2051736721_668 | Let $m = 164$ and $n = 51033$. Define $a = -38416$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq m$ and $n \equiv 0 \pmod{m}$. Define $u$ to be the sum of all elements in $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = u$. Define $m'$ to be the m... | 24,341 | graphs = [
Graph(
let={
"_m": Const(164),
"_n": Const(51033),
"a": Const(-38416),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/B1"
] | f6d1e2 | modular_mod_compute_v1 | null | 6 | 0 | [
"B1",
"SUM_DIVISIBLE"
] | 2 | 0.004 | 2026-02-08T15:37:30.539969Z | {
"verified": true,
"answer": 24341,
"timestamp": "2026-02-08T15:37:30.543911Z"
} | cfc8bb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1307
},
"timestamp": "2026-02-16T10:00:12.013Z",
"answer": 24341
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f1446d | antilemma_k3_v1_153355830_178 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $82585$, where $\phi$ denotes Euler's totient function. | 82,585 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=82585), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T02:55:41.471409Z | {
"verified": true,
"answer": 82585,
"timestamp": "2026-02-08T02:55:41.472009Z"
} | 07c1a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 457
},
"timestamp": "2026-02-10T11:51:36.624Z",
"answer": 82585
},
{
"i... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.97,
"mid": -1.31,
"hi": 0.9
} | ||
a4ac8f | nt_sum_divisors_compute_v1_1742523217_1187 | Let $c=81401$. Consider all positive integers $p$ and $q$ such that $pq=18$, $\gcd(p,q)=1$, and $p<q$. Let $d$ be the number of such integers $p$. For each integer $j$ with $0 \le j \le 66561$, consider the binomial coefficient $\binom{66561}{j}$, and let $T$ be the number of integers $j$ with $0 \le j \le 66561$ such ... | 77,120 | graphs = [
Graph(
let={
"_c": Const(81401),
"_m": Const(7),
"_n": Const(2),
"n1": Const(1),
"v": SmallOmega(n=Ref(name='n1')),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Sum(Coun... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8/MAX_PRIME_BELOW/WILSON",
"OMEGA_ZERO"
] | 3484ed | nt_sum_divisors_compute_v1 | null | 7 | 2 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"OMEGA_ZERO",
"V8",
"WILSON"
] | 5 | 0.01 | 2026-02-08T03:29:50.561836Z | {
"verified": true,
"answer": 77120,
"timestamp": "2026-02-08T03:29:50.571467Z"
} | 19b1de | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 380,
"completion_tokens": 6865
},
"timestamp": "2026-02-10T04:45:30.737Z",
"answer": 77120
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "OMEGA_ZERO",... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
a3f024 | geo_count_lattice_triangle_v1_548369836_361 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(111,196)$, and $(22,111)$, multiplied by $2$. Let $B$ be the sum of the greatest common divisors of the absolute differences of the coordinates along each side of the triangle, that is,
$$
B = \gcd(111, 196) + \gcd(|22 - 111|, |111 - 196|) + \gcd(|0 - 22|,... | 2,670 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=111)), Mul(Const(value=22), Sub(left=Const(value=0), right=Const(value=196))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const(value=196))), GCD(a=Abs(arg=Sub(left=Const(value=22), rig... | NT | null | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 7 | 0 | null | null | 0.002 | 2026-02-08T02:53:18.539324Z | {
"verified": true,
"answer": 2670,
"timestamp": "2026-02-08T02:53:18.541567Z"
} | 415aa6 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 585
},
"timestamp": "2026-02-09T05:19:28.536Z",
"answer": 12
},
... | 0 | [] | {
"lo": 2.59,
"mid": 6.26,
"hi": 10
} | ||||
3bdee9 | modular_mod_compute_v1_784195855_1423 | Let $m$ be the number of integers $t$ such that $27 \leq t \leq 19743$ and there exist positive integers $a \leq 1589$ and $b \leq 45$ satisfying $t = 12a + 15b$. Compute the remainder when $-11449$ is divided by $m$. | 1,673 | graphs = [
Graph(
let={
"a": Const(-11449),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=1589)), Geq(left... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:00:56.125345Z | {
"verified": true,
"answer": 1673,
"timestamp": "2026-02-08T05:00:56.126538Z"
} | 58af86 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 5469
},
"timestamp": "2026-02-11T22:41:15.473Z",
"answer": 1673
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
41afcd | antilemma_k3_v1_1915831931_2577 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $81802$, where $\phi$ denotes Euler's totient function. Let $r$ be the remainder when $|x|$ is divided by $11$. Compute the $r$-th Bell number. | 203 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=81802), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:57:47.044649Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T16:57:47.045257Z"
} | 0cc92c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 526
},
"timestamp": "2026-02-17T17:10:00.426Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
558955 | nt_count_divisors_in_range_v1_898971024_312 | Let $a$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 36$. Let $b$ be the minimum value of $x_1 + y_1$ where $x_1$ and $y_1$ are positive integers such that $xy = 3415104$. Let $n = 277200$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 130 | graphs = [
Graph(
let={
"_n": Const(36),
"n": Const(277200),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), exp... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.067 | 2026-02-08T15:20:10.248247Z | {
"verified": true,
"answer": 130,
"timestamp": "2026-02-08T15:20:10.314811Z"
} | 99cc1c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 4285
},
"timestamp": "2026-02-16T03:20:07.846Z",
"answer": 130
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ec648f | antilemma_sum_equals_v1_784195855_3978 | Let $m=3698$. For integers $a$ and $b$ with $1\le a\le 12$ and $1\le b\le 6$, consider all integers $t$ with $5\le t\le 42$ that can be written in the form
$$t=2a+3b$$
for some such $a$ and $b$. Let $n$ be the number of such integers $t$.
Let $x$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le 35$, ... | 1,814 | graphs = [
Graph(
let={
"_m": Const(3698),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=12)), Geq(left=V... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS",
"COMB1",
"COUNT_SUM_EQUALS"
] | efb6cd | antilemma_sum_equals_v1 | negation_mod | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.009 | 2026-02-08T06:43:45.370899Z | {
"verified": true,
"answer": 1814,
"timestamp": "2026-02-08T06:43:45.379568Z"
} | f88baa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 2995
},
"timestamp": "2026-02-24T06:55:49.215Z",
"answer": 1814
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"sta... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
6d527d | sequence_fibonacci_compute_v1_601307018_2102 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $5a^2 + 10ab + 5b^2 = \min\{x + y : x > 0, y > 0, xy = 1464100\}$. Let $S = F_n$, the $n$-th Fibonacci number. Find the remainder when $62223 \cdot S$ is divided by $82666$. | 7,784 | graphs = [
Graph(
let={
"_m": Const(25),
"_n": Const(10),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_m")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(5), ... | ALG | null | COMPUTE | sympy | B3 | [
"B3/QF_PSD_COUNT"
] | d7caca | sequence_fibonacci_compute_v1 | null | 7 | 0 | [
"B3",
"QF_PSD_COUNT"
] | 2 | 0.008 | 2026-03-10T02:48:44.710799Z | {
"verified": true,
"answer": 7784,
"timestamp": "2026-03-10T02:48:44.719064Z"
} | 3e16fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1998
},
"timestamp": "2026-03-29T04:21:51.499Z",
"answer": 7784
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
adce9a | nt_count_digit_sum_v1_124444284_9940 | Let $C$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq 18496$ and $\binom{18496}{j}$ is odd. Let $t = |C|$. Let $D$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = t$. Let $P$ be the set of all values $xy$ where $(x,y) \in D$. Let $m$ be the largest element of $P$. L... | 20,270 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(267289),
"target_sum": Const(34),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
... | ALG | COMB | COUNT | sympy | V8 | [
"V8/B1"
] | 5644f0 | nt_count_digit_sum_v1 | mod_exp | 7 | 0 | [
"B1",
"V8"
] | 2 | 12.167 | 2026-02-08T12:43:50.701645Z | {
"verified": true,
"answer": 20270,
"timestamp": "2026-02-08T12:44:02.868491Z"
} | e07e35 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 28635
},
"timestamp": "2026-02-24T16:19:19.155Z",
"answer": 20270
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lem... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
ee457f | nt_count_gcd_equals_v1_865884756_2109 | Let $k = 428$ and $d = 2$. Determine the number of positive integers $n$ such that $1 \leq n \leq 28657$ and $\gcd(n, k) = d$. Denote this number by $r$. Let $m$ be the smallest divisor of $31603$ that is at least $2$. Compute the Bell number $B_s$, where $s$ is the remainder when $|r|$ is divided by $m$. | 2 | graphs = [
Graph(
let={
"_n": Const(31603),
"upper": Const(28657),
"k": Const(428),
"d": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_gcd_equals_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 6.648 | 2026-02-08T16:30:11.452289Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:30:18.100389Z"
} | ff2762 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1448
},
"timestamp": "2026-02-17T05:18:41.307Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
262843 | nt_sum_totient_over_divisors_v1_458359167_5444 | Let $n = 49866$. Define $\text{result}$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Compute the remainder when $44121 \cdot \text{result}$ is divided by $58108$. | 52,690 | graphs = [
Graph(
let={
"n": Const(49866),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(58108)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V5"
] | e79893 | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"LIN_FORM",
"V5"
] | 2 | 0.021 | 2026-02-08T12:30:02.892389Z | {
"verified": true,
"answer": 52690,
"timestamp": "2026-02-08T12:30:02.913589Z"
} | e1a0d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 2542
},
"timestamp": "2026-02-15T02:01:10.946Z",
"answer": 52690
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ba479d | algebra_quadratic_discriminant_v1_1820931509_185 | Let $a = -10$, $b = \sum_{k=1}^{2} k$, and $c = 6$. Let $P$ be the set of all positive integers $p$ for which there exists an integer $q$ such that $p < q$, $pq = 54$, and $\gcd(p, q) = 1$. Compute $b^{|P|} - 4ac$. Find the value of this expression. | 249 | graphs = [
Graph(
let={
"a": Const(-10),
"b": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"c": Const(6),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(na... | NT | null | COMPUTE | sympy | K2 | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | ac053f | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.014 | 2026-02-08T11:24:01.894076Z | {
"verified": true,
"answer": 249,
"timestamp": "2026-02-08T11:24:01.908383Z"
} | 4dd7cc | 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": 845
},
"timestamp": "2026-02-14T13:09:54.819Z",
"answer": 249
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"statu... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
3b2752 | antilemma_sum_equals_v1_677425708_634 | Let $N$ be the number of integers $t$ such that $12 \leq t \leq 129$ and there exist integers $a$ and $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 12$, and $t = 5a + 7b$. Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 94$, $1 \leq j \leq 94$, and $i + j = N$. Compute $$\sum_{... | 439 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS",
"ONE_BINOM_N"
] | f9469e | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM",
"ONE_BINOM_N"
] | 3 | 0.019 | 2026-02-08T03:38:05.814740Z | {
"verified": true,
"answer": 439,
"timestamp": "2026-02-08T03:38:05.834184Z"
} | e7c9ac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T22:40:25.805Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
dddedc | nt_count_coprime_v1_1918700295_4269 | Let $n$ be a positive integer such that $1 \leq n \leq 24025$ and $\gcd(n, 4) = 1$. Let $R$ be the number of such integers $n$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9604$. Define $T$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the remainder wh... | 35,262 | graphs = [
Graph(
let={
"upper": Const(24025),
"k": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
"Q": Mod(value=Sum(Pow(Ref("re... | NT | null | COUNT | sympy | B3 | [
"B3"
] | d720b5 | nt_count_coprime_v1 | quadratic_mod | 5 | 0 | [
"B3"
] | 1 | 3.692 | 2026-02-08T09:16:08.789338Z | {
"verified": true,
"answer": 35262,
"timestamp": "2026-02-08T09:16:12.481514Z"
} | 069c70 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1515
},
"timestamp": "2026-02-14T02:19:26.065Z",
"answer": 35262
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a1bfe6 | modular_count_residue_v1_124444284_5183 | Let $T$ be the set of all positive integers $t$ such that $5 \leq t \leq 26$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $m$ be the number of elements in $T$. Let $R$ be the set of all ordered pairs $(i,j)$ such that $1 \leq i \leq 18$, $1 \leq j \leq 19$... | 1,638 | graphs = [
Graph(
let={
"_n": Const(20),
"upper": Const(32768),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), ri... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 7b3310 | modular_count_residue_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 4.526 | 2026-02-08T06:26:04.204099Z | {
"verified": true,
"answer": 1638,
"timestamp": "2026-02-08T06:26:08.730190Z"
} | a933ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1611
},
"timestamp": "2026-02-13T01:03:03.678Z",
"answer": 1638
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a27d6f | nt_min_coprime_above_v1_1520064083_1196 | Let $s$ be the largest prime number $n$ such that $2 \leq n \leq 2160$. Let $m$ be the smallest integer $n$ such that $n > s$, $n \leq 2465$, and $\gcd(n, 302) = 1$. Determine the value of $m$. | 2,155 | graphs = [
Graph(
let={
"start": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(2160)), IsPrime(Var("n"))))),
"upper": Const(2465),
"modulus": Const(302),
"result": MinOverSet(set=SolutionsSet(var=Var("n"),... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.05 | 2026-02-08T03:50:02.696139Z | {
"verified": true,
"answer": 2155,
"timestamp": "2026-02-08T03:50:02.746150Z"
} | 002308 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 3370
},
"timestamp": "2026-02-10T16:03:06.245Z",
"answer": 2155
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
650801 | comb_sum_binomial_row_v1_1218484723_1643 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 25$ such that $2b^2 + 2a^2 - 4ab = 242$. Compute $2^n$, where $n$ is this number. | 16,384 | graphs = [
Graph(
let={
"_n": Const(25),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(2), Pow(... | COMB | null | SUM | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.001 | 2026-02-25T03:20:40.875949Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-25T03:20:40.877436Z"
} | e66692 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 501
},
"timestamp": "2026-03-29T00:39:40.302Z",
"answer": 16384
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
3614bc | antilemma_k3_v1_1248542787_737 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $67846$. Compute the remainder when $37633x$ is divided by $60572$. | 17,574 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=67846), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(37633), Ref("x")), modulus=Const(60572)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:21:36.046675Z | {
"verified": true,
"answer": 17574,
"timestamp": "2026-02-08T03:21:36.047254Z"
} | 228789 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1374
},
"timestamp": "2026-02-09T20:32:53.756Z",
"answer": 17574
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
f2e2dd | algebra_poly_eval_v1_898971024_168 | Let $y$ be the number of prime numbers in the interval $[2, 23]$. Compute the value of
\[
\frac{24y^5 + 14y^4 - 39y^3 + 4y^2 + 5y - 36}{31}.
\] | 47,772 | graphs = [
Graph(
let={
"_n": Const(3),
"y": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(23)), IsPrime(Var("n"))))),
"result": Div(Sum(Mul(Const(24), Pow(Ref("y"), Const(5))), Mul(Const(14), Pow(Ref("y"), Const(4)... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | algebra_poly_eval_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.004 | 2026-02-08T15:15:50.193665Z | {
"verified": true,
"answer": 47772,
"timestamp": "2026-02-08T15:15:50.197274Z"
} | 5c7e01 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 835
},
"timestamp": "2026-02-16T02:41:15.192Z",
"answer": 47772
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f013b5 | nt_count_intersection_v1_655260480_4170 | Let $N = 10000$. Consider the set of all positive integers $n$ such that $1 \leq n \leq N$, $11$ divides $n$, and $\gcd(n, 15) = 1$. Let $c$ be the number of such integers.
Let $P$ be the set of all prime numbers $p$ such that $2 \leq p \leq 3559$. Let $d$ be the number of elements in $P$.
Compute the remainder when ... | 3,668 | graphs = [
Graph(
let={
"_n": Const(3559),
"N": Const(10000),
"a": Const(11),
"b": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=V... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 0edcc2 | nt_count_intersection_v1 | two_moduli | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.354 | 2026-02-08T17:46:56.967295Z | {
"verified": true,
"answer": 3668,
"timestamp": "2026-02-08T17:46:57.321563Z"
} | 99c383 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 2603
},
"timestamp": "2026-02-18T07:48:00.942Z",
"answer": 3668
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7f40c3 | nt_count_divisible_and_v1_153355830_2762 | Let $d_1$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 24$. Let $d_2 = 18$.
Determine the number of positive integers $n$ such that $n \leq 133056$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 3,696 | graphs = [
Graph(
let={
"_n": Const(24),
"upper": Const(133056),
"d1": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 9.291 | 2026-02-08T07:19:51.213800Z | {
"verified": true,
"answer": 3696,
"timestamp": "2026-02-08T07:20:00.505022Z"
} | 163a0f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 511
},
"timestamp": "2026-02-15T18:58:30.195Z",
"answer": 3695
},
{
"id": 11,
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "V7",
"status":... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
2f7fa3 | algebra_poly_eval_v1_809748730_1436 | Let $m = 11$. Compute
$$
\max\{n \mid 2 \leq n \leq 6,\ n\ \text{is prime}\} \cdot m^3 - 2m^2 - 5m - 8.
$$
Let $r$ be the absolute value of this result, and define $n = r + 2$. The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Find the smallest positive integer $k$... | 2,388 | graphs = [
Graph(
let={
"m": Const(11),
"result": Sum(Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6)), IsPrime(Var("n"))))), Pow(Ref("m"), Const(3))), Mul(Const(-2), Pow(Ref("m"), Const(2))), Mul(Const(-5), Ref("m")), Const... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T12:25:38.575131Z | {
"verified": true,
"answer": 2388,
"timestamp": "2026-02-08T12:25:38.576673Z"
} | b1e3d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 2799
},
"timestamp": "2026-02-15T01:17:01.114Z",
"answer": 2388
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e5a610 | modular_sum_quadratic_residues_v1_601307018_4777 | Let $p$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 427812$. Compute $\frac{p(p - 1)}{4}$. | 53,015 | graphs = [
Graph(
let={
"_n": Const(4),
"p": 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(427812)))), expr=Abs(arg=Sub(left=Var(name='... | NT | null | SUM | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"B3_DIFF"
] | 1 | 0.003 | 2026-03-10T05:28:08.716994Z | {
"verified": true,
"answer": 53015,
"timestamp": "2026-03-10T05:28:08.720206Z"
} | 6485ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 12232
},
"timestamp": "2026-03-29T13:26:05.478Z",
"answer": 6271268
},
{... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
4d3ce3 | comb_binomial_compute_v1_1353956133_369 | Let $n$ be the number of positive integers $j$ at most $14$ such that $j^d \leq 537824$, where $d$ is the smallest divisor of $4235$ that is at least $2$. Let $k = \sum_{k=1}^{3} k$. Compute $\binom{n}{k}$. | 3,003 | graphs = [
Graph(
let={
"_m": Const(4235),
"_n": Const(14),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/C3",
"SUM_ARITHMETIC"
] | 8ab5e0 | comb_binomial_compute_v1 | null | 5 | 0 | [
"C3",
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 3 | 0.003 | 2026-02-08T11:25:41.586631Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T11:25:41.589418Z"
} | 321b1d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 973
},
"timestamp": "2026-02-14T13:42:32.608Z",
"answer": 3003
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"sta... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e32a58 | geo_visible_lattice_v1_601307018_597 | For each integer $a$ with $0 \le a \le 960$, define $M = (a^2 + 394) \bmod 961$, $R = (M^2 + 394) \bmod 961$, $S = (R^2 + 394) \bmod 961$, and $T = (S^2 + 394) \bmod 961$. Let $n$ be the number of such $a$ for which $T = a$, $M \ne a$, $R \ne a$, and $S \ne a$. Compute the number of lattice points $(x,y)$ with $1 \le x... | 2,203 | graphs = [
Graph(
let={
"_n": Const(394),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(960)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a"))))),
... | GEOM | GEOM | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | geo_visible_lattice_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.09 | 2026-03-10T01:07:24.362685Z | {
"verified": true,
"answer": 2203,
"timestamp": "2026-03-10T01:07:24.452266Z"
} | 092a6c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T23:33:30.027Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
}
] | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
db55c0 | comb_catalan_compute_v1_655260480_118 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 17$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Define $C_n$ to be the $n$th Catalan number. Compute the remainder when $89971 \cdot C_n$ is divided by $97494$. | 83,200 | 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=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.019 | 2026-02-08T15:13:16.043773Z | {
"verified": true,
"answer": 83200,
"timestamp": "2026-02-08T15:13:16.063203Z"
} | e7fb7c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 6210
},
"timestamp": "2026-02-24T20:20:30.308Z",
"answer": 83200
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
691ece | modular_mod_compute_v1_1918700295_4497 | Let $a = 49729$, $m = 86436$, and $n_0 = 85555$. Let $r$ be the remainder when $a$ is divided by $m$. Let $c$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 186$. Let $Q$ be the remainder when $c - r$ is divided by $n_0$. Find the value of $Q$. | 44,475 | graphs = [
Graph(
let={
"_n": Const(85555),
"a": Const(49729),
"m": Const(86436),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(a... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | modular_mod_compute_v1 | negation_mod | 3 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T09:24:45.263345Z | {
"verified": true,
"answer": 44475,
"timestamp": "2026-02-08T09:24:45.264715Z"
} | ee45e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 532
},
"timestamp": "2026-02-14T04:03:20.805Z",
"answer": 44475
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
10e3a6 | nt_count_divisible_and_v1_124444284_7176 | Let $N$ be the number of positive integers $n$ such that $1 \le n \le 132012$, $n$ is divisible by $12$, and the remainder when $n$ is divided by $18$ equals $\sum_{k=0}^{7} (-1)^k \binom{7}{k}$. Find $N$. | 3,667 | graphs = [
Graph(
let={
"upper": Const(132012),
"d1": Const(12),
"d2": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 4.388 | 2026-02-08T08:54:26.313622Z | {
"verified": true,
"answer": 3667,
"timestamp": "2026-02-08T08:54:30.701901Z"
} | 46d20e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1005
},
"timestamp": "2026-02-24T10:07:12.986Z",
"answer": 3667
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
621782 | geo_count_lattice_rect_v1_1526740231_80 | Let $a = 121$ and $b = 157$. Define a lattice point as a point $(x, y)$ in the plane where both $x$ and $y$ are integers. Compute the number of lattice points in the rectangle defined by $0 \leq x \leq a$ and $0 \leq y \leq b$. | 19,276 | graphs = [
Graph(
let={
"a": Const(121),
"b": Const(157),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T11:20:42.738272Z | {
"verified": true,
"answer": 19276,
"timestamp": "2026-02-08T11:20:42.738986Z"
} | 289f86 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 274
},
"timestamp": "2026-02-24T13:22:40.388Z",
"answer": 19276
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
8b38b3 | nt_min_with_divisor_count_v1_784195855_6284 | Let $ m = 4 $ and $ n = 2 $. Consider all pairs of positive integers $ (x, y) $ such that $ x + y = m $. Let $ P $ be the set of all values of $ xy $ for such pairs. Let $ d $ be the largest prime number $ p $ satisfying $ n \leq p \leq \max(P) $. Now let $ S $ be the set of positive integers $ k $ such that $ 1 \leq k... | 4 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"upper": Const(53824),
"div_count": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"),... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"B1/MAX_PRIME_BELOW"
] | 2fc9f0 | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"B1",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 2.628 | 2026-02-08T08:32:14.124589Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T08:32:16.752811Z"
} | 20e0c5 | 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": 531
},
"timestamp": "2026-02-13T19:32:40.318Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
c5257d | antilemma_sum_equals_v1_124444284_9855 | Let $S$ be the set of all ordered pairs $(i,j)$ of integers such that $1 \le i \le 19$, $1 \le j \le 19$, and $i + j = 20$. Let $x$ be the number of elements in $S$. Compute $\sum_{n=1}^{x} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 60 | graphs = [
Graph(
let={
"_n": Const(20),
"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(19)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T12:42:15.410461Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T12:42:15.420700Z"
} | 0f648f | 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": 1207
},
"timestamp": "2026-02-24T16:14:05.630Z",
"answer": 60
},
{
"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_SUM",
"status":... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
8a3cce | geo_count_lattice_triangle_v1_458359167_4122 | Let $A$ be the area of the triangle with vertices at $(100, 64)$, $(24, 111)$, and $(0, 0)$, multiplied by 2. Let $B$ be the number of lattice points on the boundary of this triangle, computed using the formula
\[
B = \gcd(100, 64) + \gcd(|24 - 100|, |111 - 64|) + \gcd(|0 - 24|, |0 - 111|).
\]
Compute the quantity
\[
\... | 4,779 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=111)), Mul(Const(value=24), Sub(left=Const(value=0), right=Const(value=64))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(value=64))), GCD(a=Abs(arg=Sub(left=Const(value=24), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.003 | 2026-02-08T11:32:03.513441Z | {
"verified": true,
"answer": 4779,
"timestamp": "2026-02-08T11:32:03.516118Z"
} | afbd6d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 868
},
"timestamp": "2026-02-14T15:28:00.812Z",
"answer": 4779
},
{
... | 1 | [] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||||
084a19_n | modular_modexp_compute_v1_601307018_2651 | A game designer creates a puzzle where two players must pick positive integers $x$ and $y$ such that their product is exactly $684$. The score is the absolute difference $|x - y|$, and the goal is to minimize this score. Let $a$ be the smallest possible score. The system then computes $M = a^{128} \bmod 84100$ as a sec... | 83,907 | NT | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | modular_modexp_compute_v1 | null | 4 | null | [
"B3_DIFF"
] | 1 | 0.002 | 2026-03-10T03:19:10.998354Z | null | c92d30 | 084a19 | narrative | 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": 7455
},
"timestamp": "2026-03-29T16:29:08.823Z",
"answer": 83907
},
{
"... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
e1c8e6 | diophantine_product_count_v1_153355830_471 | Let $n = 21$ and $k = 240$. Define
$$
S = \sum_{i=1}^{21} \phi(i) \left\lfloor \frac{21}{i} \right\rfloor.
$$
Let $T$ be the number of positive integers $x$ such that $1 \leq x \leq S$, $x$ divides $k$, and $\frac{k}{x} \leq S$.
Compute $T$. | 18 | graphs = [
Graph(
let={
"_n": Const(21),
"k": Const(240),
"upper": Summation(var="k", start=Const(1), end=Const(21), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | diophantine_product_count_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.01 | 2026-02-08T03:07:30.832988Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T03:07:30.843204Z"
} | 6c0cd1 | 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": 3827
},
"timestamp": "2026-02-10T12:54:29.832Z",
"answer": 18
},
{
"id"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
c7683d | nt_sum_divisors_mod_v1_2051736721_4959 | Let $n = 27720$, and let $\sigma$ denote the sum of all positive divisors of $n$. Let $M = 11257$, and define $r$ to be the remainder when $\sigma$ is divided by $M$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1951169220$, $\gcd(p, q) = 1$, and $p < q$.... | 32,573 | graphs = [
Graph(
let={
"n": Const(27720),
"M": Const(11257),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(30), Ref("result")), CountOverSet(set=So... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 14fbb8 | nt_sum_divisors_mod_v1 | quadratic_mod | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T18:17:00.367300Z | {
"verified": true,
"answer": 32573,
"timestamp": "2026-02-08T18:17:00.369310Z"
} | a3003f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 4389
},
"timestamp": "2026-02-18T15:59:05.833Z",
"answer": 32573
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ede4e2_n | modular_sum_quadratic_residues_v1_601307018_2589 | Two positive numbers $x$ and $y$ multiply to $147773833$. Let $D$ be the smallest possible value of $|x - y|$. Let $R$ be the largest prime number not exceeding $D$. A device generates values of the form $50a^2 - 90ab + 41b^2$ where $a$ and $b$ are integers from $1$ to $14$. Let $p$ be how many distinct positive output... | 7,439 | NT | null | SUM | sympy | B3_DIFF | [
"B3_DIFF/MAX_PRIME_BELOW/QF_PSD_DISTINCT"
] | 2d97d2 | modular_sum_quadratic_residues_v1 | null | 7 | null | [
"B3_DIFF",
"MAX_PRIME_BELOW",
"QF_PSD_DISTINCT"
] | 3 | 0.009 | 2026-03-10T03:16:45.592188Z | null | eab7dd | ede4e2 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T16:28:22.323Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{... | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
494acc | nt_min_coprime_above_v1_1978505735_2425 | Let $n$ be a positive integer. Define $A$ as the set of all positive integers $n$ such that $1 \leq n \leq 11369$ and $\gcd(n, 20) = 1$. Let $S$ be the number of elements in $A$. Determine the smallest integer $n_1$ such that $4096 < n_1 \leq S$ and $\gcd(n_1, 442) = 1$. | 4,099 | graphs = [
Graph(
let={
"_n": Const(11369),
"start": Const(4096),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"modulus": Const(442),
... | NT | null | EXTREMUM | sympy | C4 | [
"C4"
] | 08d162 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.041 | 2026-02-08T16:53:28.436250Z | {
"verified": true,
"answer": 4099,
"timestamp": "2026-02-08T16:53:28.476852Z"
} | 5948b0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1224
},
"timestamp": "2026-02-17T14:03:05.840Z",
"answer": 4099
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
358d04 | antilemma_sum_equals_v1_1520064083_3425 | Let $m = 40$. Determine the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = m$. Call this number $n$. Now consider the set of all ordered pairs $(i, j)$ where $1 \leq i \leq 19$ and $1 \leq j \leq 20$. Compute the number of such pairs for which $i + j = n$. | 19 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.043 | 2026-02-08T05:39:08.258404Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T05:39:08.301073Z"
} | 966128 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1921
},
"timestamp": "2026-02-24T04:16:41.745Z",
"answer": 19
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
d655af | comb_binomial_compute_v1_1218484723_1179 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 7496644$. Let $k$ be the number of ordered pairs $(a, b)$ with $1 \le a, b \le 30$ satisfying
$$
27b^3 + 108a b^2 + 64a^3 + C \cdot a^2 b = 551368,
$$
where $C$ is the number of pairs $(a_1, b_1)$ with $1 \le a_... | 76,361 | graphs = [
Graph(
let={
"_m": Const(25),
"_n": Const(30),
"n": Const(15),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/POLY3_COUNT",
"B3"
] | bc07bb | comb_binomial_compute_v1 | negation_mod | 7 | 0 | [
"B3",
"POLY3_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.008 | 2026-02-25T02:58:08.813191Z | {
"verified": true,
"answer": 76361,
"timestamp": "2026-02-25T02:58:08.820854Z"
} | 0c5502 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 307,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T00:11:30.717Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"... | {
"lo": 0.8,
"mid": 3.7,
"hi": 5.71
} | ||
89261d | comb_binomial_compute_v1_1218484723_4458 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that $-56a^3 - 6ab^2 + 36a^2b = -728$. Let $M = \binom{12}{k}$. Find the remainder when $44121 \cdot M$ is divided by $54083$. | 6,214 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": Const(12),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Mul(Const(-5... | COMB | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | comb_binomial_compute_v1 | null | 4 | 0 | [
"POLY3_COUNT"
] | 1 | 0.002 | 2026-02-25T06:05:36.578874Z | {
"verified": true,
"answer": 6214,
"timestamp": "2026-02-25T06:05:36.580607Z"
} | 5108a5 | 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": 3141
},
"timestamp": "2026-03-29T15:49:09.202Z",
"answer": 6214
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "n... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
ee6246 | sequence_count_fib_divisible_v1_1918700295_2772 | Let $u = 674$ and $d = 10$. Determine the number of positive integers $n$ such that $1 \leq n \leq 674$ and the $n$th Fibonacci number is divisible by $10$. | 44 | graphs = [
Graph(
let={
"upper": Const(674),
"d": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"SUM_DIVISIBLE"
] | 02dbe3 | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"SUM_DIVISIBLE"
] | 2 | 0.18 | 2026-02-08T08:12:06.078471Z | {
"verified": true,
"answer": 44,
"timestamp": "2026-02-08T08:12:06.258866Z"
} | 6f8131 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 1301
},
"timestamp": "2026-02-13T15:46:39.283Z",
"answer": 44
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c1ce94 | sequence_count_fib_divisible_v1_865884756_3628 | Let $n = 5717$. Define $\text{upper}$ to be the number of prime numbers $p$ such that $2 \leq p \leq n$. Let $d = 13$. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \leq \text{upper}$ and $d$ divides the $n_1$-th Fibonacci number. | 107 | graphs = [
Graph(
let={
"_n": Const(5717),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"d": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), condit... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.051 | 2026-02-08T17:31:30.143524Z | {
"verified": true,
"answer": 107,
"timestamp": "2026-02-08T17:31:30.194894Z"
} | 5d5697 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 2189
},
"timestamp": "2026-02-18T03:34:52.880Z",
"answer": 107
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5f866a | comb_binomial_compute_v1_124444284_6961 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 324$. Let $s_1$ be the minimum value of $x + y$ as $(x, y)$ ranges over $P$. Now, let $Q$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = s_1$. Let $s_2$ be the minimum value of $x + y$ as $(x, y)$ ranges... | 792 | 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(324)))), expr=Sum(Var("x"), Var("y")))),
"n": MinOverSet(se... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | comb_binomial_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T08:44:00.572272Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T08:44:00.573998Z"
} | 7aa143 | 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": 786
},
"timestamp": "2026-02-24T09:58:36.108Z",
"answer": 792
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
320547 | nt_count_divisors_in_range_v1_1526740231_192 | Let $T$ be the set of all positive integers $t$ such that $10 \leq t \leq 2548$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 630$, $1 \leq b \leq 94$, and $t = 3a + 7b$. Let $m = |T|$. Let $P$ be the set of all prime numbers $n$ such that $2 \leq n \leq m$. Define $p_{\text{max}}$ to be the maximum... | 76,659 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(20160),
"a": Const(8),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condi... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.027 | 2026-02-08T11:23:38.464625Z | {
"verified": true,
"answer": 76659,
"timestamp": "2026-02-08T11:23:38.491419Z"
} | c93d74 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 6925
},
"timestamp": "2026-02-14T13:08:28.703Z",
"answer": 76659
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
328f45 | antilemma_k2_v1_1742523217_4480 | Compute the value of $$\sum_{k=1}^{166} \phi(k) \left\lfloor \frac{166}{k} \right\rfloor.$$ | 13,861 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(166), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(166), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T07:19:00.728702Z | {
"verified": true,
"answer": 13861,
"timestamp": "2026-02-08T07:19:00.729117Z"
} | 0821c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 594
},
"timestamp": "2026-02-13T09:20:09.062Z",
"answer": 13861
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2863c0 | alg_poly_orbit_hensel_v1_1218484723_3268 | Define a sequence modulo $1681$ by $N = a^2 + 694 \bmod 1681$, $M = N^2 + 694 \bmod 1681$, and $R = M^2 + 694 \bmod 1681$. Find the number of non-negative integers $a$ with $0 \leq a \leq 159694$ such that $R = a$, $N \neq a$, and $M \neq a$. | 285 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(694)), modulus=Const(1681)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(694)), modulus=Const(1681)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(694)), modulus=Const(1681)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 4 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.029 | 2026-02-25T04:58:31.664150Z | {
"verified": true,
"answer": 285,
"timestamp": "2026-02-25T04:58:31.692839Z"
} | 536bd7 | 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": 9832
},
"timestamp": "2026-03-29T09:16:38.997Z",
"answer": 285
},
{
"id... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
99b596 | comb_factorial_compute_v1_1526740231_23 | Let $\mathcal{P}$ be the set of all positive integers $p$ for which there exists an integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m = 18$ and define $\ell$ to be the number of elements in $\mathcal{P}$. Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 20482$ and $\binom{... | 61,407 | graphs = [
Graph(
let={
"_m": Const(20482),
"_n": Const(76371),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Const(20482), k=Var("j")), modulus=CountOverSet(set=SolutionsSet(var=Var(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8"
] | 93b9b8 | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.003 | 2026-02-08T11:18:33.297611Z | {
"verified": true,
"answer": 61407,
"timestamp": "2026-02-08T11:18:33.300612Z"
} | f92bd2 | 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": 2386
},
"timestamp": "2026-02-14T11:50:07.966Z",
"answer": 61407
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"le... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2b055b | comb_factorial_compute_v1_1439011603_1928 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 39$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{5}$. Compute the value of $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(39),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=5))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | comb_factorial_compute_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T16:23:14.265353Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T16:23:14.267203Z"
} | 9dfb39 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 862
},
"timestamp": "2026-02-17T01:45:14.505Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5dc96d | diophantine_fbi2_min_v1_458359167_4506 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 1296$. Let $S$ be the set of integers $d$ such that $2 \leq d \leq 82$, $d$ divides $k$, and $\frac{k}{d} \geq 7$. Define $r$ to be the smallest element of $S$. Let $T$ be the set of integers $t$ with $10 \leq t... | 31 | graphs = [
Graph(
let={
"_n": Const(1296),
"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")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | ad075d | diophantine_fbi2_min_v1 | negation_mod | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.032 | 2026-02-08T11:49:17.962483Z | {
"verified": true,
"answer": 31,
"timestamp": "2026-02-08T11:49:17.994391Z"
} | feab16 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 2040
},
"timestamp": "2026-02-14T20:04:57.667Z",
"answer": 31
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0e16c2 | nt_sum_divisors_mod_v1_124444284_5781 | Let $n$ be the number of positive integers $t$ such that $25 \leq t \leq 270$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 106$, and $t = 7a + 2b + 16$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute $\sigma(n)$ modulo $11587$, and let this value be $r$. ... | 29,184 | graphs = [
Graph(
let={
"_n": Const(66420),
"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 | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:50:00.769790Z | {
"verified": true,
"answer": 29184,
"timestamp": "2026-02-08T06:50:00.772161Z"
} | b45349 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 3679
},
"timestamp": "2026-02-13T05:09:57.446Z",
"answer": 29184
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b95fc0 | comb_binomial_compute_v1_784195855_795 | Let $ n = 12 $, and let $ k $ be the largest prime number between $ 2 $ and $ 6 $, inclusive. Define $ \binom{n}{k} $ to be the binomial coefficient $ \frac{n!}{k!(n-k)!} $. Let $ Q $ be the smallest positive integer $ m $ such that the $ m $-th Fibonacci number is divisible by $ \left| \binom{n}{k} \right| + 2 $. Find... | 597 | graphs = [
Graph(
let={
"n": Const(12),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6)), IsPrime(Var("n"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=R... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T04:37:32.679246Z | {
"verified": true,
"answer": 597,
"timestamp": "2026-02-08T04:37:32.680459Z"
} | dcebcd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 5725
},
"timestamp": "2026-02-10T17:26:17.043Z",
"answer": 597
},
{
"i... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
3f0e1a | antilemma_v8_lucas_1742523217_535 | Let $m = 52655$. Let $n$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $x$ be the number of nonnegative integers $j$ with $0 \leq j \leq m$ such that $$
\binom{52655}{j} \equiv 1 \pmod{n}.
$$Let $c = 53891$. Compute the remainder whe... | 27,916 | graphs = [
Graph(
let={
"_m": Const(52655),
"_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=24)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8",
"V8"
] | 8c6b98 | antilemma_v8_lucas | null | 7 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.005 | 2026-02-08T03:06:50.946220Z | {
"verified": true,
"answer": 27916,
"timestamp": "2026-02-08T03:06:50.950778Z"
} | 1aee83 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 3140
},
"timestamp": "2026-02-09T19:12:18.200Z",
"answer": 27916
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status"... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
d5dc33 | nt_count_divisible_and_v1_1439011603_776 | Let $d_2$ be the number of integers $t$ with $27 \leq t \leq 96$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 9$, and $t = 21a + 6b$. Compute the number of positive integers $n \leq 105768$ such that $n$ is divisible by $12$ and $n$ is divisible by $d_2$. | 2,938 | graphs = [
Graph(
let={
"upper": Const(105768),
"d1": Const(12),
"d2": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 3.62 | 2026-02-08T15:42:34.456808Z | {
"verified": true,
"answer": 2938,
"timestamp": "2026-02-08T15:42:38.076987Z"
} | 46f02d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 307
},
"timestamp": "2026-02-16T06:18:15.673Z",
"answer": 8814
},
{
"id": 11,... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} |
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