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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
469718 | nt_sum_divisors_compute_v1_677425708_212 | Let $n = 45796$. Compute the sum of all positive divisors of $n$. | 80,899 | graphs = [
Graph(
let={
"n": Const(45796),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | OMEGA_ZERO | [
"OMEGA_ZERO",
"WILSON"
] | 4e9ec6 | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"OMEGA_ZERO",
"WILSON"
] | 2 | 0.003 | 2026-02-08T03:08:31.666337Z | {
"verified": true,
"answer": 80899,
"timestamp": "2026-02-08T03:08:31.669669Z"
} | 7c4e76 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1302
},
"timestamp": "2026-02-08T20:23:58.558Z",
"answer": 80899
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status"... | {
"lo": -0.55,
"mid": 1.57,
"hi": 3.38
} | ||
7cd0d3 | comb_count_surjections_v1_717093673_1139 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 7$, $1 \leq j \leq 8$, and $i + j = 9$. Let $k$ be the number of ordered pairs $(i_1, j_1)$ of integers such that $1 \leq i_1 \leq 2$, $1 \leq j_1 \leq 2$, and $i_1 + j_1 = 3$. Compute the remainder when $44121 \cdot k! \cdot S(n, k)$ ... | 68,501 | graphs = [
Graph(
let={
"_n": Const(84473),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(9)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.038 | 2026-02-08T15:53:08.173296Z | {
"verified": true,
"answer": 68501,
"timestamp": "2026-02-08T15:53:08.211484Z"
} | 673e6c | 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": 866
},
"timestamp": "2026-02-24T18:53:29.740Z",
"answer": 68501
},
{
"... | 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": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
bc067c | nt_sum_divisors_compute_v1_1116507919_302 | Let $a$ be the number of positive integers $n$ such that $1 \leq n \leq 66$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $b = 23$ and define $e = \sum_{d \mid \gcd(a,b)} \mu(d)$, where $\mu$ denotes the M\"obius function. Let $s$ be the number of distinct prime factors of $29$, and let $n = 24025... | 31,449 | graphs = [
Graph(
let={
"_n": Const(66),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
"b... | NT | null | COMPUTE | sympy | L3C | [
"L3C/MOBIUS_COPRIME",
"OMEGA_ONE"
] | 3ccab1 | nt_sum_divisors_compute_v1 | null | 6 | 2 | [
"L3C",
"MOBIUS_COPRIME",
"OMEGA_ONE"
] | 3 | 0.002 | 2026-02-08T02:30:43.815799Z | {
"verified": true,
"answer": 31449,
"timestamp": "2026-02-08T02:30:43.818227Z"
} | 9a5cd1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 328,
"completion_tokens": 1546
},
"timestamp": "2026-02-08T19:21:31.571Z",
"answer": 31449
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "OMEGA_ONE",
"... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
159243 | geo_count_lattice_rect_v1_397696148_730 | Let $a = 233$ and $b = 81$. Define the rectangle $R$ as the set of all lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $N$ be the number of lattice points in $R$. Given that $N \times 22106$ leaves a remainder when divided by $56951$, compute that remainder. | 55,831 | graphs = [
Graph(
let={
"a": Const(233),
"b": Const(81),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(22106),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(56951)),
},
goal=Ref("Q"),
)... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 5 | 0 | null | null | 0.001 | 2026-02-08T11:42:53.996843Z | {
"verified": true,
"answer": 55831,
"timestamp": "2026-02-08T11:42:53.998238Z"
} | c47e82 | 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": 3169
},
"timestamp": "2026-02-24T14:30:45.930Z",
"answer": 55831
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
66d77d | alg_qf_psd_count_v1_1218484723_4935 | Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \leq a, b, c \leq 34$ such that $$30a^2 + 70ab + 125b^2 - 50ac + 20bc + 70c^2 = 53050.$$ | 13 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(34)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(34)), Geq(Var("c"), Const(1)), Leq(Var("c"), Const(34)), Eq(Sum(Mul(Co... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"COUNT_PRIMES/POLY_ORBIT_HENSEL",
"ONE_PHI_2"
] | 3aee8a | alg_qf_psd_count_v1 | null | 4 | null | [
"COUNT_PRIMES",
"ONE_PHI_2",
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT_LEQ"
] | 4 | 2.753 | 2026-02-25T06:34:43.815338Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-25T06:34:46.567886Z"
} | aba1e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T18:38:08.179Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
afc2b5 | nt_max_prime_below_v1_48377204_1496 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $m \leq n \leq 17689$. Let $M$ be the largest element of $T$. Find the ... | 17,683 | graphs = [
Graph(
let={
"_n": Const(79975),
"upper": Const(17689),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.451 | 2026-02-08T16:08:05.843513Z | {
"verified": true,
"answer": 17683,
"timestamp": "2026-02-08T16:08:08.294859Z"
} | b619a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 2876
},
"timestamp": "2026-02-16T21:13:38.261Z",
"answer": 17683
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b4fe34 | modular_min_modexp_v1_1440796553_227 | Let $T$ be the set of all integers $t$ such that $18 \leq t \leq 308$ and there exist positive integers $a \leq 30$, $b \leq 30$ satisfying $t = 3a + 7b + 8$. Let $N$ be the number of elements in $T$. Let $m$ be the largest prime number not exceeding $N$. Find the smallest positive integer $x \leq 138$ such that $7^x \... | 67 | 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=30)), Geq(left=Var(name='b'), right=Const(value... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | modular_min_modexp_v1 | null | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.014 | 2026-02-08T11:39:06.088836Z | {
"verified": true,
"answer": 67,
"timestamp": "2026-02-08T11:39:06.103138Z"
} | 44486b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 6791
},
"timestamp": "2026-02-14T17:39:21.993Z",
"answer": 67
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6ca109 | antilemma_k2_v1_1915831931_3715 | Let $n = 260$. Define $x = \sum_{k=1}^{260} \phi(k) \left\lfloor \frac{260}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $r$ be the remainder when $|x|$ is divided by $11$. Compute the Bell number $B_r$, which counts the number of partitions of a set of size $r$. | 203 | graphs = [
Graph(
let={
"_n": Const(260),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(260), Var("k"))))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T17:50:58.806067Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T17:50:58.806985Z"
} | a3f1b6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 954
},
"timestamp": "2026-02-18T09:23:10.123Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
116194 | modular_sum_quadratic_residues_v1_2051736721_2455 | Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 4x - 5180 = 0$. Let $p$ be the number of integers $t$ with $16 \leq t \leq 376$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 31$, $1 \leq b \leq 11$, and $t = 10a + 6b$. Compute $\frac{p(p-1)}{n}$. | 7,439 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-4), Var("x")), Const(-5180)), Const(0)))),
"p": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), co... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"VIETA_SUM/LIN_FORM"
] | eaa1fa | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"VIETA_SUM"
] | 3 | 0.004 | 2026-02-08T16:41:17.416140Z | {
"verified": true,
"answer": 7439,
"timestamp": "2026-02-08T16:41:17.419929Z"
} | b94f75 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 4022
},
"timestamp": "2026-02-17T10:32:03.197Z",
"answer": 7439
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c5d958 | alg_poly3_count_v1_601307018_4048 | Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \le a, b, c \le 26$ such that $$19305b c^{2} + 10296 a^{2} c - 21450a b^{2} + \min\{ x + y : x > 0, y > 0, x y = 18404100, x \le y \} \cdot a^{2} b + 96525 b^{2} c + 36179 c^{3} - 28314a c^{2} - 1287 a^{3} - 42900a b c = -1144.$$ | 26 | graphs = [
Graph(
let={
"_n": Const(96525),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(26)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(26)), Geq(Var("c"), Const(1)), Leq(Var... | ALG | null | COUNT | sympy | B3_DIFF | [
"B3"
] | 0cd20d | alg_poly3_count_v1 | null | 7 | 0 | [
"B3",
"B3_DIFF"
] | 2 | 2.445 | 2026-03-10T04:39:55.663617Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-03-10T04:39:58.109116Z"
} | a4c7a4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T10:55:17.469Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
dea6db | nt_count_coprime_v1_865884756_1062 | Let $k$ be the number of integers $t$ with $21 \leq t \leq 66$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 6$, and $t = 15a + 6b$. Determine the number of positive integers $n$ with $1 \leq n \leq 37249$ such that $\gcd(n, k) = 1$. | 12,417 | graphs = [
Graph(
let={
"upper": Const(37249),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 3.119 | 2026-02-08T15:45:36.158897Z | {
"verified": true,
"answer": 12417,
"timestamp": "2026-02-08T15:45:39.277974Z"
} | 9407f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1049
},
"timestamp": "2026-02-16T12:06:55.587Z",
"answer": 12417
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b02eac | algebra_poly_eval_v1_238844314_839 | Let $a$ be the number of prime numbers $n$ such that $2 \leq n \leq 23$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Let $m$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Compute $2a^2 + m \cdot a + 4$. | 202 | graphs = [
Graph(
let={
"_m": Const(23),
"_n": Const(2),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"result": Sum(Mul(Const(2), Pow(Ref("a"), Const(2))), Mul(MinOverS... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES",
"B3"
] | 38fcc0 | algebra_poly_eval_v1 | null | 3 | 0 | [
"B3",
"COUNT_PRIMES"
] | 2 | 0.007 | 2026-02-08T13:38:47.815186Z | {
"verified": true,
"answer": 202,
"timestamp": "2026-02-08T13:38:47.821918Z"
} | 28e281 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 378
},
"timestamp": "2026-02-15T18:39:20.634Z",
"answer": 202
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
014a1f | geo_count_lattice_triangle_v1_1978505735_3023 | Let $n = 100$. Define the quantity
$$
\text{area\_2x} = \left| 111n - 7 \cdot 47 \right|.
$$
Let $S$ be the set of all integers $k$ such that $1 \leq k \leq 201$ and the sum of the binary digits of $k$ is even. Define
$$
\text{boundary} = \gcd(100, 47) + \gcd(7 - |S|, 64) + \gcd(7, 111).
$$
Let
$$
\text{result} = \frac... | 20,091 | graphs = [
Graph(
let={
"_n": Const(100),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_n'), Const(value=111)), Mul(Const(value=7), Sub(left=Const(value=0), right=Const(value=47))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(value=47))), GCD(a=Abs(arg=Sub(... | ALG | NT | COUNT | sympy | L3B | [
"L3B"
] | cc148f | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"L3B"
] | 1 | 0.01 | 2026-02-08T17:18:29.995678Z | {
"verified": true,
"answer": 20091,
"timestamp": "2026-02-08T17:18:30.006013Z"
} | 5d831b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 2378
},
"timestamp": "2026-02-18T00:31:36.567Z",
"answer": 20091
},
... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
77d58a | nt_max_prime_below_v1_677425708_3723 | Let $ S $ be the set of all positive integers $ p $ for which there exists a positive integer $ q $ such that $ p \cdot q = 12 $, $ \gcd(p, q) = 1 $, and $ p < q $. Let $ m $ be the number of elements in $ S $. Let $ T $ be the set of all prime numbers $ n $ such that $ n \geq m $ and $ n \leq 21609 $. Determine the va... | 21,601 | graphs = [
Graph(
let={
"upper": Const(21609),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.503 | 2026-02-08T05:54:59.565735Z | {
"verified": true,
"answer": 21601,
"timestamp": "2026-02-08T05:55:00.068961Z"
} | ece094 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 1603
},
"timestamp": "2026-02-12T16:43:46.665Z",
"answer": 21601
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9890f7 | modular_mod_compute_v1_865884756_2427 | Let $a = 6889$. Let $m$ be the smallest integer greater than or equal to 2 that divides 4112783. Compute the remainder when $a$ is divided by $m$. | 808 | graphs = [
Graph(
let={
"a": Const(6889),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(4112783))))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
goal=Ref("result"),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_mod_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T16:46:26.153831Z | {
"verified": true,
"answer": 808,
"timestamp": "2026-02-08T16:46:26.156922Z"
} | 5917c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 1964
},
"timestamp": "2026-02-17T11:09:41.933Z",
"answer": 808
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e2f658 | algebra_quadratic_discriminant_v1_655260480_1629 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = N$, where $N$ is the number of positive integers $n \leq 20$ satisfying $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $s$ be the minimum value of $x + y$ over all such pairs. Compute $|(-18)^2 - (-1) \cdot s \cdot (-8... | 0 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": Const(-18),
"c": Const(-81),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=... | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"L3C/B3"
] | 4d8a41 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B3",
"BINOMIAL_ALTERNATING",
"L3C"
] | 3 | 0.049 | 2026-02-08T16:15:38.355697Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T16:15:38.404373Z"
} | 5f682e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 816
},
"timestamp": "2026-02-17T00:06:39.746Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e48320 | modular_mod_compute_v1_1918700295_4056 | Let $S$ be the set of all integers $t$ such that $28 \leq t \leq 6704$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 159$, $1 \leq b \leq 903$, and $t = 8a + 6b + 14$. Let $m$ be the number of elements in $S$. Find the remainder when $-32768$ is divided by $m$. | 562 | graphs = [
Graph(
let={
"a": 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'), right=Const(value=159)), Geq(left=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:06:19.582445Z | {
"verified": true,
"answer": 562,
"timestamp": "2026-02-08T09:06:19.583351Z"
} | dde297 | 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": 5010
},
"timestamp": "2026-02-14T00:41:44.796Z",
"answer": 562
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
68118f | geo_visible_lattice_v1_1915831931_3598 | Let $n = 103$. A lattice point $(x, y)$ is said to be visible from the origin if $\gcd(x, y) = 1$. Compute the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. | 6,555 | graphs = [
Graph(
let={
"n": Const(103),
"result": VisibleLatticePoints(n=Ref(name='n')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 1.11 | 2026-02-08T17:46:59.610985Z | {
"verified": true,
"answer": 6555,
"timestamp": "2026-02-08T17:47:00.720684Z"
} | 8ea9fe | 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": 2717
},
"timestamp": "2026-02-18T08:03:48.972Z",
"answer": 6555
},
{... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
3a7871 | antilemma_k2_v1_124444284_3826 | Let $m = 2$. Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 312x - 26289 = 0$. Compute the sum $\sum_{k=1}^{312} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. | 48,828 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-312), Var("x")), Const(-26289)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Const(312), expr=Mul(EulerPhi(n=Var("k")... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T05:37:50.653410Z | {
"verified": true,
"answer": 48828,
"timestamp": "2026-02-08T05:37:50.654531Z"
} | 67aa97 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 866
},
"timestamp": "2026-02-12T11:21:51.810Z",
"answer": 48828
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
305042 | nt_num_divisors_compute_v1_1520064083_7364 | Let $n$ be the smallest integer greater than or equal to $2$ that divides $56129$. Compute the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(56129))))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T08:59:06.704376Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T08:59:06.705478Z"
} | d3bafa | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 461
},
"timestamp": "2026-02-15T20:27:57.743Z",
"answer": 3
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
ee4486 | lin_form_endings_v1_1470522791_1370 | Let $a = 84$ and $b = 60$. Define $r$ to be the greatest common divisor of $a$ and $b$. Let $k = 6709$ and $M = 72298$. Compute the remainder when $k \cdot \left\lfloor \frac{84}{r} \right\rfloor$ is divided by $M$. | 46,963 | graphs = [
Graph(
let={
"a_coeff": Const(84),
"b_coeff": Const(60),
"_inner_result": Floor(Div(Const(84), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(6709),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:36:22.230483Z | {
"verified": true,
"answer": 46963,
"timestamp": "2026-02-08T13:36:22.231316Z"
} | 042e7a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 493
},
"timestamp": "2026-02-16T04:52:09.370Z",
"answer": 46963
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
4ed221 | antilemma_cartesian_v1_238844314_1179 | Let $n = 14$. Consider the set of all ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 12$, $1 \leq j \leq 12$, and $i + j = n$. Let $s$ be the number of elements in this set. Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 17$ and $1 \leq b \leq 49$. Compute the Bell number of the rem... | 4,140 | graphs = [
Graph(
let={
"_n": Const(14),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Const(49)))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=CountOverSet(set=SolutionsSet(var=Tup... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | fe8f6f | antilemma_cartesian_v1 | bell_mod | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.027 | 2026-02-08T14:01:47.978898Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T14:01:48.006278Z"
} | 133a31 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 773
},
"timestamp": "2026-02-24T19:30:56.589Z",
"answer": 4140
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -3.9,
"mid": -1.69,
"hi": 1.31
} | ||
a1cfd9 | diophantine_product_count_v1_677425708_1819 | Let $ k = 240 $ and $ u = 86 $. Determine the number of positive integers $ x $ such that $ 1 \leq x \leq u $, $ x $ divides $ 240 $, and $ \frac{240}{x} \leq 86 $. | 16 | graphs = [
Graph(
let={
"k": Const(240),
"upper": Const(86),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper")))... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_product_count_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.03 | 2026-02-08T04:28:54.255279Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T04:28:54.285001Z"
} | e3dc80 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1186
},
"timestamp": "2026-02-10T01:29:28.094Z",
"answer": 16
},
{
"id"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
abdbaa | nt_sum_divisors_compute_v1_458359167_3700 | Let $ n = 20449 $. Compute the sum of the positive divisors of $ n $, and denote this sum by $ s $. Let $ p $ be the largest prime number less than or equal to 11. Determine the value of the Bell number $ B_r $, where $ r $ is the remainder when $ |s| $ is divided by $ p $. Compute this Bell number. | 877 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(20449),
"result": SumDivisors(n=Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(11)), I... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_sum_divisors_compute_v1 | bell_mod | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.169 | 2026-02-08T11:16:13.600085Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T11:16:13.769583Z"
} | b4f9e7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 773
},
"timestamp": "2026-02-14T11:22:25.735Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
921730 | comb_count_derangements_v1_2051736721_3109 | Let $N$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 55$, $1 \leq j \leq 111$, and $\gcd(i,j) = 1$. Let $d$ be the smallest integer greater than or equal to 2 that divides $N$. Compute the number of derangements of $d$ elements, denoted by $!d$. | 1,854 | graphs = [
Graph(
let={
"_m": Const(2),
"_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(55)), right=IntegerRange(start=Const(1), end=... | NT | COMB | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID/MIN_PRIME_FACTOR"
] | 36715f | comb_count_derangements_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T17:07:05.477377Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T17:07:05.480422Z"
} | efd85f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 3929
},
"timestamp": "2026-02-17T19:08:57.132Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4405a6 | antilemma_coprime_grid_v1_1248542787_286 | Compute the number of ordered pairs $(i, j)$ with $1 \leq i \leq 46$ and $1 \leq j \leq 50$ such that $\gcd(i, j) = 1$. | 1,418 | graphs = [
Graph(
let={
"x": 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(46)), right=IntegerRange(start=Const(1), end=Const(50))))),
},
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | antilemma_coprime_grid_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0 | 2026-02-08T03:02:50.490391Z | {
"verified": true,
"answer": 1418,
"timestamp": "2026-02-08T03:02:50.490793Z"
} | a826d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 3136
},
"timestamp": "2026-02-09T02:23:21.027Z",
"answer": 1418
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
dc6fa5 | comb_factorial_compute_v1_397696148_1983 | Let $m = 448$. Define $A$ to be the set of all positive integers $k$ such that $1 \leq k \leq m$ and $64$ divides $k$. Let $n$ be the largest prime number satisfying $2 \leq n \leq |A|$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(448),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_m")), Divides(divisor=Const(64), dividend=Var("k"))), domain='positive_integers')),
"n": MaxOverSet(set=SolutionsSet(var=... | NT | null | COMPUTE | sympy | C2 | [
"C2/MAX_PRIME_BELOW"
] | 38c8ef | comb_factorial_compute_v1 | null | 4 | 0 | [
"C2",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T12:53:06.939685Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T12:53:06.941340Z"
} | cb1e4b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 350
},
"timestamp": "2026-02-15T06:41:41.541Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V1",
"s... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
3535f0 | nt_max_prime_below_v1_48377204_2910 | Let $n = 66421$ and let $u = 30000$. Define $S$ to be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all prime numbers $n$ such that $n \geq |S|$ and $n \leq u$. Suppose $T$ is nonempty, and let $m$ be the max... | 70,537 | graphs = [
Graph(
let={
"_n": Const(66421),
"upper": Const(30000),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.944 | 2026-02-08T17:03:37.679469Z | {
"verified": true,
"answer": 70537,
"timestamp": "2026-02-08T17:03:38.623293Z"
} | 65f3db | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 4646
},
"timestamp": "2026-02-17T18:51:24.002Z",
"answer": 70537
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7e4bbb | geo_count_lattice_triangle_v1_458359167_4207 | Let $A$ be the area of a triangle with vertices at $(0, 0)$, $(144, 196)$, and $(144, 231)$. Compute $2A$.
Let $B$ be the number of lattice points on the boundary of this triangle, including the vertices. By Pick's Theorem, the area $A$ satisfies
$$
A = I + \frac{B}{2} - 1,
$$
where $I$ is the number of interior latti... | 2,500 | graphs = [
Graph(
let={
"_n": Const(144),
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=196)), Mul(Const(value=144), Sub(left=Const(value=0), right=Const(value=231))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(value=231))), GCD(a=Abs(ar... | ALG | NT | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.007 | 2026-02-08T11:37:34.945892Z | {
"verified": true,
"answer": 2500,
"timestamp": "2026-02-08T11:37:34.952512Z"
} | 74be7f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1331
},
"timestamp": "2026-02-14T16:37:22.353Z",
"answer": 2500
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "n... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e2297b | lin_form_endings_v1_784195855_1215 | Let $a = 24$ and $b = 30$. Compute $\gcd(a, b)$, and denote it by $d$. Let $k = 53$. Compute $\gcd(k, d)$, and denote it by $g$. Define $r = \left\lfloor \frac{k}{g} \right\rfloor$. Let $s = 18434 \cdot r$. Compute the remainder when $s$ is divided by $53195$. Determine the value of this remainder. | 19,492 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(30),
"k_val": Const(53),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(18... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:54:13.730331Z | {
"verified": true,
"answer": 19492,
"timestamp": "2026-02-08T04:54:13.731482Z"
} | 657851 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 722
},
"timestamp": "2026-02-11T22:28:39.202Z",
"answer": 19492
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
529260 | algebra_poly_eval_v1_1520064083_3981 | Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 121$. Compute $b^3 - 10b^2 + 10b + 2$. | 6,030 | graphs = [
Graph(
let={
"_n": Const(10),
"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(121)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T05:59:51.272348Z | {
"verified": true,
"answer": 6030,
"timestamp": "2026-02-08T05:59:51.273751Z"
} | 30fb2e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 391
},
"timestamp": "2026-02-11T23:27:33.456Z",
"answer": 5852
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
154d0b | nt_count_divisible_and_v1_1526740231_186 | Let $d_1 = 10$ and let $d_2 = \sum_{k=1}^{5} k$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 35790$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute the number of elements in $S$. | 1,193 | graphs = [
Graph(
let={
"upper": Const(35790),
"d1": Const(10),
"d2": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 1.196 | 2026-02-08T11:23:19.672357Z | {
"verified": true,
"answer": 1193,
"timestamp": "2026-02-08T11:23:20.868549Z"
} | 7a3bb6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 423
},
"timestamp": "2026-02-15T21:48:07.376Z",
"answer": 1193
},
{
"id": 11,
... | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
f1feec | nt_min_coprime_above_v1_1978505735_220 | Let $S$ be the set of all integers $n$ such that $65536 < n \leq 66039$ and $\gcd(n, 493) = 1$. Let $m$ be the smallest element of $S$. Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 1951$ and there exist positive integers $a \leq 32$ and $b \leq 597$ for which $t = 5a + 3b$. Compute the remainder when... | 24,882 | graphs = [
Graph(
let={
"start": Const(65536),
"upper": Const(66039),
"modulus": Const(493),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | nt_min_coprime_above_v1 | negation_mod | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.225 | 2026-02-08T15:13:58.845938Z | {
"verified": true,
"answer": 24882,
"timestamp": "2026-02-08T15:13:59.070882Z"
} | 575155 | 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": 5277
},
"timestamp": "2026-02-16T02:11:35.404Z",
"answer": 24882
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1dde0d | geo_visible_lattice_v1_124444284_6287 | Let $n = 111$. Define $Q$ to be the remainder when $44121$ multiplied by the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$ is divided by $90610$. A lattice point $(x, y)$ is visible if $\gcd(x, y) = 1$. Compute $Q$. | 46,895 | graphs = [
Graph(
let={
"n": Const(111),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(90610)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.39 | 2026-02-08T08:15:53.872775Z | {
"verified": true,
"answer": 46895,
"timestamp": "2026-02-08T08:15:54.263040Z"
} | 392568 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 5184
},
"timestamp": "2026-02-24T09:10:55.538Z",
"answer": 46895
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
7bf89a | nt_sum_gcd_range_mod_v1_1520064083_4576 | Let $N = 1024$. Define $k$ to be the number of positive integers $n$ such that $1 \leq n \leq 4403$, $7$ divides $n$, and $\gcd(n, 15) = 1$. Let
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $M = 11887$, and define $r$ to be the remainder when $\text{sum}$ is divided by $M$. Finally, let $Q$ be the remainder when $... | 35,492 | graphs = [
Graph(
let={
"N": Const(1024),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4403)), Divides(divisor=Const(7), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(15)), Const(1))))),
"M": Const(11887),
... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.048 | 2026-02-08T06:19:54.619560Z | {
"verified": true,
"answer": 35492,
"timestamp": "2026-02-08T06:19:54.667961Z"
} | 6c8fc2 | 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": 3714
},
"timestamp": "2026-02-12T22:53:08.318Z",
"answer": 35492
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1afb36 | comb_count_permutations_fixed_v1_1218484723_2599 | Let $D_n$ denote the number of derangements of $n$ elements. Let $N = 12$ and define $m = \sum_{k=0}^{N} (-1)^k \binom{N}{k}$. Let $M = m$, and define $f = \sum_{k=0}^{M} (-1)^k \binom{M}{k}$. Let $n = 8f$. Let $R = 12$ and define $t = \sum_{k=0}^{R} (-1)^k \binom{R}{k}$. Let $S = \binom{n}{6} \cdot D_{n-6}$ and $T = 6... | 62,973 | graphs = [
Graph(
let={
"n3": Const(12),
"t": Summation(var="k1", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n3"), k=Var("k1")))),
"n2": Const(12),
"m": Summation(var="k2", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 4 | 3 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-25T04:21:38.006639Z | {
"verified": true,
"answer": 62973,
"timestamp": "2026-02-25T04:21:38.009085Z"
} | 555277 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 761
},
"timestamp": "2026-03-29T05:37:08.899Z",
"answer": 62973
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||
efad02 | sequence_fibonacci_compute_v1_1353956133_119 | Let $n$ be the number of ordered pairs $(i,j)$ of integers with $1 \le i \le 25$ and $1 \le j \le 25$ such that $i + j = 26$. Let $F_n$ be the $n$-th Fibonacci number. Compute the value of $$\sum_{i = s}^{t-1} d_i (i+1)^2 + 36100,$$ where $d_i$ is the $i$-th decimal digit of $|F_n|$ (starting from the units digit as $i... | 36,368 | graphs = [
Graph(
let={
"_n": Const(26),
"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(25)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | b9499e | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T11:19:04.530052Z | {
"verified": true,
"answer": 36368,
"timestamp": "2026-02-08T11:19:04.541087Z"
} | 5f7a42 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 1797
},
"timestamp": "2026-02-24T13:17:36.666Z",
"answer": 36368
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
049b95 | comb_count_permutations_fixed_v1_458359167_208 | Let $n = 7$ and $k = \sum_{k=1}^{2} k$. Compute $\binom{n}{k} \cdot ! (n - k)$, where $!m$ denotes the number of permutations of $m$ elements with no fixed points. | 315 | graphs = [
Graph(
let={
"n": Const(7),
"k": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T03:04:13.221383Z | {
"verified": true,
"answer": 315,
"timestamp": "2026-02-08T03:04:13.223447Z"
} | 48b03d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 500
},
"timestamp": "2026-02-10T13:17:23.382Z",
"answer": 315
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
b3c1a5 | nt_count_primes_v1_397696148_1077 | Let $N$ be the number of prime numbers $n$ such that $2 \leq n \leq 12996$. Let $d_0$ be the smallest divisor of $2431$ that is at least $2$. Compute the Bell number corresponding to the remainder when $|N|$ is divided by $d_0$. | 877 | graphs = [
Graph(
let={
"upper": Const(12996),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=Solutions... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_primes_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.289 | 2026-02-08T12:20:27.414303Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T12:20:27.702899Z"
} | 192662 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1817
},
"timestamp": "2026-02-15T00:24:33.836Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
81e489 | algebra_quadratic_discriminant_v1_717093673_971 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $b = -4$ and $c = -6$. Define $\Delta = b^2 - 4ac$. Compute $18213 \cdot \Delta \bmod 58990$. | 44,822 | graphs = [
Graph(
let={
"_n": Const(2),
"a": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T15:46:08.937677Z | {
"verified": true,
"answer": 44822,
"timestamp": "2026-02-08T15:46:08.940387Z"
} | ba2964 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1740
},
"timestamp": "2026-02-16T13:57:08.613Z",
"answer": 44822
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8b1035_n | algebra_poly_eval_v1_601307018_2964 | A bakery sells boxes of cookies in batches that follow a special formula: when $9$ boxes are ordered, the total cost in dollars is given by $20 \cdot 9^3 - 12 \cdot 9^2 - 17 \cdot 9 - 15$. This total is then split evenly across $\sum_{k=0}^{3} 2^k$ departments for reimbursement. How many dollars does each department pa... | 896 | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | algebra_poly_eval_v1 | null | 2 | null | [
"SUM_GEOM"
] | 1 | 0.005 | 2026-03-10T03:35:46.931499Z | null | 6e932a | 8b1035 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 521
},
"timestamp": "2026-03-29T17:01:45.379Z",
"answer": 896
},
{
"id"... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
5b2b0b | algebra_quadratic_discriminant_v1_865884756_691 | Let $a$ be the smallest divisor of $105$ that is at least $2$. Let $c$ be the number of positive integers $p$ for which there exists an integer $q > p$ such that $p \cdot q = 5400$ and $\gcd(p, q) = 1$. Compute $|(-3)^2 - a \cdot c \cdot (-9)|$. | 117 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(105))))),
"b": Const(-3),
"c": Const(-9),
"result": Sub(Pow(Ref("b"), Ref("_n")),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | a3b634 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.007 | 2026-02-08T15:33:22.342517Z | {
"verified": true,
"answer": 117,
"timestamp": "2026-02-08T15:33:22.349505Z"
} | bd44bd | 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": 1396
},
"timestamp": "2026-02-16T08:42:47.477Z",
"answer": 117
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTO... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8e47ce | nt_max_prime_below_v1_1248542787_825 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $P$. Define $S$ to be the set of all prime numbers $n$ such that $m \leq n \leq 38416$. Determine the maximum value of $S$. | 38,393 | graphs = [
Graph(
let={
"upper": Const(38416),
"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 | 0.898 | 2026-02-08T03:26:42.074767Z | {
"verified": true,
"answer": 38393,
"timestamp": "2026-02-08T03:26:42.972714Z"
} | 2de6e0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 6540
},
"timestamp": "2026-02-09T21:37:11.380Z",
"answer": 38393
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6c8070 | nt_count_digit_sum_v1_677425708_3863 | Let $T$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 60$. Compute the number of positive integers $n \leq 99999$ such that the sum of the digits of $n$ is equal to $T$. | 3,246 | graphs = [
Graph(
let={
"_n": Const(60),
"upper": Const(99999),
"target_sum": 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(n... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 3.595 | 2026-02-08T05:58:46.241917Z | {
"verified": true,
"answer": 3246,
"timestamp": "2026-02-08T05:58:49.837123Z"
} | e91ef4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 1879
},
"timestamp": "2026-02-12T18:27:13.170Z",
"answer": 3246
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1dd6bf | antilemma_sum_equals_v1_1978505735_348 | Let $ n = 94 $. Let $ x $ be the number of ordered pairs $ (i, j) $ of positive integers such that $ i + j = n $, $ 1 \leq i \leq 93 $, and $ 1 \leq j \leq 94 $. Find the remainder when $ 44121 \cdot x $ is divided by 81047. | 50,903 | graphs = [
Graph(
let={
"_n": Const(94),
"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(93)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.171 | 2026-02-08T15:19:55.211441Z | {
"verified": true,
"answer": 50903,
"timestamp": "2026-02-08T15:19:55.382104Z"
} | d47d26 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 834
},
"timestamp": "2026-02-24T20:35:10.550Z",
"answer": 50903
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.26
} | ||
f520c2 | modular_modexp_compute_v1_1520064083_8995 | Let $e$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 18818$. Let $a = 5$ and $m = 90000$.
Compute the remainder when $18496 - a^e$ is divided by $97559$, where the exponentiation is performed modulo $m$.
| 82,930 | graphs = [
Graph(
let={
"_n": Const(97559),
"a": Const(5),
"e": 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... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_modexp_compute_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T10:28:21.622791Z | {
"verified": true,
"answer": 82930,
"timestamp": "2026-02-08T10:28:21.624241Z"
} | 8389c5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1801
},
"timestamp": "2026-02-14T07:33:43.967Z",
"answer": 82930
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e5f2a8 | comb_sum_binomial_row_v1_1820931509_771 | Let $p$ be a positive integer. Suppose there exists a positive integer $q$ such that $p \cdot q = 339570$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such integers $p$. Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=339570)), Eq(left=GCD(a=Var(name='p'), b=Var(name... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T11:52:50.882595Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T11:52:50.883685Z"
} | a5e165 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 2861
},
"timestamp": "2026-02-14T20:52:44.436Z",
"answer": 65536
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
37d618 | nt_sum_divisors_mod_v1_1520064083_9717 | Let $n$ be the sum of all positive integers at most 360 that are divisible by 120. Let $\sigma$ denote the sum of the positive divisors of $n$. Find the remainder when $\sigma$ is divided by 10657. | 2,418 | graphs = [
Graph(
let={
"_n": Const(120),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(360)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0))))),
"M": Const(10657),
"sigma": SumDivisors(n=Ref("n... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.003 | 2026-02-08T10:58:59.233836Z | {
"verified": true,
"answer": 2418,
"timestamp": "2026-02-08T10:58:59.236680Z"
} | cac7cf | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 523
},
"timestamp": "2026-02-15T21:06:32.486Z",
"answer": 2418
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
0ce18c | alg_poly4_count_v1_1218484723_4623 | Let $S = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 35,\ 10a_1^2 - 18a_1b_1 + 25b_1^2 \le 4640 \}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 374$ and $1 \le b \le S$ such that $$1024a^3b + 512a^4 + 32b^4 + 256ab^3 + 768a^2b^2 = 30739072320000.$$ | 67 | graphs = [
Graph(
let={
"_n": Const(25),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(374)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_count_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 1.852 | 2026-02-25T06:17:57.549990Z | {
"verified": true,
"answer": 67,
"timestamp": "2026-02-25T06:17:59.401569Z"
} | 183203 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 7733
},
"timestamp": "2026-03-29T16:36:00.802Z",
"answer": 48
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
0d6884 | geo_count_lattice_triangle_v1_655260480_5547 | Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 8100$, and define $s = \min\{x + y : (x, y) \in A\}$. Let $B$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 20$, and define $p = \max\{x_1 y_1 : (x_1, y_1) \in B\}$. Define $$A_{2x} = \left| ... | 3,076 | graphs = [
Graph(
let={
"_c": Const(121),
"_m": Const(180),
"_n": Const(180),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_c'), Const(value=100)), Mul(Const(value=33), Sub(left=Const(value=0), right=Ref(name='_n'))))),
"boundary": Sum(GCD(a=Abs(arg=Const(... | ALG | NT | COUNT | sympy | L3C | [
"L3C",
"B1",
"B3"
] | 90b314 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B1",
"B3",
"L3C"
] | 3 | 0.013 | 2026-02-08T18:33:22.398064Z | {
"verified": true,
"answer": 3076,
"timestamp": "2026-02-08T18:33:22.410641Z"
} | 655a16 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 1074
},
"timestamp": "2026-02-18T17:31:04.016Z",
"answer": 3076
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9e256a | nt_sum_divisors_mod_v1_809748730_1158 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 32400$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $10463$. | 1,170 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10463)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T12:12:02.222303Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T12:12:02.225086Z"
} | 51f48e | 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": 778
},
"timestamp": "2026-02-14T22:49:57.383Z",
"answer": 1170
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
94c70c | nt_sum_divisors_compute_v1_655260480_4439 | Let $n = 23716$. Let $s$ be the sum of the positive divisors of $n$. Define $d_k$ to be the $k$-th decimal digit of $|s|$, where $d_0$ is the units digit. Let $m$ be the number of digits in $|s|$. Compute
$$
\sum_{i=0}^{m-1} d_i (i+1)^2 + 11664.
$$ | 11,868 | graphs = [
Graph(
let={
"n": Const(23716),
"result": SumDivisors(n=Ref("n")),
"_c": Const(11664),
"Q": Sum(Summation(var="i", start=Summation(var="k", start=Const(0), end=Const(2), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(2), k=Var("k")))), end=Sub(Num... | COMB | NT | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_sum_divisors_compute_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.003 | 2026-02-08T17:56:31.565232Z | {
"verified": true,
"answer": 11868,
"timestamp": "2026-02-08T17:56:31.568223Z"
} | b22a93 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1020
},
"timestamp": "2026-02-18T10:22:31.536Z",
"answer": 11868
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f48eac | nt_sum_totient_over_divisors_v1_1520064083_4972 | Let $n$ be the smallest sum $x + y$ where $x$ and $y$ are positive integers such that $xy = 7601049$. Define $Q$ to be the remainder when $93367$ multiplied by the sum of $\phi(d)$ over all positive divisors $d$ of $n$ is divided by $90547$. Find the value of $Q$. | 65,943 | graphs = [
Graph(
let={
"_n": Const(90547),
"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(7601049)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.007 | 2026-02-08T06:32:00.428400Z | {
"verified": true,
"answer": 65943,
"timestamp": "2026-02-08T06:32:00.435322Z"
} | 8e72bc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1392
},
"timestamp": "2026-02-13T01:02:01.356Z",
"answer": 65943
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
75cc91 | antilemma_cartesian_v1_1918700295_2483 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 30$ and $1 \leq j \leq 40$. Compute the remainder when $|x|$ is divided by $57746$. | 1,200 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(30)), right=IntegerRange(start=Const(1), end=Const(40)))),
"Q": Mod(value=Abs(arg=Ref(name='x')), modulus=Const(57746)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T07:54:54.605229Z | {
"verified": true,
"answer": 1200,
"timestamp": "2026-02-08T07:54:54.605795Z"
} | 7446c2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 435
},
"timestamp": "2026-02-24T08:39:56.972Z",
"answer": 1200
},
{
"id... | 2 | [
{
"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": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
b0b5ca | geo_visible_lattice_v1_1742523217_3226 | Let $n = 121$. The number of visible lattice points $(x, y)$ with $1 \leq x, y \leq 121$ is the number of such pairs with $\gcd(x, y) = 1$. Let this count be $V$. Compute the remainder when $780 - V$ is divided by $67836$. | 59,625 | graphs = [
Graph(
let={
"n": Const(121),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(780),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(67836)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.317 | 2026-02-08T05:44:42.975824Z | {
"verified": true,
"answer": 59625,
"timestamp": "2026-02-08T05:44:43.292332Z"
} | 24f64b | 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": 19679
},
"timestamp": "2026-02-24T04:27:42.187Z",
"answer": 59625
},
{
... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
72e7b4 | diophantine_product_count_v1_124444284_4680 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Let $S$ be the set of all positive integers $x$ such that $1 \le x \le 129$, $x$ divides $k$, and $\frac{k}{x} \le 129$. Let $n$ be the number of elements in $S$. Compute the smallest positive integer $... | 30 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(129600)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(1... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.013 | 2026-02-08T06:11:33.439440Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T06:11:33.452056Z"
} | 03abbf | 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": 1986
},
"timestamp": "2026-02-12T21:04:21.106Z",
"answer": 30
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5ef248 | antilemma_k2_v1_1520064083_8875 | Let $m = 94$ and let $n = \sum_{d \mid m} \phi(d)$, where $\phi$ denotes Euler's totient function. Define $x = \sum_{k=1}^{94} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$. Compute $24649 - x$. | 20,184 | graphs = [
Graph(
let={
"_m": Const(94),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Const(94), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(2464... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.003 | 2026-02-08T10:25:36.960059Z | {
"verified": true,
"answer": 20184,
"timestamp": "2026-02-08T10:25:36.962782Z"
} | b81ced | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 805
},
"timestamp": "2026-02-14T07:22:07.404Z",
"answer": 20184
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
85111f | nt_min_coprime_above_v1_1470522791_222 | Let $m$ be the smallest integer greater than $1$ that divides $22629049$. Compute the smallest integer $n$ such that $12544 < n \le 12621$ and $\gcd(n, m) = 1$. | 12,545 | graphs = [
Graph(
let={
"start": Const(12544),
"upper": Const(12621),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(22629049))))),
"result": MinOverSet(set=SolutionsSet(var=... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.011 | 2026-02-08T12:54:50.506647Z | {
"verified": true,
"answer": 12545,
"timestamp": "2026-02-08T12:54:50.517438Z"
} | 0b03d6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 524
},
"timestamp": "2026-02-16T04:09:21.955Z",
"answer": 12547
},
{
"id": 11... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
e52fbc | antilemma_sum_equals_v1_1918700295_4423 | Let $N = 7 \times 8 = 56$. Compute the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 56$ and $1 \leq j \leq 56$ such that $i + j = N$. | 55 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(8)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.056 | 2026-02-08T09:22:00.080103Z | {
"verified": true,
"answer": 55,
"timestamp": "2026-02-08T09:22:00.136574Z"
} | df2784 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 294
},
"timestamp": "2026-02-24T11:07:39.935Z",
"answer": 55
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
ed612e | comb_binomial_compute_v1_1218484723_6704 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 20$ satisfying $17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 111537$. Compute $14641 - \binom{15}{k}$. | 8,206 | graphs = [
Graph(
let={
"n": Const(15),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Eq(Sum(Mul(Const(102), Pow(Var("a"), Const(2)), Pow... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_binomial_compute_v1 | null | 5 | 0 | [
"POLY4_COUNT"
] | 1 | 0.002 | 2026-02-25T08:13:11.357808Z | {
"verified": true,
"answer": 8206,
"timestamp": "2026-02-25T08:13:11.359587Z"
} | ea93d2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 773
},
"timestamp": "2026-03-30T02:38:13.539Z",
"answer": 8206
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
bd4cb7 | nt_max_prime_below_v1_397696148_2852 | Let $P$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all prime numbers $n$ such that $P \leq n \leq 16384$. Compute the largest element of $S$, take its absolute value, and find the remainder when this rema... | 2 | graphs = [
Graph(
let={
"_n": Const(11),
"upper": Const(16384),
"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... | NT | COMB | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.515 | 2026-02-08T14:06:29.729543Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T14:06:30.244656Z"
} | be0475 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1527
},
"timestamp": "2026-02-16T00:10:22.541Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
318a32 | modular_min_linear_v1_151522320_2272 | Let $b$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 1854$. Let $x$ be the smallest positive integer such that $1 \leq x \leq 35060$ and $22321x \equiv b \pmod{35060}$. Compute the smallest positive integer $k$ for which the $k$-th Fibonacci number is divisible by $|x| + 2... | 252 | graphs = [
Graph(
let={
"_n": Const(1854),
"a": Const(22321),
"b": 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 | EXTREMUM | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_min_linear_v1 | null | 7 | 0 | [
"COMB1"
] | 1 | 2.389 | 2026-02-08T04:42:54.740514Z | {
"verified": true,
"answer": 252,
"timestamp": "2026-02-08T04:42:57.129707Z"
} | fa10be | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 3719
},
"timestamp": "2026-02-11T21:48:25.951Z",
"answer": 252
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
3baddc | comb_factorial_compute_v1_397696148_1197 | Let $n$ be the largest prime number less than or equal to 10. Let $r = n!$. Compute the remainder when $44121 \cdot r$ is divided by 57998. | 5,508 | graphs = [
Graph(
let={
"_n": Const(57998),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(10)), IsPrime(Var("n"))))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), mo... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T12:25:01.198930Z | {
"verified": true,
"answer": 5508,
"timestamp": "2026-02-08T12:25:01.199667Z"
} | 381c8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 982
},
"timestamp": "2026-02-15T01:03:25.053Z",
"answer": 5508
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6221fa | nt_count_divisible_v1_798873815_21 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 288$ and $7$ divides the $n$-th Fibonacci number. Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 72900$ and $n \equiv d \pmod{7}$, where $d$ is the sum of $\mu(k)$ over all positive divisors $k$ of $\gcd(P, N)$, and $P$ is the... | 10,414 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(288)), Divides(divisor=Const(7), dividend=Fibonacci(arg=Var(name='n')))))),
"upper": Const(72900),
"divisor": Const(7),
"result... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/COUNT_PRIMES/MOBIUS_COPRIME"
] | f93279 | nt_count_divisible_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"COUNT_PRIMES",
"MOBIUS_COPRIME"
] | 3 | 3.899 | 2026-02-08T02:23:47.194963Z | {
"verified": true,
"answer": 10414,
"timestamp": "2026-02-08T02:23:51.093647Z"
} | d1b97e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 1699
},
"timestamp": "2026-02-08T18:30:15.910Z",
"answer": 10414
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL... | {
"lo": -7.46,
"mid": -4.17,
"hi": -1.14
} | ||
2ace25 | algebra_quadratic_discriminant_v1_1918700295_4641 | Let $a = 2$, $b = \sum_{k=1}^{4} k$, and $c = -28$. Let $P$ be the set of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 180$, $\gcd(p, q) = 1$, and $p < q$. Compute $b^2 - 2 \cdot |P| \cdot c$. | 324 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2),
"b": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"c": Const(-28),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPo... | NT | null | COMPUTE | sympy | V8 | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | ac053f | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC",
"V8"
] | 3 | 0.023 | 2026-02-08T09:29:37.885431Z | {
"verified": true,
"answer": 324,
"timestamp": "2026-02-08T09:29:37.908160Z"
} | e0727d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1177
},
"timestamp": "2026-02-14T04:32:50.665Z",
"answer": 324
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c79b6a | comb_sum_binomial_row_v1_1125832087_337 | Let $h = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $n_1 = 6h$. Define $u = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $c$ be the number of integers $t$ such that $5 \leq t \leq 1855$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 338$, $1 \leq b \leq 393$, and $t = 2a + 3b$. Let $r = 2^{12}$. Let $m ... | 47,967 | graphs = [
Graph(
let={
"_n": Const(50214),
"n2": Const(0),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Mul(Const(6), Ref("h")),
"u": Summation(var="k", start=Con... | COMB | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | de7e70 | comb_sum_binomial_row_v1 | negation_mod | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T03:02:03.223768Z | {
"verified": true,
"answer": 47967,
"timestamp": "2026-02-08T03:02:03.225792Z"
} | 44c9ef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 5992
},
"timestamp": "2026-02-23T21:22:12.845Z",
"answer": 47967
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
7ba1fc | comb_factorial_compute_v1_1918700295_560 | Let $n$ be the number of integers $t$ such that $15 \leq t \leq 42$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 6a + 9b$. Compute $n!$. | 40,320 | 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... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_factorial_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T03:18:56.779335Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T03:18:56.783055Z"
} | 6c8037 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 501
},
"timestamp": "2026-02-10T13:55:21.529Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
a45245 | modular_mod_compute_v1_601307018_2271 | Let $N$ be the largest positive divisor $d$ of $4028033$ such that $d^2 \leq 4028033$. Let $S = -71824 \bmod 41209$. Let $C = \left|\{ (a, b) : 1 \leq a \leq 25,\ 1 \leq b \leq 25,\ 2b^2 - 2ab + 13a^2 \leq 2425 \}\right|$. Compute the remainder when $(S \bmod 307) + N \cdot (S \bmod C)$ is divided by $71334$. | 52,553 | graphs = [
Graph(
let={
"_m": Const(71334),
"_n": Const(307),
"a": Const(-71824),
"m": Const(41209),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)),... | NT | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"B3_CLOSEST"
] | ea8e86 | modular_mod_compute_v1 | two_moduli | 6 | 0 | [
"B3_CLOSEST",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.01 | 2026-03-10T02:56:10.063413Z | {
"verified": true,
"answer": 52553,
"timestamp": "2026-03-10T02:56:10.073245Z"
} | 6af9ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T04:55:31.272Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
982b80 | sequence_lucas_compute_v1_655260480_5309 | Let $T$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 121$ and $n_1 \equiv 0 \pmod{121}$. Let $s$ be the sum of the elements of $T$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = s$. Let $L_n$ denote the $n$-th Lucas number, defined b... | 3,579 | graphs = [
Graph(
let={
"_n": Const(66656),
"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")), SumOverSet(set=SolutionsSet(var=Var("n1"), con... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/B3"
] | 07ffbd | sequence_lucas_compute_v1 | null | 5 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.004 | 2026-02-08T18:25:18.268809Z | {
"verified": true,
"answer": 3579,
"timestamp": "2026-02-08T18:25:18.272744Z"
} | a037ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 4267
},
"timestamp": "2026-02-18T16:53:00.374Z",
"answer": 3579
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b7854f | alg_qf_psd_min_v1_1419126231_1 | Let $A = \left| \{ t \mid t = 6a + 14b + 1,\ 1 \le a \le 2066,\ 1 \le b \le 483,\ 21 \le t \le 19159 \} \right|$. Let $P = \min\{x + y \mid x > 0, y > 0,\ xy = 9054081\}$. Find the minimum value of $Aab + Pb^2 + 4425a^2$ over all positive integers $a, b$ with $1 \le a, b \le 29$. | 20,001 | graphs = [
Graph(
let={
"_m": Const(4425),
"_n": Const(29),
"result": MinOverSet(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(29)))),... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | alg_qf_psd_min_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.021 | 2026-02-25T09:29:10.865040Z | {
"verified": true,
"answer": 20001,
"timestamp": "2026-02-25T09:29:10.886081Z"
} | abeb94 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T06:24:09.770Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
9033c6 | algebra_quadratic_discriminant_v1_2051736721_2276 | Let $m = 20$ and let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 270$, $\gcd(p, q) = 1$, and $p < q$. Let $b$ be the largest positive divisor of $460$ that is at most $m$. Compute the absolute value of $b^k - n \cdot (-2) \cdot (-50)$, where $k$ is the number... | 0 | graphs = [
Graph(
let={
"_m": Const(20),
"_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=270)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COPRIME_PAIRS",
"MAX_DIVISOR"
] | b2a4e9 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_DIVISOR"
] | 2 | 0.008 | 2026-02-08T16:33:31.046197Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T16:33:31.053795Z"
} | 2fd158 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 2531
},
"timestamp": "2026-02-17T06:35:07.289Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "o... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4513fc | antilemma_sum_equals_v1_153355830_1868 | Let $x$ be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 94$, $1 \leq j \leq 94$, and $i + j = 95$. Let $y$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8434$. Find the remainder when $y \cdot x$ is divided by $83685$. | 61,658 | graphs = [
Graph(
let={
"_n": Const(95),
"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(94)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | a8cbfb | antilemma_sum_equals_v1 | affine_mod | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.004 | 2026-02-08T06:44:42.586704Z | {
"verified": true,
"answer": 61658,
"timestamp": "2026-02-08T06:44:42.590266Z"
} | 88a3d3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1040
},
"timestamp": "2026-02-24T07:01:52.066Z",
"answer": 61658
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
c42880 | diophantine_fbi2_count_v1_1820931509_691 | Let $n = 8100$. Define $k$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 8100$. Now let $S$ be the set of all integers $d$ such that $3 \leq d \leq 182$, $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 184$. Let $r$ be the number of elements in $S$. Compute the re... | 10,336 | graphs = [
Graph(
let={
"_n": Const(8100),
"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 | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T11:49:29.539899Z | {
"verified": true,
"answer": 10336,
"timestamp": "2026-02-08T11:49:29.549971Z"
} | ee97ca | 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": 1335
},
"timestamp": "2026-02-14T19:30:03.467Z",
"answer": 10336
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b6760e | nt_num_divisors_compute_v1_1248542787_962 | Let $n = 39601$. Compute the number of positive divisors of $n$. | 3 | graphs = [
Graph(
let={
"n": Const(39601),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.067 | 2026-02-08T03:31:02.276622Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T03:31:02.343676Z"
} | 76731b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 235
},
"timestamp": "2026-02-09T10:35:54.158Z",
"answer": 3
},
{
"id": ... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
be119e | comb_sum_binomial_row_v1_1520064083_7780 | Let $n$ be the number of positive integers at most 115 that are divisible by 5 and relatively prime to 21. Compute $2^n$. | 16,384 | graphs = [
Graph(
let={
"_n": Const(115),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(5), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"result": Pow(Const(2),... | NT | null | SUM | sympy | C5 | [
"C5"
] | 1d9668 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.003 | 2026-02-08T09:18:23.508445Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-08T09:18:23.511186Z"
} | 06718b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 79,
"completion_tokens": 1039
},
"timestamp": "2026-02-14T03:01:09.144Z",
"answer": 16384
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
86aea9 | nt_sum_totient_over_divisors_v1_124444284_7625 | Let $T$ be the set of all integers $t$ such that $10 \leq t \leq 2898$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 119$, $1 \leq b \leq 363$, and $t = 3a + 7b$. Let $n$ be the number of elements in $T$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's t... | 2,877 | 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=119)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T09:13:39.311439Z | {
"verified": true,
"answer": 2877,
"timestamp": "2026-02-08T09:13:39.315074Z"
} | 009763 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 6892
},
"timestamp": "2026-02-14T02:06:11.767Z",
"answer": 2877
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4f4853 | nt_count_coprime_v1_458359167_2528 | Let $n = 11011$ and let $d_{\min}$ be the smallest divisor of $n$ that is at least 2. Let
$$
k = \sum_{k=1}^{d_{\min}} \varphi(k) \cdot \left\lfloor \frac{\max\{n \mid 2 \leq n \leq 8,\ n\ \text{is prime}\}}{k} \right\rfloor.
$$
Determine the value of the number of positive integers $m$ such that $1 \leq m \leq 22222$ ... | 9,524 | graphs = [
Graph(
let={
"_n": Const(11011),
"upper": Const(22222),
"k": Summation(var="k", start=Const(1), end=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))), expr=Mul(EulerPhi(n=Var("k")),... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2",
"MAX_PRIME_BELOW/K2"
] | 816350 | nt_count_coprime_v1 | null | 6 | 0 | [
"K2",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 3.104 | 2026-02-08T06:18:43.080698Z | {
"verified": true,
"answer": 9524,
"timestamp": "2026-02-08T06:18:46.184591Z"
} | 349f1a | 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": 1445
},
"timestamp": "2026-02-12T22:46:21.114Z",
"answer": 9524
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a96683 | comb_count_partitions_v1_1978505735_2145 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 484$. Let $m$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $n$ be the largest prime number $p$ such that $2 \leq p \leq m$. Compute the number of unordered partitions of $n$. | 63,261 | graphs = [
Graph(
let={
"_m": Const(2),
"_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(484)))), expr=Sum(Var("x"), Var("y")))),
... | NT | COMB | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | comb_count_partitions_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T16:40:34.293668Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T16:40:34.295430Z"
} | 793a83 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1227
},
"timestamp": "2026-02-17T11:09:50.464Z",
"answer": 63261
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fcae50 | nt_count_divisible_v1_784195855_7636 | Let $m = 17$. Define $N$ to be the number of positive integers $k$ such that $1 \leq k \leq 104448$ and $m$ divides $k$. Let $S$ be the set of all positive integers $t$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 36$, $1 \leq b \leq 9$, $9 \leq t \leq 270$, and $t = 7a + 2b$. Let $D$ be the number of... | 1,365 | graphs = [
Graph(
let={
"_m": Const(17),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(104448)), Divides(divisor=Ref("_m"), dividend=Var("k"))), domain='positive_integers')),
"upper": Const(32768),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/C2",
"C2/C2"
] | e8bf21 | nt_count_divisible_v1 | null | 7 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 1.029 | 2026-02-08T09:25:25.387995Z | {
"verified": true,
"answer": 1365,
"timestamp": "2026-02-08T09:25:26.416783Z"
} | a9a7d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 3057
},
"timestamp": "2026-02-14T03:49:38.993Z",
"answer": 1365
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cec71e_n | alg_linear_system_2x2_v1_1419126231_98 | A robot follows a path determined by two linear equations. The determinant of the system is $\det = -2 \cdot (-12) - (-9) \cdot 13$. To find the intersection point, it computes the numerators: $M$ for the $x$-coordinate using constants $-146254$ and $-639108$ with the sum $\sum_{k=0}^2 3^k$, and $R$ for the $y$-coordin... | 71,102 | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | alg_linear_system_2x2_v1 | null | 3 | null | [
"SUM_GEOM"
] | 1 | 0.002 | 2026-02-25T09:38:04.080742Z | null | a0ddb7 | cec71e | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 2338
},
"timestamp": "2026-03-31T03:15:51.748Z",
"answer": 71102
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
71e96e | algebra_quadratic_discriminant_v1_865884756_5446 | Let $S$ be the set of all ordered pairs of positive integers $(p, q)$ such that $p \cdot q = 3557400$, $\gcd(p, q) = 1$, and $p < q$. Let $b$ be the number of elements in $S$. Compute $b^2 - 4 \cdot (-1) \cdot (-64)$. | 0 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-1),
"b": 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=3557400)), Eq(left=GC... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"COUNT_COPRIME_GRID"
] | 2 | 0.011 | 2026-02-08T18:36:02.503599Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T18:36:02.514151Z"
} | be83d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1553
},
"timestamp": "2026-02-18T18:09:10.784Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ec1e5c | nt_sum_gcd_range_mod_v1_2051736721_5773 | Let $N$ be the value of
\[
\sum_{k_1=1}^{S} \varphi(k_1) \left\lfloor \frac{45}{k_1} \right\rfloor,
\]
where $S = \sum_{k_2=1}^{9} \varphi(k_2) \left\lfloor \frac{9}{k_2} \right\rfloor$ and $\varphi(n)$ denotes Euler's totient function. Let $\text{sum}$ be the sum of $\gcd(n, 504)$ for all positive integers $n$ from $1... | 401 | graphs = [
Graph(
let={
"_n": Const(9),
"N": Summation(var="k1", start=Const(1), end=Summation(var="k2", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k2")), Floor(Div(Const(9), Var("k2"))))), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(45), Var("k1"))))),
"... | NT | null | COMPUTE | sympy | B3 | [
"B3",
"K2/K2"
] | f90a31 | nt_sum_gcd_range_mod_v1 | negation_mod | 7 | 0 | [
"B3",
"K2"
] | 2 | 0.049 | 2026-02-08T18:47:51.496485Z | {
"verified": true,
"answer": 401,
"timestamp": "2026-02-08T18:47:51.545362Z"
} | 364a24 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 4756
},
"timestamp": "2026-02-18T19:37:13.013Z",
"answer": 401
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6db458 | geo_count_lattice_triangle_v1_601307018_2509 | Let $S = \left|111 \cdot 196 + 64 \cdot (-128)\right|$. Let $T = \gcd(111, 128) + \gcd\left(|64 - 111|, \left| N - 128 \right|\right) + \gcd\left(64, \left| \min\{ |x - y| : x, y > 0,\, xy = 77421 \} \right|\right)$, where $N$ is the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 25$ such ... | 6,780 | graphs = [
Graph(
let={
"_c": Const(64),
"_m": Const(10),
"_n": Const(77421),
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=196)), Mul(Ref(name='_c'), Sub(left=Const(value=0), right=Const(value=128))))),
"boundary": Sum(GCD(a=Abs(arg=Con... | GEOM | NT | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/QF_PSD_COUNT_LEQ",
"B3_DIFF"
] | 9b0774 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3_DIFF",
"MAX_DIVISOR",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.021 | 2026-03-10T03:13:30.182218Z | {
"verified": true,
"answer": 6780,
"timestamp": "2026-03-10T03:13:30.202853Z"
} | 0ef780 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 312,
"completion_tokens": 8968
},
"timestamp": "2026-03-29T05:33:05.128Z",
"answer": 6780
},
{
"i... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
08432f_n | comb_catalan_compute_v1_1218484723_687 | A theater director is casting a play that requires 10 pairs of actors to enter the stage one after another, such that no pair enters before their cue and actors always enter in the correct order within each pair. The number of valid entry sequences is the 10th Catalan number. How many such sequences are possible? | 16,796 | COMB | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE/HALFPLANE_COUNT"
] | 1fa792 | comb_catalan_compute_v1 | null | 2 | null | [
"HALFPLANE_COUNT",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.093 | 2026-02-25T02:26:09.377106Z | null | 4703aa | 08432f | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 212
},
"timestamp": "2026-03-30T15:45:45.213Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "HALFPLANE_COUNT",
"status": "ok_later"
},
{
"lemma": "PO... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
b444c9 | comb_sum_binomial_row_v1_2051736721_928 | Let $n = 15$. Compute $2^n$, and let $R$ be the absolute value of this result. Let $p$ be the largest prime number less than or equal to $11$. Compute the Bell number $B_{R \bmod p}$. Find the remainder when this Bell number is divided by $51249$. | 13,477 | graphs = [
Graph(
let={
"_n": Const(51249),
"n": Const(15),
"result": Pow(Const(2), Ref("n")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), ... | NT | COMB | SUM | sympy | LTE_SUM | [
"MAX_PRIME_BELOW"
] | 88ea9c | comb_sum_binomial_row_v1 | bell_mod | 5 | 0 | [
"LTE_SUM",
"MAX_PRIME_BELOW"
] | 2 | 0.013 | 2026-02-08T15:45:49.446546Z | {
"verified": true,
"answer": 13477,
"timestamp": "2026-02-08T15:45:49.459829Z"
} | 561b82 | 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": 531
},
"timestamp": "2026-02-16T12:33:06.925Z",
"answer": 13477
},
{... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f2d073 | comb_catalan_compute_v1_151522320_358 | Let $T$ be the set of all integers $t$ such that $20 \leq t \leq 32$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 3a + 2b + 15$. Let $n$ be the number of elements in $T$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:10:48.727722Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T03:10:48.729249Z"
} | 27fb35 | 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": 1626
},
"timestamp": "2026-02-10T13:26:45.448Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
951523 | geo_count_lattice_rect_v1_124444284_7294 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 24$ and $0 \leq y \leq 79$. | 2,000 | graphs = [
Graph(
let={
"a": Const(24),
"b": Const(79),
"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 | 0.002 | 2026-02-08T08:59:21.144090Z | {
"verified": true,
"answer": 2000,
"timestamp": "2026-02-08T08:59:21.145983Z"
} | 1fb0c7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 98
},
"timestamp": "2026-02-24T10:23:31.521Z",
"answer": 2000
},
{
"id"... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
d0b53d | nt_sum_divisors_range_v1_1520064083_2586 | Let $P$ be the set of all prime numbers $n$ such that $2 \leq n \leq 6288$. Compute the largest element of $P$. Let $N$ be this largest prime. Compute the sum of the number of positive divisors of each integer from $1$ to $N$, inclusive. | 55,949 | graphs = [
Graph(
let={
"_n": Const(6288),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n... | NT | null | SUM | sympy | ONE_PHI_2 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_divisors_range_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 2 | 3.06 | 2026-02-08T04:52:19.881925Z | {
"verified": true,
"answer": 55949,
"timestamp": "2026-02-08T04:52:22.941946Z"
} | d40d3c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 4466
},
"timestamp": "2026-02-11T22:24:06.983Z",
"answer": 55949
},
{
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
49fec0 | nt_num_divisors_compute_v1_655260480_1180 | Let $n = 95548$. Let $r_1$ and $r_2$ be the roots of the quadratic equation $x^2 - 6000x + 315191 = 0$. Define $s = r_1 + r_2$. Compute the number of positive divisors of $s$, then find the remainder when $28327$ times this number is divided by $n$. | 82,052 | graphs = [
Graph(
let={
"_n": Const(95548),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-6000), Var("x")), Const(315191)), Const(0)))),
"result": NumDivisors(n=Ref("n")),
"Q": Mod(value=Mul(Const(28327), R... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.005 | 2026-02-08T15:58:34.052628Z | {
"verified": true,
"answer": 82052,
"timestamp": "2026-02-08T15:58:34.057764Z"
} | 6dde89 | 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": 706
},
"timestamp": "2026-02-16T19:09:07.213Z",
"answer": 82052
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f99cb8_l | comb_count_permutations_fixed_v1_1918700295_2934 | Let $c = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, and let $a = 4c$. Let $n_1 = a + 4$. Define $t = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n$ be the number of integers $t$ in the range $10 \leq t \leq 30$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 4a + 6b$. Let $k =... | 0 | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 1f40c5 | comb_count_permutations_fixed_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.004 | 2026-02-08T08:19:21.787111Z | {
"verified": false,
"answer": 168,
"timestamp": "2026-02-08T08:19:21.791043Z"
} | e6701f | f99cb8 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 310,
"completion_tokens": 2626
},
"timestamp": "2026-02-24T09:19:14.672Z",
"answer": 168
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma":... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | |
ffd404 | geo_count_lattice_rect_v1_2051736721_2706 | Compute the number of lattice points $(x,y)$ such that $0 \leq x \leq 128$ and $0 \leq y \leq 70$. | 9,159 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(70),
"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 | 2026-02-08T16:51:38.124355Z | {
"verified": true,
"answer": 9159,
"timestamp": "2026-02-08T16:51:38.125745Z"
} | 22e5a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 483
},
"timestamp": "2026-02-17T13:13:26.940Z",
"answer": 9159
},
{
... | 1 | [] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||||
0b1eda | algebra_quadratic_discriminant_v1_865884756_1796 | Let $a = 1$, $b = 0$, and $c = -64$. Define $\Delta = b^2 - 4ac$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $\Delta + 2$. | 132 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(0),
"c": Const(-64),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
... | NT | null | COMPUTE | sympy | V8 | [
"C2"
] | 9685eb | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"C2",
"V8"
] | 2 | 0.022 | 2026-02-08T16:18:02.078238Z | {
"verified": true,
"answer": 132,
"timestamp": "2026-02-08T16:18:02.100259Z"
} | 7d57dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 1339
},
"timestamp": "2026-02-17T00:23:53.742Z",
"answer": 132
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
16a6ae | nt_sum_totient_over_divisors_v1_124444284_5174 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 13264164$. Let $s$ be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $n$ be the largest positive divisor of $53151348$ that is less than or equal to $s$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 7,284 | 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(13264164)))), expr=Sum(Var("x"), Var("y")))),
"n": MaxOverS... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 33b851 | nt_sum_totient_over_divisors_v1 | null | 7 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.011 | 2026-02-08T06:26:00.789945Z | {
"verified": true,
"answer": 7284,
"timestamp": "2026-02-08T06:26:00.801202Z"
} | 0da175 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 2462
},
"timestamp": "2026-02-12T23:44:59.830Z",
"answer": 7284
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c86be7 | algebra_poly_eval_v1_865884756_3045 | Let $y$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Compute $6y^3 - 3y^2 + 4y - 4$. | 1,935 | graphs = [
Graph(
let={
"_n": Const(2),
"y": 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")), Con... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | algebra_poly_eval_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T17:08:08.383603Z | {
"verified": true,
"answer": 1935,
"timestamp": "2026-02-08T17:08:08.386480Z"
} | b8e313 | 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": 738
},
"timestamp": "2026-02-17T19:57:14.778Z",
"answer": 1935
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b0c9d8 | comb_count_surjections_v1_124444284_7201 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 10$, $1 \le i \le 8$, and $1 \le j \le 9$. Let $k = 4$. Define $r = k! \cdot S(n,k)$, where $S(n,k)$ denotes the Stirling number of the second kind. Compute the remainder when $87268 \cdot r$ is divided by $50413$. | 42,948 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(10)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(9))))),
"k": Co... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T08:54:44.352605Z | {
"verified": true,
"answer": 42948,
"timestamp": "2026-02-08T08:54:44.363038Z"
} | 85dde3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 3068
},
"timestamp": "2026-02-24T10:09:43.765Z",
"answer": 42948
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
e8c292_n | alg_poly3_count_v1_1218484723_2832 | A game designer creates levels where players collect tokens $a$ and $b$ under constraints. The maximum token $a$ a player can carry is determined by a lattice count $A$: first compute $|S|$ for combinations of inputs generating values between $12$ and $2283$ via $7a_1+5b_1$, then count pairs $(a_1,b_1)$ in $[1,30]^2$ s... | 178 | ALG | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/QF_PSD_COUNT_LEQ"
] | 77251b | alg_poly3_count_v1 | null | 7 | null | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.185 | 2026-02-25T04:33:36.601702Z | null | 2c25e8 | e8c292 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 9434
},
"timestamp": "2026-03-30T19:08:23.209Z",
"answer": 178
},
{
"id... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
7c1bf1 | diophantine_product_count_v1_168721529_427 | Let $k = 120$. Define $u$ to be the number of integers $t$ such that $27 \leq t \leq 312$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 21$, and $t = 15a + 12b$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Compute ... | 14 | graphs = [
Graph(
let={
"k": Const(120),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=V... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.071 | 2026-02-08T13:02:59.961395Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T13:03:00.032487Z"
} | 6542f8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 5023
},
"timestamp": "2026-02-09T04:56:26.383Z",
"answer": 14
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -2,
"mid": 1.85,
"hi": 5.2
} | ||
92579b | algebra_quadratic_discriminant_v1_124444284_2643 | Let $a = -10$, $b = -6$, and $c = 4$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$. Let $P$ be the maximum value of $xy$ over all such pairs. Define $D = b^2 - 4a c P$. Let $\text{result} = 2 \cdot [D > 0] + [D = 0]$, where $[\cdot]$ denotes the Iverson bracket (1 if the con... | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-10),
"b": Const(-6),
"c": Const(4),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.005 | 2026-02-08T04:52:06.204357Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T04:52:06.208902Z"
} | 3ea47f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 339
},
"timestamp": "2026-02-11T21:59:48.408Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
70b05a | comb_count_partitions_v1_124444284_2444 | Let $T$ be the set of all integers $t$ such that $18 \leq t \leq 124$ and there exist positive integers $a \leq 6$ and $b \leq 8$ for which $t = 10a + 8b$. Let $n$ be the number of elements in $T$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $92330 \cdot p(n)$ is divided by $57... | 14,518 | graphs = [
Graph(
let={
"_n": Const(57329),
"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... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:40:41.464803Z | {
"verified": true,
"answer": 14518,
"timestamp": "2026-02-08T04:40:41.467129Z"
} | b07ccb | 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": 14358
},
"timestamp": "2026-02-24T01:27:43.830Z",
"answer": 14518
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
6d0569 | antilemma_k3_v1_898971024_1397 | Let $x = \sum_{d \mid 31885} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $44121 \cdot x$ is divided by $90371$. | 83,099 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=31885), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(90371)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:06:02.426357Z | {
"verified": true,
"answer": 83099,
"timestamp": "2026-02-08T16:06:02.427602Z"
} | a1e063 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 1198
},
"timestamp": "2026-02-16T20:21:38.135Z",
"answer": 83099
},
{... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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