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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
79761d | antilemma_product_of_sums_v1_1520064083_1057 | Let $S_1 = \sum_{k=1}^{20} k$. Let $S_2$ be the sum of $i \cdot j$ over all ordered pairs $(i, j)$ with $1 \leq i \leq 4$ and $1 \leq j \leq 7$. Let $x = S_1 \cdot S_2$. Let $d_i$ denote the $i$-th decimal digit of $|x|$, starting from $i=0$ for the units digit. Suppose $x$ has $\ell$ digits, so $i$ ranges from $0$ to ... | 4,769 | graphs = [
Graph(
let={
"S1": Summation(var="k", start=Const(1), end=Const(20), expr=Var("k")),
"S2": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), righ... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 4 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T03:45:25.931782Z | {
"verified": true,
"answer": 4769,
"timestamp": "2026-02-08T03:45:25.932625Z"
} | 94d7b0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 519
},
"timestamp": "2026-02-18T06:05:34.195Z",
"answer": 4769
}
] | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
b0c6f4 | nt_sum_divisors_compute_v1_458359167_1579 | Compute the sum of all positive divisors of $44444$. | 79,968 | graphs = [
Graph(
let={
"n": Const(44444),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | BIG_OMEGA_ZERO | [
"BIG_OMEGA_ZERO",
"MOBIUS_COPRIME",
"LIOUVILLE_ONE"
] | 8557b9 | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"BIG_OMEGA_ZERO",
"LIOUVILLE_ONE",
"MOBIUS_COPRIME"
] | 3 | 0.004 | 2026-02-08T04:45:57.248615Z | {
"verified": true,
"answer": 79968,
"timestamp": "2026-02-08T04:45:57.252677Z"
} | 33931e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1053
},
"timestamp": "2026-02-11T21:52:42.977Z",
"answer": 79968
},
{
... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"stat... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
048d38 | comb_factorial_compute_v1_1218484723_7378 | Let $n$ be the number of non-negative integers $j$ with $0 \le j \le 1282$ such that
$$\binom{\left|\{(a, b) : 1 \le a \le \left|\{(a_1, b_1) : 1 \le a_1 \le 40,\ 1 \le b_1 \le 40,\ -189a_1^{3} = -23625\}\right|,\ 1 \le b \le 40,\ 25b^{2} + 34a^{2} + 22ab \le 65610\}\right|}{j} \bmod 2 = 1.$$
Let $S = n!$. Find the rem... | 4,980 | graphs = [
Graph(
let={
"_c": Const(22847),
"_m": Const(2),
"_n": Const(70806),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(1282)), Eq(Mod(value=Binom(n=CountOverSet(set=SolutionsSet(var=Tuple(ele... | COMB | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"POLY3_COUNT/QF_PSD_COUNT_LEQ/V8"
] | cd9964 | comb_factorial_compute_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"POLY3_COUNT",
"QF_PSD_COUNT_LEQ",
"V8"
] | 4 | 0.062 | 2026-02-25T08:47:12.412471Z | {
"verified": true,
"answer": 4980,
"timestamp": "2026-02-25T08:47:12.474804Z"
} | 829820 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T04:17:00.764Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
084548 | antilemma_k3_v1_1520064083_8844 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $21915$, where $\phi$ denotes Euler's totient function. | 21,915 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=21915), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T10:25:01.851847Z | {
"verified": true,
"answer": 21915,
"timestamp": "2026-02-08T10:25:01.852072Z"
} | d05eba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 878
},
"timestamp": "2026-02-14T07:20:56.388Z",
"answer": 21915
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1163d2 | nt_count_divisors_in_range_v1_151522320_104 | Let $p = 47$ and $q = 11$. Define $n_2 = p \cdot q$. Let $h = \lambda(n_2)$, where $\lambda$ denotes the Liouville function. Let $n_1 = 2$ and define $f = \left(\sum_{d \mid n_1} \phi(d)\right) - n_1$, where $\phi$ is Euler's totient function. Let $n = 5040$ and $a = 1 + f$. Let $b$ be the number of positive integers $... | 51,842 | graphs = [
Graph(
let={
"p": Const(47),
"q": Const(11),
"n2": Mul(Ref("p"), Ref("q")),
"h": LiouvilleLambda(n=Ref(name='n2')),
"n1": Const(2),
"f": Sub(SumOverDivisors(n=Ref(name='n1'), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("n1"... | NT | null | COUNT | sympy | EULER_TOTIENT_SUM | [
"EULER_TOTIENT_SUM",
"LIOUVILLE_ONE",
"LIN_FORM"
] | 42b0ed | nt_count_divisors_in_range_v1 | null | 5 | 2 | [
"EULER_TOTIENT_SUM",
"LIN_FORM",
"LIOUVILLE_ONE"
] | 3 | 0.025 | 2026-02-08T02:58:42.156075Z | {
"verified": true,
"answer": 51842,
"timestamp": "2026-02-08T02:58:42.180721Z"
} | c1a289 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 375,
"completion_tokens": 5904
},
"timestamp": "2026-02-08T23:07:18.224Z",
"answer": 51842
},
{
... | 1 | [
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
c71c15 | diophantine_product_count_v1_865884756_1336 | Let $k$ be the number of prime numbers $n$ such that $2 \leq n \leq 281$. Let $S$ be the set of positive integers $x$ such that $1 \leq x \leq 36$, $x$ divides $k$, and $\frac{k}{x} \leq 36$. Compute the value of $11664 - |S|$. | 11,654 | graphs = [
Graph(
let={
"_n": Const(2),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(281)), IsPrime(Var("n"))))),
"upper": Const(36),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), conditio... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | diophantine_product_count_v1 | null | 5 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.006 | 2026-02-08T15:57:27.244157Z | {
"verified": true,
"answer": 11654,
"timestamp": "2026-02-08T15:57:27.249982Z"
} | 1d83e3 | 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": 1226
},
"timestamp": "2026-02-16T17:56:01.141Z",
"answer": 11654
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fecce0 | comb_catalan_compute_v1_1978505735_4861 | Let $a = 4$ and $b = 3$, and define $n_2 = a + b$. Compute
$$
c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = c$. Compute
$$
v = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}.
$$
Let $s$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Define $n = s \cdot v$. C... | 58,786 | graphs = [
Graph(
let={
"a": Const(4),
"b": Const(3),
"n2": Sum(Ref("a"), Ref("b")),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("c"),
"v": Summat... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_catalan_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.004 | 2026-02-08T18:36:16.777695Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T18:36:16.781746Z"
} | d2f9de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 1041
},
"timestamp": "2026-02-18T18:00:47.839Z",
"answer": 58786
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"l... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
5ee9ea | geo_count_lattice_triangle_v1_601307018_7927 | Let $R = \left|111 \cdot 256 + 256 \cdot (-49)\right|$,
$$
S = \gcd(111, 49) + \gcd(|256 - 111|, |256 - 49|) + \gcd(|0 - 256|, |0 - 256|),
$$
and
$$
T = \frac{R + 2 - S}{\left|\left\{ (a, b) : 1 \leq a, b \leq 15,\ 216a^3b + 82b^4 + 162a^4 + C \cdot ab^3 + 540a^2b^2 = 104992 \right\}\right|},
$$
where $C = \left|\left... | 40,153 | graphs = [
Graph(
let={
"_m": Const(111),
"_n": Const(540),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_m'), Const(value=256)), Mul(Const(value=256), Sub(left=Const(value=0), right=Const(value=49))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const... | GEOM | NT | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY4_COUNT"
] | a605ae | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.021 | 2026-03-10T08:28:38.653314Z | {
"verified": true,
"answer": 40153,
"timestamp": "2026-03-10T08:28:38.673837Z"
} | b68725 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 356,
"completion_tokens": 22795
},
"timestamp": "2026-04-19T07:50:58.560Z",
"answer": 40153
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
37f51c | nt_max_prime_below_v1_124444284_225 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 14$. Let $r$ be the largest prime number $p$ such that $13^{v_{13}(n \cdot 13)} \leq p \leq 26569$. Compute the remainder when $51287 \cdot r$ is divided by $82290$. | 5,347 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(14)), IsPrime(Var("n"))))),
"upper": Const(26569),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), MaxKDivide... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K13"
] | b92fdf | nt_max_prime_below_v1 | null | 4 | 0 | [
"K13",
"MAX_PRIME_BELOW"
] | 2 | 2.898 | 2026-02-08T03:04:56.262781Z | {
"verified": true,
"answer": 5347,
"timestamp": "2026-02-08T03:04:59.160948Z"
} | 6e5aa2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 6613
},
"timestamp": "2026-02-08T23:59:06.373Z",
"answer": 5347
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status":... | {
"lo": -6.49,
"mid": 0.45,
"hi": 7.05
} | ||
d9dca8 | nt_num_divisors_compute_v1_458359167_5387 | Let $ n = 45369 $. Let $ d(n) $ denote the number of positive divisors of $ n $. Compute $ d(n) $. | 9 | graphs = [
Graph(
let={
"n": Const(45369),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.184 | 2026-02-08T12:27:16.953433Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T12:27:17.137564Z"
} | 04a665 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 460
},
"timestamp": "2026-02-15T00:58:37.716Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
666bcb | nt_count_divisors_in_range_v1_1116507919_418 | Let $n = 221760$. Define $a = \sum_{k=\phi(1)}^{3} k$ and $b = 24642$. Let $S$ be the set of all positive divisors $d$ of $n$ such that $a \leq d \leq b$. Compute the remainder when $44121$ multiplied by the number of elements in $S$ is divided by $97667$. | 2,065 | graphs = [
Graph(
let={
"n": Const(221760),
"a": Summation(var="k", start=EulerPhi(n=Const(1)), end=Const(3), expr=Var("k")),
"b": Const(24642),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), G... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"ONE_PHI_1"
] | 342157 | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"ONE_PHI_1",
"SUM_ARITHMETIC"
] | 2 | 0.191 | 2026-02-08T02:34:05.590972Z | {
"verified": true,
"answer": 2065,
"timestamp": "2026-02-08T02:34:05.782377Z"
} | 9ae5c8 | 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": 2235
},
"timestamp": "2026-02-08T19:31:51.083Z",
"answer": 2065
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
97945b | modular_count_residue_v1_151522320_1729 | Let $r$ be the sum of all real solutions $x$ to the equation $x^2 - 11x + 18 = 0$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 44944$ and $n \equiv r \pmod{12}$. | 3,745 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(44944),
"m": Const(12),
"r": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-11), Var("x")), Const(18)), Const(0)))),
"result": CountOverSet(set=... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_count_residue_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 1.708 | 2026-02-08T04:19:02.867853Z | {
"verified": true,
"answer": 3745,
"timestamp": "2026-02-08T04:19:04.576051Z"
} | 80826e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 643
},
"timestamp": "2026-02-10T16:18:05.321Z",
"answer": 3745
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
0b1156 | geo_count_lattice_rect_v1_1419126231_792 | Find the number of lattice points $(x, y)$ such that $0 \leq x \leq 81$ and $0 \leq y \leq 183$. | 15,088 | graphs = [
Graph(
let={
"a": Const(81),
"b": Const(183),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | GEOM | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-25T10:17:11.840916Z | {
"verified": true,
"answer": 15088,
"timestamp": "2026-02-25T10:17:11.841416Z"
} | 916b8f | 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": 207
},
"timestamp": "2026-03-30T10:02:00.145Z",
"answer": 15088
},
{
"i... | 1 | [] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||||
435e00 | modular_product_range_v1_168721529_2094 | Let $S$ be the set of all integers $t$ such that $7 \leq t \leq 42$ and $t = 4a + 3b$ for some integers $a$ and $b$ with $1 \leq a \leq 6$ and $1 \leq b \leq 6$. Let $k$ be the number of elements in $S$. Compute the remainder when $$\prod_{i=k}^{107} i$$ is divided by $10391$. | 5,558 | graphs = [
Graph(
let={
"_n": Const(107),
"prod": MathProduct(expr=Var("i"), var="i", start=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(na... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_product_range_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-08T14:07:03.551316Z | {
"verified": true,
"answer": 5558,
"timestamp": "2026-02-08T14:07:03.559365Z"
} | eb7b06 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 8121
},
"timestamp": "2026-02-11T11:02:34.750Z",
"answer": 5558
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": 0.22,
"hi": 7.52
} | ||
354cd2 | comb_count_permutations_fixed_v1_898971024_1917 | Let $t = \sum_{k_1=0}^{0} (-1)^{k_1} \binom{0}{k_1}$ and let $v = \sum_{k_2=0}^{0} (-1)^{k_2} \binom{0}{k_2}$, where the upper limit of the sum for $v$ is defined as $\sum_{k_3=0}^{10} (-1)^{k_3} \binom{10}{k_3}$ minus $\sum_{k_4=0}^{4} (-1)^{k_4} \binom{4}{k_4}$. Let $r = \binom{5}{3} \cdot !2$, where $!2$ denotes the... | 31,090 | graphs = [
Graph(
let={
"n2": Const(0),
"t": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"n1": Const(0),
"v": Summation(var="k2", start=Summation(var="k3", start=Summation(var="k4", ... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.004 | 2026-02-08T16:25:47.106608Z | {
"verified": true,
"answer": 31090,
"timestamp": "2026-02-08T16:25:47.110286Z"
} | 3566e8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 1371
},
"timestamp": "2026-02-24T20:52:54.231Z",
"answer": 31090
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
009015 | nt_count_digit_sum_v1_784195855_5105 | Let $U = 99999$ and $s = 26$. Define $N$ to be the number of positive integers $n$ such that $1 \le n \le U$ and the sum of the decimal digits of $n$ is equal to $s$.
Let $c = 47$. Consider the decimal digits of $|N|$, indexed starting from $0$ at the units place. Let $t$ be the number of digits in $|N|$, and define
$... | 177 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": Const(26),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
"_c": Const(47),
... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 7.27 | 2026-02-08T07:40:26.047465Z | {
"verified": true,
"answer": 177,
"timestamp": "2026-02-08T07:40:33.317475Z"
} | 13eb87 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 2705
},
"timestamp": "2026-02-24T08:20:02.066Z",
"answer": 177
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
3f8487_n | alg_poly_orbit_legendre_v1_1218484723_4274 | A cryptographic function processes an input $a$ modulo 23 through two transformation paths: one via exponentiation ($a^{11}$), the other via a cubic polynomial ($a^3 + 4a$). These yield values $N$ and $M$. The process repeats on $M$ to get $R$ and $T$. The sum $S = N + R$ must be divisible by 3. How many inputs $a$ fro... | 2,284 | ALG | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 6 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.013 | 2026-02-25T05:54:59.233801Z | null | c67a39 | 3f8487 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 8265
},
"timestamp": "2026-03-30T21:24:08.610Z",
"answer": 2284
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
058ce1 | diophantine_product_count_v1_655260480_1729 | Let $k$ be the number of integers $t$ such that $14 \leq t \leq 197$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 36$, and $t = 2a + 5b + 7$.
Let $u$ be the number of integers $t_1$ such that $7 \leq t_1 \leq 61$ and there exist integers $a$ and $b$ with $1 \leq a \leq 13$, $1 \leq b \le... | 12 | graphs = [
Graph(
let={
"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=5)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.009 | 2026-02-08T16:18:55.962663Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T16:18:55.971819Z"
} | f39105 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 5576
},
"timestamp": "2026-02-17T01:17:40.628Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
79626a | lin_form_endings_v1_798873815_451 | Let $a = 60$ and $b = 75$. Define $r = \left\lfloor \frac{60}{\gcd(a, b)} \right\rfloor$. Let $s = 12666 \cdot r$, and let $x$ be the remainder when $s$ is divided by $81955$. Compute $x$. | 50,664 | graphs = [
Graph(
let={
"a_coeff": Const(60),
"b_coeff": Const(75),
"_inner_result": Floor(Div(Const(60), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(12666),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T02:38:49.976087Z | {
"verified": true,
"answer": 50664,
"timestamp": "2026-02-08T02:38:49.978230Z"
} | 68ab07 | 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": 505
},
"timestamp": "2026-02-08T19:32:46.780Z",
"answer": 50664
},
{
"i... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"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",
"status... | {
"lo": -7.73,
"mid": -5.64,
"hi": -3.79
} | ||
785728 | comb_count_permutations_fixed_v1_153355830_2336 | Let $ d $ be the smallest divisor of $ 539539 $ that is at least $ 2 $. Compute $ \binom{10}{d} \cdot !(10 - d) $, where $ !n $ denotes the number of derangements of $ n $ elements. | 240 | graphs = [
Graph(
let={
"n": Const(10),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(539539))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T07:04:01.206466Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T07:04:01.208271Z"
} | f2dae2 | 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": 1115
},
"timestamp": "2026-02-13T07:29:13.716Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
cf966d | sequence_count_fib_divisible_v1_784195855_387 | Let $T$ be the number of integers $t$ with $9 \leq t \leq 143$ for which there exist positive integers $a \leq 26$ and $b \leq 13$ such that $t = 2a + 7b$. Let $d$ be the smallest divisor of $31603$ that is greater than $1$. Determine the number of positive integers $n \leq T$ such that $d$ divides the $n$-th Fibonacci... | 4,404 | graphs = [
Graph(
let={
"_n": Const(31603),
"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=26)), Geq(le... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.143 | 2026-02-08T03:07:34.764689Z | {
"verified": true,
"answer": 4404,
"timestamp": "2026-02-08T03:07:34.907634Z"
} | faeae3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 6821
},
"timestamp": "2026-02-11T08:57:13.929Z",
"answer": 4404
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
af3991 | nt_count_with_divisor_count_v1_784195855_4435 | Let $n$ be a positive integer such that $1 \leq n \leq 11236$ and the number of positive divisors of $n$ is exactly 7. Compute the number of such integers $n$. | 2 | graphs = [
Graph(
let={
"upper": Const(11236),
"div_count": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("r... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K3"
] | 7bbb8e | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"K3",
"SUM_ARITHMETIC"
] | 2 | 2.96 | 2026-02-08T07:06:01.873216Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T07:06:04.832953Z"
} | 1dc4a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 790
},
"timestamp": "2026-02-13T07:40:08.271Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
0c8b71 | antilemma_k3_v1_784195855_3512 | Compute
$$
\sum_{d \mid 6715} \phi(d),
$$
where $\phi(n)$ denotes Euler's totient function. | 6,715 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=6715), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T06:28:03.740785Z | {
"verified": true,
"answer": 6715,
"timestamp": "2026-02-08T06:28:03.741028Z"
} | 947ad5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 471
},
"timestamp": "2026-02-13T00:35:33.908Z",
"answer": 6715
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
d10caf | nt_count_divisible_and_v1_153355830_2245 | Let $\text{upper} = 111660$ and $d_1 = 6$. Define
$$
d_2 = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 3,722 | graphs = [
Graph(
let={
"upper": Const(111660),
"d1": Const(6),
"d2": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 4 | 0 | [
"K2"
] | 1 | 4.672 | 2026-02-08T07:00:14.376342Z | {
"verified": true,
"answer": 3722,
"timestamp": "2026-02-08T07:00:19.048518Z"
} | 03c5d4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 634
},
"timestamp": "2026-02-15T18:50:15.770Z",
"answer": 3722
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
982aa8 | modular_modexp_compute_v1_458359167_4310 | Let $a$ be the smallest divisor of $175$ that is at least $2$. Let $e$ be the number of positive integers $n$ with $1 \leq n \leq 23809$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Compute the remainder when $a^e$ is divided by $78606$. Find the value of this remainder. | 73,727 | graphs = [
Graph(
let={
"_n": Const(23809),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(175))))),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"L3C"
] | 156825 | modular_modexp_compute_v1 | null | 5 | 0 | [
"L3C",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T11:41:33.453517Z | {
"verified": true,
"answer": 73727,
"timestamp": "2026-02-08T11:41:33.455729Z"
} | 61053e | 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": 2854
},
"timestamp": "2026-02-14T17:12:36.362Z",
"answer": 73727
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
54ab39 | nt_count_divisors_in_range_v1_124444284_845 | Let $n = 20160$. Let $a$ be the smallest divisor of $29645$ that is at least $2$. Let $b = 20165$. Consider the set of all positive integers $d$ such that $d$ divides $n$, $a \leq d$, and $d \leq b$. Compute the number of elements in this set. Multiply this number by $34901$, and find the remainder when the product is ... | 26,240 | graphs = [
Graph(
let={
"n": Const(20160),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(29645))))),
"b": Const(20165),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condi... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.186 | 2026-02-08T03:32:55.260446Z | {
"verified": true,
"answer": 26240,
"timestamp": "2026-02-08T03:32:55.446857Z"
} | dcea99 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1280
},
"timestamp": "2026-02-09T22:56:34.022Z",
"answer": 26240
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
4a41f5 | nt_min_crt_v1_898971024_8 | Let $m$ 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 $k$ be the largest prime number less than or equal to $10$. Determine the value of the smallest positive integer $n_1$ such that $1 \leq n_1 \leq 28$, $n_1 \equiv 1 \pmod... | 9 | graphs = [
Graph(
let={
"_n": Const(10),
"m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=270)), Eq(left=GCD(a=Var(name='p'), b=Var(name='... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | nt_min_crt_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.13 | 2026-02-08T15:09:00.086836Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T15:09:00.216982Z"
} | 93b255 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1969
},
"timestamp": "2026-02-16T00:54:01.308Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6feea3 | nt_max_prime_below_v1_397696148_169 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $L = |P|$. Let $B$ be the set of all prime numbers $n$ such that $L \leq n \leq 11449$. Determine the largest element of $B$. | 11,447 | graphs = [
Graph(
let={
"upper": Const(11449),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.27 | 2026-02-08T11:19:37.177221Z | {
"verified": true,
"answer": 11447,
"timestamp": "2026-02-08T11:19:37.447583Z"
} | 79188b | 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": 1382
},
"timestamp": "2026-02-14T12:19:08.151Z",
"answer": 11447
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "n... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
a33fbe | antilemma_cartesian_v1_1918700295_4628 | Let $x$ be the number of ordered pairs $(a, b)$ of integers such that $1 \leq a \leq 27$ and $1 \leq b \leq 35$. Find the remainder when $44121 \cdot x$ is divided by $85912$. | 27,025 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(27)), right=IntegerRange(start=Const(1), end=Const(35)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(85912)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T09:29:16.139802Z | {
"verified": true,
"answer": 27025,
"timestamp": "2026-02-08T09:29:16.140345Z"
} | c0fd33 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T11:30:00.079Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
dd3d2f | sequence_count_fib_divisible_v1_1742523217_5528 | Let $u$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 112225$.
Let $d$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 2315250$ and $\gcd(p, q) = 1$.
Determine the number of positive integers $n$ such that $1 \le n... | 111 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(112225)))), expr=Sum(Var("x"), Var("y")))),
"d": CountOv... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.084 | 2026-02-08T11:02:48.220273Z | {
"verified": true,
"answer": 111,
"timestamp": "2026-02-08T11:02:48.304200Z"
} | b1f3f2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 4104
},
"timestamp": "2026-02-14T10:16:31.048Z",
"answer": 111
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
971f04 | comb_catalan_compute_v1_1439011603_2494 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 20$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 5a + 2b$. Let $C_n$ denote the $n$th Catalan number. Compute the remainder when $83461 \cdot C_n$ is divided by $89832$. | 72,428 | graphs = [
Graph(
let={
"_n": Const(89832),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T16:50:12.153849Z | {
"verified": true,
"answer": 72428,
"timestamp": "2026-02-08T16:50:12.156675Z"
} | 7a4625 | 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": 2598
},
"timestamp": "2026-02-17T13:32:11.453Z",
"answer": 72428
},
... | 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": "V8_SUM",
"s... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
ada22a | v1_endings_v1_1742523217_858 | Let $n = 27744$, $p = 7$, and $q = 5$. Let $v_p$ be the largest integer $k$ such that $p^k$ divides $n!$, and let $v_q$ be the largest integer $k$ such that $q^k$ divides $n!$. Compute the remainder when $v_p \cdot v_q$ is divided by $100000$.
Find the value of this remainder. | 28,151 | graphs = [
Graph(
let={
"n_val": Const(27744),
"p_val": Const(7),
"q_val": Const(5),
"n_fact": Factorial(Ref("n_val")),
"vp": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
"vq": MaxKDivides(target=Ref("n_fact"), base=Ref("q_val"... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 5 | null | [
"V1"
] | 1 | 0 | 2026-02-08T03:18:03.531128Z | {
"verified": true,
"answer": 28151,
"timestamp": "2026-02-08T03:18:03.531413Z"
} | e3fe1b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 862
},
"timestamp": "2026-02-09T23:42:30.644Z",
"answer": 42013
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "n... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
9b0e8f | alg_poly_orbit_count_v1_1218484723_2775 | Let $a$ be a non-negative integer with $0 \le a \le 78384$. Define the sequence $N, M, R, S, T$ by:
$$
\begin{aligned}
N &= (a^2 + a - 31) \bmod 61, \\
M &= (N^2 + N - 31) \bmod 61, \\
R &= (M^2 + M - 31) \bmod 61, \\
S &= (R^2 + R - 31) \bmod 61, \\
T &= (S^2 + S - 31) \bmod 61.
\end{aligned}
$$
Find the number of suc... | 6,425 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-31)), modulus=Const(61)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-31)), modulus=Const(61)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-31)), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.03 | 2026-02-25T04:29:09.516779Z | {
"verified": true,
"answer": 6425,
"timestamp": "2026-02-25T04:29:09.546342Z"
} | bb2f67 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 13296
},
"timestamp": "2026-03-29T06:31:27.800Z",
"answer": 6425
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
e35bc5 | nt_count_intersection_v1_1915831931_2833 | Let $N$ be the number of positive integers $n \leq 60000$ such that the $n$-th Fibonacci number is divisible by $8$. Let $a = 5$ and $b = 14$. Compute the number of positive integers $n_1 \leq N$ such that $n_1$ is divisible by $a$ and $\gcd(n_1, b) = 1$. | 857 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(60000)), Divides(divisor=Const(8), dividend=Fibonacci(arg=Var(name='n')))))),
"a": Const(5),
"b": Const(14),
"result": CountOver... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_intersection_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.748 | 2026-02-08T17:10:02.053286Z | {
"verified": true,
"answer": 857,
"timestamp": "2026-02-08T17:10:02.801253Z"
} | 942221 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 2073
},
"timestamp": "2026-02-17T20:24:23.577Z",
"answer": 857
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
57fb75 | algebra_poly_eval_v1_601307018_6406 | Let $m$ be the smallest positive integer $d$ such that $d \mid 1001$. Compute $7m^3 - 4m^2 + 7m - 4$. | 2,250 | graphs = [
Graph(
let={
"_n": Const(7),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1001))))),
"result": Sum(Mul(Const(7), Pow(Ref("m"), Const(3))), Mul(Const(-4), Pow(Ref("m"), Const(2))),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.007 | 2026-03-10T07:04:58.613161Z | {
"verified": true,
"answer": 2250,
"timestamp": "2026-03-10T07:04:58.619886Z"
} | 452e25 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 750
},
"timestamp": "2026-04-19T04:18:06.024Z",
"answer": 6
},
{
"id... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
476612 | comb_bell_compute_v1_1874849503_1250 | Let $m = 54$ and $n = 3$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $P$ be the set of all values of $xy$ as $(x, y)$ ranges over this set. Let $j$ be a positive integer satisfying $1 \le j \le 9$ and $j^n \le \max(P)$. Let $n$ be the number of such integers $j$. Comp... | 21,147 | graphs = [
Graph(
let={
"_m": Const(54),
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(9)), Leq(Pow(Var("j"), Ref("_n")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"),... | COMB | null | COMPUTE | sympy | B1 | [
"B1/C3"
] | 0a705f | comb_bell_compute_v1 | null | 6 | 0 | [
"B1",
"C3"
] | 2 | 0.003 | 2026-02-08T13:43:36.642534Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T13:43:36.645987Z"
} | b606c8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 991
},
"timestamp": "2026-02-10T02:46:57.867Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
852a9c | algebra_poly_eval_v1_458359167_1117 | Let $x = 30$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 133225$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $m$ be the minimum value in $T$. Let $k$ be the largest integer such that $2^k \leq m$. Compute $6x^2 + kx + 1$. | 5,671 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"x": Const(30),
"result": Sum(Mul(Const(6), Pow(Ref("x"), Ref("_m"))), Mul(MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_VAL"
] | 2438e8 | algebra_poly_eval_v1 | null | 4 | 0 | [
"B3",
"MAX_VAL"
] | 2 | 0.004 | 2026-02-08T04:23:17.425878Z | {
"verified": true,
"answer": 5671,
"timestamp": "2026-02-08T04:23:17.429778Z"
} | ba213c | 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": 1079
},
"timestamp": "2026-02-10T16:27:27.756Z",
"answer": 5671
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
573d91 | comb_count_derangements_v1_151522320_956 | Let $m = 2$ and $n = 17711$. Define $p$ to be the largest prime number such that $m \leq p \leq 9$. Let $D(p)$ denote the number of derangements of $p$ elements, that is, the number of permutations of $p$ elements with no fixed points.
Let $s = D(p)$, and let $d_k$ denote the $k$-th decimal digit of $|s|$, where $k=0$... | 17,823 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(17711),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Sum(Su... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MOBIUS_COPRIME"
] | 43dda6 | comb_count_derangements_v1 | digits_weighted_mod | 5 | 0 | [
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | 2 | 0.004 | 2026-02-08T03:41:12.667979Z | {
"verified": true,
"answer": 17823,
"timestamp": "2026-02-08T03:41:12.672226Z"
} | c54f33 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 1091
},
"timestamp": "2026-02-18T04:10:03.123Z",
"answer": 17823
}
] | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
68b580 | nt_sum_over_divisible_v1_784195855_3260 | Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = 400$. Let $d$ be the largest prime number $n$ such that $2 \leq n \leq s$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 84681$ and $n$ is divisible by $d$. Compute the remainder when $... | 39,080 | graphs = [
Graph(
let={
"_n": Const(77416),
"upper": Const(84681),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(... | NT | null | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 2.769 | 2026-02-08T06:19:00.841186Z | {
"verified": true,
"answer": 39080,
"timestamp": "2026-02-08T06:19:03.610464Z"
} | 00a78b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 3521
},
"timestamp": "2026-02-12T22:29:37.887Z",
"answer": 39080
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2b58d8 | comb_count_derangements_v1_124444284_8924 | Let $n$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 3$ and $1 \leq j \leq 3$ such that $\gcd(i, j) = 1$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"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(3)), right=IntegerRange(start=Const(1), end=Const(3))))),
"res... | NT | COMB | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | comb_count_derangements_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T11:58:58.086237Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T11:58:58.087199Z"
} | 59c6a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 756
},
"timestamp": "2026-02-14T22:03:41.343Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3c260f | nt_count_divisible_v1_1431428450_1008 | Let $A$ be the set of all positive integers $n$ such that $n \leq 75076$ and $n$ is divisible by 27. Let $r$ be the number of elements in $A$. Compute the Bell number $B_k$, where $k = r \bmod p$, and $p$ is the largest prime number satisfying $2 \leq p \leq 11$. | 4,140 | graphs = [
Graph(
let={
"upper": Const(75076),
"divisor": Const(27),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"Q": Be... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_count_divisible_v1 | bell_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.492 | 2026-02-08T13:50:57.876845Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T13:51:00.368782Z"
} | a564d2 | 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": 878
},
"timestamp": "2026-02-15T21:29:38.447Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"st... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
3d5397 | modular_min_linear_v1_1742523217_1248 | Let $m = 87494$, $a = 81211$, $b = 81378$, and $n = 72064$. Let $x_0$ be the smallest positive integer $x$ such that $1 \leq x \leq m$ and $ax \equiv b \pmod{m}$. Compute the value of $$ x_0 + \left(2^{x_0 \bmod 15}\right) \bmod n. $$ | 31,948 | graphs = [
Graph(
let={
"_n": Const(72064),
"a": Const(81211),
"b": Const(81378),
"m": Const(87494),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var(... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 129eee | modular_min_linear_v1 | mod_exp | 6 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 4.438 | 2026-02-08T03:34:41.885970Z | {
"verified": true,
"answer": 31948,
"timestamp": "2026-02-08T03:34:46.323939Z"
} | 76d1d7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 3130
},
"timestamp": "2026-02-10T05:40:02.571Z",
"answer": 57394
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
e040cf | nt_num_divisors_compute_v1_124444284_5574 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Determine the value of the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), L... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.036 | 2026-02-08T06:43:04.185325Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T06:43:04.221573Z"
} | 9a76c6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 348
},
"timestamp": "2026-02-15T17:42:55.677Z",
"answer": 4
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
9661a9 | comb_count_permutations_fixed_v1_1439011603_2863 | Let $n=8$ and $k=2$. Let $!m$ denote the number of permutations of $m$ elements with no fixed points.
Define
$$Q = \binom{n}{k}\, !(n-k).$$
Compute $Q$. | 7,420 | graphs = [
Graph(
let={
"n": Const(8),
"k": Const(2),
"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/B1/B3",
"ONE_PHI_2"
] | a1ddc3 | comb_count_permutations_fixed_v1 | null | 2 | 0 | [
"B1",
"B3",
"ONE_PHI_2",
"SUM_ARITHMETIC"
] | 4 | 0.022 | 2026-02-08T17:03:02.657602Z | {
"verified": true,
"answer": 7420,
"timestamp": "2026-02-08T17:03:02.679402Z"
} | b8ef36 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 687
},
"timestamp": "2026-02-17T17:47:15.442Z",
"answer": 7420
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_PH... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
a73dcd | algebra_poly_eval_v1_1918700295_1927 | Let $d$ be the smallest integer greater than or equal to $2$ that divides $77$. Compute the value of $8d^3 - 2d^2 + 10d + 2$. | 2,718 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(77))))),
"result": Sum(Mul(Const(8), Pow(Ref("a"), Const(3))), Mul(Const(-2), Pow(Ref("a"), Const(2))), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T06:11:10.111263Z | {
"verified": true,
"answer": 2718,
"timestamp": "2026-02-08T06:11:10.113323Z"
} | 084dcc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 471
},
"timestamp": "2026-02-13T11:21:28.300Z",
"answer": 2718
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
5d6249 | antilemma_sum_equals_v1_677425708_3831 | Let $m = 2$ and $n = 65$. Define $x$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$, $1 \leq i \leq 63$, and $1 \leq j \leq 64$.
Let $A$ be the sum
$$
\sum_{i=0}^{d-1} \left( \text{the } i\text{-th digit of } |x| \right) \cdot (i+1)^m,
$$
where $d$ is the number of decimal digits... | 3,871 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(65),
"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(63)), right=IntegerR... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | 3bc3e0 | antilemma_sum_equals_v1 | digits_weighted_mod | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T05:57:18.855202Z | {
"verified": true,
"answer": 3871,
"timestamp": "2026-02-08T05:57:18.861510Z"
} | 95c1e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 334,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T05:11:49.726Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
24c792 | nt_count_divisible_and_v1_1978505735_5564 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 77940$, $n \equiv r \pmod{10}$, and $n \equiv 0 \pmod{15}$, where
$$
r = \sum_{k=0}^{2} (-1)^k \binom{2}{k} \quad \text{and} \quad s = \sum_{k_1=0}^{8} (-1)^{k_1} \binom{8}{k_1},
$$
but with $r$ taken as $s$ modulo $10$. Find the number of eleme... | 2,598 | graphs = [
Graph(
let={
"upper": Const(77940),
"d1": Const(10),
"d2": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Summation(var=... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 6.145 | 2026-02-08T19:05:01.550982Z | {
"verified": true,
"answer": 2598,
"timestamp": "2026-02-08T19:05:07.695502Z"
} | 5a1cd3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1498
},
"timestamp": "2026-02-18T21:18:20.300Z",
"answer": 2598
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
0c0826 | geo_count_lattice_rect_v1_655260480_4203 | Let $a = 128$ and $b = 57$. The number of lattice points in the rectangle $[0, a] \times [0, b]$ is denoted by $r$. Compute $13 \cdot r$. | 97,266 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(57),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(13),
"Q": Mul(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.005 | 2026-02-08T17:48:05.644591Z | {
"verified": true,
"answer": 97266,
"timestamp": "2026-02-08T17:48:05.649392Z"
} | a49634 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 551
},
"timestamp": "2026-02-18T08:42:19.557Z",
"answer": 97266
},
{
... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||||
0b243f | comb_count_partitions_v1_1520064083_3978 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of positive integers $t$ such that $36 \le t \le 231$ and $t = 15a + 21b$ for some integers $a$ and $b$ with $1 \le a \le 7$ and $1 \le b \le 6$. Let $n_... | 44,583 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM/MAX_PRIME_BELOW"
] | 56a8ee | comb_count_partitions_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.003 | 2026-02-08T05:59:51.243750Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T05:59:51.246442Z"
} | 964967 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 2979
},
"timestamp": "2026-02-12T18:03:05.872Z",
"answer": 44583
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_F... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
16c944 | comb_count_derangements_v1_124444284_10121 | Let $n$ be the number of positive integers $p$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 617400$ for some positive integer $q$. Compute the value of the subfactorial of $n$, denoted $!n$, which counts the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=617400)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T12:50:10.949822Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T12:50:10.950681Z"
} | 0b2e00 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1898
},
"timestamp": "2026-02-15T06:23:50.628Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
429289 | sequence_fibonacci_compute_v1_1918700295_4410 | Let $m = 3$, and let $s = \sum_{k=1}^{m} k$. Define $n = \sum_{k=1}^{s} k$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 10,946 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Var("k")),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result")... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/SUM_ARITHMETIC"
] | 2a57af | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T09:21:46.549916Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T09:21:46.550803Z"
} | 0d9e57 | 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": 456
},
"timestamp": "2026-02-14T03:16:43.783Z",
"answer": 10946
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
187fc0 | comb_count_derangements_v1_655260480_3391 | Let $n = 7$. Define $d_n$ to be the number of derangements of $n$ distinct objects. Compute the remainder when $99985 \cdot d_n$ is divided by $75412$. | 9,494 | graphs = [
Graph(
let={
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(99985), Ref("result")), modulus=Const(75412)),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"VIETA_SUM"
] | 4b11a6 | comb_count_derangements_v1 | null | 2 | 0 | [
"BINOMIAL_ALTERNATING",
"VIETA_SUM"
] | 2 | 0.021 | 2026-02-08T17:21:39.989079Z | {
"verified": true,
"answer": 9494,
"timestamp": "2026-02-08T17:21:40.009829Z"
} | df995c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 1666
},
"timestamp": "2026-02-18T00:52:11.165Z",
"answer": 9494
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
8ea081 | diophantine_fbi2_count_v1_124444284_6505 | Let $n = 3$. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 32400$. Let $T$ be the set of all integers $t$ for which there exist positive integers $a \leq 22$ and $b \leq 5$ such that $t = 9a + 21b$ and $30 \leq t \leq 303$. Let $c$ be the number of elements in $T$.... | 16 | graphs = [
Graph(
let={
"_n": Const(3),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T08:29:40.340394Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T08:29:40.348759Z"
} | d4ab87 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 3517
},
"timestamp": "2026-02-13T19:01:02.453Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5a4e62 | diophantine_product_count_v1_1520064083_7393 | Let $n = 8836$. Define $s$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $T$ be the set of all ordered pairs $(i, j)$ with $1 \leq i \leq 186$ and $1 \leq j \leq 187$ such that $i + j = s$. Let $u$ be the number of elements in $T$. Now consider the set o... | 20 | graphs = [
Graph(
let={
"_n": Const(8836),
"k": Const(420),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), conditio... | NT | null | COUNT | sympy | LIN_FORM | [
"B3/COUNT_SUM_EQUALS"
] | 63dc97 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 3.271 | 2026-02-08T09:00:32.225295Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T09:00:35.496387Z"
} | 30560d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 2050
},
"timestamp": "2026-02-13T23:32:37.184Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
9fa767 | comb_count_surjections_v1_865884756_1323 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 12$. Compute the value of
$$
(44121 \cdot (2! \cdot S(n, 2))) \bmod 59834,
$$
where $S(n, k)$ denotes the Stirling number of the second kind. | 42,972 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(12))))),
"k":... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T15:57:12.479674Z | {
"verified": true,
"answer": 42972,
"timestamp": "2026-02-08T15:57:12.482343Z"
} | 0f9b41 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1300
},
"timestamp": "2026-02-24T19:13:19.021Z",
"answer": 42972
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
08441e | geo_visible_lattice_v1_1520064083_7204 | Let $n = 64$. Define $L$ to be the number of ordered pairs $(x,y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x,y) = 1$.
Compute the remainder when $44121 \cdot L$ is divided by $86446$. | 57,689 | graphs = [
Graph(
let={
"n": Const(64),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(86446)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.092 | 2026-02-08T08:50:36.841708Z | {
"verified": true,
"answer": 57689,
"timestamp": "2026-02-08T08:50:36.933274Z"
} | e8e248 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 6933
},
"timestamp": "2026-02-24T10:04:13.324Z",
"answer": 57689
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
dcda22 | algebra_vieta_sum_v1_655260480_4679 | Let $n = 2$. Define $f(x) = x^n - 11x + c$, where $c$ is the number of integers $t$ in the range $21 \leq t \leq 84$ such that $t = 6a + 15b$ for some integers $a$ and $b$ with $1 \leq a \leq 9$ and $1 \leq b \leq 2$. Compute the sum of all integers $x$ such that $f(x) = 0$. | 11 | graphs = [
Graph(
let={
"_n": Const(2),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-11), Var("x")), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condit... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"LIN_FORM"
] | 7b2633 | algebra_vieta_sum_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-08T18:03:12.762102Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T18:03:12.774275Z"
} | cf2954 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 932
},
"timestamp": "2026-02-18T12:41:59.054Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
84139d | comb_count_derangements_v1_124444284_110 | Let $n$ be the largest prime number less than or equal to $1 + 2 + 3 + 4$. Let $d_n$ denote the number of derangements of $n$ elements. Compute the remainder when $44121 \cdot d_n$ is divided by $61123$. | 17,760 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(4), expr=Var("k"))), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/MAX_PRIME_BELOW"
] | bde608 | comb_count_derangements_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.001 | 2026-02-08T02:59:05.493132Z | {
"verified": true,
"answer": 17760,
"timestamp": "2026-02-08T02:59:05.494546Z"
} | de204b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 8136
},
"timestamp": "2026-02-09T13:45:55.543Z",
"answer": 17760
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status"... | {
"lo": -3.55,
"mid": 0.8,
"hi": 4.81
} | ||
a2fa40 | nt_min_coprime_above_v1_349078426_914 | Let $n$ be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $r$ be the smallest integer greater than $85264$ and at most $85709$ such that $\gcd(r, 435) = 1$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6002500$. ... | 46,403 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | f85381 | nt_min_coprime_above_v1 | quadratic_mod | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.056 | 2026-02-08T13:20:14.501016Z | {
"verified": true,
"answer": 46403,
"timestamp": "2026-02-08T13:20:14.557471Z"
} | bbef28 | 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": 2510
},
"timestamp": "2026-02-15T13:21:48.609Z",
"answer": 46403
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e7d106 | antilemma_sum_equals_v1_238844314_519 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 100$ and $1 \leq i, j \leq 98$. Compute the value of $$\sum_{i=0}^{\lfloor \log_{10} |x| \rfloor} \left( \text{digit}_i(x) \cdot (i+1)^2 \right) + 88,$$ where $\text{digit}_i(x)$ denotes the $i$th decimal digit of $x$ (starting from ... | 131 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(100)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(98)), right=IntegerRange(start=Const(1), end=Const(98))))),
"Q":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T13:23:12.595489Z | {
"verified": true,
"answer": 131,
"timestamp": "2026-02-08T13:23:12.599547Z"
} | 3208d4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 559
},
"timestamp": "2026-02-24T17:54:17.591Z",
"answer": 131
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
9fc468 | geo_count_lattice_triangle_v1_1218484723_822 | Let $M = \left|180 \cdot 120 + 36 \cdot (-222)\right|$, $P = \left|\{ (a, b) : 1 \leq a, b \leq 40,\ 25b^2 -18ab + 10a^2 \leq 2825 \}\right|$, and
$$
R = \gcd(180, P) + \gcd(|36 - 180|, |120 - 222|) + \gcd(|0 - 36|, |0 - 120|).
$$
Let $S = \frac{M + 2 - R}{2}$ and $Q = |S|$. Compute $Q$. | 6,793 | graphs = [
Graph(
let={
"_n": Const(36),
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=120)), Mul(Const(value=36), Sub(left=Const(value=0), right=Const(value=222))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=180)), b=Abs(arg=CountOverSet(set=SolutionsSet(var=... | GEOM | NT | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.009 | 2026-02-25T02:32:43.225263Z | {
"verified": true,
"answer": 6793,
"timestamp": "2026-02-25T02:32:43.234184Z"
} | e63d9a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 31704
},
"timestamp": "2026-03-10T02:05:37.734Z",
"answer": 6795
},
{
... | 1 | [
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
d843e0 | nt_count_coprime_v1_1742523217_3019 | Let $\displaystyle k = \sum_{k=1}^{7} \phi(k) \left\lfloor \frac{7}{k} \right\rfloor$. Let $\text{result}$ be the number of positive integers $n \leq 50000$ such that $\gcd(n, k) = 1$. Compute the remainder when $25307 \cdot \text{result}$ is divided by $72288$. | 71,415 | graphs = [
Graph(
let={
"_n": Const(25307),
"upper": Const(50000),
"k": Summation(var="k", start=Const(1), end=Const(7), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(7), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Va... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_coprime_v1 | null | 5 | 0 | [
"K2"
] | 1 | 4.409 | 2026-02-08T05:29:54.679651Z | {
"verified": true,
"answer": 71415,
"timestamp": "2026-02-08T05:29:59.088299Z"
} | 059f2a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 2554
},
"timestamp": "2026-02-12T11:40:19.371Z",
"answer": 71415
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
48a7a9 | nt_count_coprime_v1_1915831931_134 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 16384$ and $\gcd(n, 10) = 1$. Let $B$ be the largest prime number at most $20$. Let $C$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 225$. Compute the remainder when $A^2 + B \cdot A + C$ is d... | 59,915 | graphs = [
Graph(
let={
"_m": Const(20),
"_n": Const(2),
"upper": Const(16384),
"k": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k"))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 73b6e3 | nt_count_coprime_v1 | quadratic_mod | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 1.311 | 2026-02-08T15:12:08.044541Z | {
"verified": true,
"answer": 59915,
"timestamp": "2026-02-08T15:12:09.355164Z"
} | 1f2767 | 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": 1173
},
"timestamp": "2026-02-16T01:52:32.722Z",
"answer": 59915
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d02b5f | comb_catalan_compute_v1_48377204_3058 | Let $S$ be the set of all integers $t$ such that $17 \leq t \leq 41$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 6a + 4b + 7$. Let $n$ be the number of elements in $S$. Find 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 | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T17:09:18.315479Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T17:09:18.318729Z"
} | bdad0d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1895
},
"timestamp": "2026-02-17T20:35:44.655Z",
"answer": 58786
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
24a462 | nt_count_divisible_v1_458359167_107 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $d = |S|$. Determine the number of positive integers $n$ such that $1 \leq n \leq 66666$ and $n$ is divisible by $d$. Compute this number. | 33,333 | graphs = [
Graph(
let={
"upper": Const(66666),
"divisor": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisible_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.064 | 2026-02-08T02:59:30.507570Z | {
"verified": true,
"answer": 33333,
"timestamp": "2026-02-08T02:59:32.571112Z"
} | df616b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 937
},
"timestamp": "2026-02-10T12:30:41.156Z",
"answer": 33333
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
04f353 | nt_count_digit_sum_v1_1742523217_1093 | Let $m=93997$.
Let $u$ be the least value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy=3956121$. Let $n$ be the greatest integer $d$ such that $1\le d\le u$ and $d$ divides $15923934$.
Let $U=84681$ and let $R$ be the number of integers $t$ with $1\le t\le U$ whose sum of decimal digits ... | 1,633 | graphs = [
Graph(
let={
"_m": Const(93997),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositiv... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_DIVISOR/MAX_PRIME_BELOW"
] | 557a87 | nt_count_digit_sum_v1 | affine_mod | 6 | 0 | [
"B3",
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 3 | 2.983 | 2026-02-08T03:25:04.384490Z | {
"verified": true,
"answer": 1633,
"timestamp": "2026-02-08T03:25:07.367203Z"
} | bc1686 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 6833
},
"timestamp": "2026-02-09T10:58:50.100Z",
"answer": 1633
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e616d9 | modular_count_residue_v1_397696148_959 | Let $ S $ be the set of all integers $ t $ such that $ 33 \leq t \leq 921 $ and there exist positive integers $ a $ and $ b $ with $ 1 \leq a \leq 25 $, $ 1 \leq b \leq 33 $, and $ t = 21a + 12b $. Let $ m $ be the number of positive integers $ n $ at most $ |S| $ such that $ 9 $ divides $ n $ and $ \gcd\left(n, \min\{... | 2,289 | graphs = [
Graph(
let={
"upper": Const(32041),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(l... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/C5",
"B3/C5"
] | 90bb65 | modular_count_residue_v1 | null | 7 | 0 | [
"B3",
"C5",
"LIN_FORM"
] | 3 | 1.094 | 2026-02-08T11:58:11.021095Z | {
"verified": true,
"answer": 2289,
"timestamp": "2026-02-08T11:58:12.115272Z"
} | 4181ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 5282
},
"timestamp": "2026-02-14T23:44:44.088Z",
"answer": 2289
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d37326 | sequence_fibonacci_compute_v1_1978505735_4293 | Let $T$ be the set of all integers $t$ such that $28 \leq t \leq 109$ and there exist integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 4$, and $t = 9a + 12b + 7$. Let $n$ be the number of elements in $T$.
Let $F_n$ denote the $n$th Fibonacci number, defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}... | 15,399 | graphs = [
Graph(
let={
"_n": Const(31053),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T18:08:36.834487Z | {
"verified": true,
"answer": 15399,
"timestamp": "2026-02-08T18:08:36.837807Z"
} | ec772d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2389
},
"timestamp": "2026-02-18T14:37:48.071Z",
"answer": 15399
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9e2c6c_n | geo_count_lattice_rect_v1_1218484723_375 | A city grid spans from the origin to the point $(333, 86)$, with streets laid out along integer coordinates. Each intersection is a lattice point. How many intersections lie within or on the boundary of this rectangular region? | 29,058 | GEOM | GEOM | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | null | null | null | 0.001 | 2026-02-25T02:04:35.005906Z | null | 38cca0 | 9e2c6c | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 281
},
"timestamp": "2026-03-30T15:25:04.645Z",
"answer": 29058
},
{
"i... | 1 | [] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |||
b77845 | modular_inverse_v1_458359167_709 | Let $a = 173$. Let $m$ be the smallest divisor of $1053924187$ that is greater than or equal to $2$. Compute the smallest positive integer $x$ such that $x \leq 1012$ and $$173x \equiv 1 \pmod{m}.$$ | 527 | graphs = [
Graph(
let={
"a": Const(173),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1053924187))))),
"upper": Const(1012),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), c... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_inverse_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.043 | 2026-02-08T03:30:48.795113Z | {
"verified": true,
"answer": 527,
"timestamp": "2026-02-08T03:30:48.837791Z"
} | e7daad | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 13088
},
"timestamp": "2026-02-23T20:11:13.243Z",
"answer": 527
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
e2c86b | antilemma_coprime_grid_v1_548369836_215 | Compute the number of ordered pairs $(i, j)$ with $1 \leq i \leq 13$ and $1 \leq j \leq 19$ such that $\gcd(i, j) = \varphi(1)$. | 166 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=Const(1))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(19))))),
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 3d404c | antilemma_coprime_grid_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 2 | 0.001 | 2026-02-08T02:49:19.781268Z | {
"verified": true,
"answer": 166,
"timestamp": "2026-02-08T02:49:19.781799Z"
} | 4d2bba | 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": 2394
},
"timestamp": "2026-02-08T20:15:17.582Z",
"answer": 166
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V3",
"status":... | {
"lo": -1.92,
"mid": 1.69,
"hi": 4.67
} | ||
08c54c | modular_mod_compute_v1_48377204_1379 | Let $n = 2$. Let $a$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 65479$ and $\binom{65479}{j} \equiv 1 \pmod{n}$. Let $m = 61009$. Compute the remainder when $a$ is divided by $m$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(2),
"a": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(65479)), Eq(Mod(value=Binom(n=Const(65479), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"m... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_mod_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T16:03:33.474619Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T16:03:33.478109Z"
} | 82e999 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 2114
},
"timestamp": "2026-02-24T19:44:16.536Z",
"answer": 8192
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
de62a8 | nt_count_gcd_equals_v1_349078426_1765 | Let $ m = 29929 $ and $ n = 152 $. Let $ u $ be the maximum value of $ xy $ over all pairs of positive integers $ (x, y) $ such that $ x + y = n $. Let $ k $ be the minimum value of $ x + y $ over all pairs of positive integers $ (x, y) $ such that $ xy = m $. Compute the number of positive integers $ d $ such that $ 1... | 2,872 | graphs = [
Graph(
let={
"_m": Const(29929),
"_n": Const(152),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n"))))... | NT | null | COUNT | sympy | B1 | [
"B1",
"B3"
] | 655d51 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.455 | 2026-02-08T13:55:11.572146Z | {
"verified": true,
"answer": 2872,
"timestamp": "2026-02-08T13:55:12.027087Z"
} | 408082 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1039
},
"timestamp": "2026-02-15T22:02:01.489Z",
"answer": 2872
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
af3dd7_n | comb_count_partitions_v1_1218484723_2128 | A bakery sells pastries in packs of 4 or 6. Each transaction uses between 1 and 3 packs of 4 and between 1 and 15 packs of 6. The total number of pastries in a transaction must be at least 10 and at most 102. Let $n$ be the number of different total counts of pastries possible under these rules. A customer wants to kno... | 25,746 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T03:51:54.512582Z | null | 45f621 | af3dd7 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2181
},
"timestamp": "2026-03-30T17:55:41.687Z",
"answer": 25746
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
1d50df | comb_sum_binomial_mod_v1_153355830_1092 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 5625$. For each pair $(x,y)$ in $S$, define $s = x + y$. Let $m$ be the minimum value of $s$ over all such pairs. Compute the remainder when $$\sum_{k=10}^{130} \binom{m}{k}$$ is divided by $11329$. | 10,744 | graphs = [
Graph(
let={
"_n": Const(11329),
"sum": Summation(var="k", start=Const(10), end=Const(130), expr=Binom(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_sum_binomial_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.012 | 2026-02-08T04:23:45.429660Z | {
"verified": true,
"answer": 10744,
"timestamp": "2026-02-08T04:23:45.441381Z"
} | 46de57 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T05:32:01.594Z",
"answer": 1343
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
1d4423 | antilemma_v1_legendre_168721529_1512 | Let $x$ be the largest integer $k$ such that $2^k$ divides $222!$. Compute $x^2 + 49x + 88$. | 57,328 | graphs = [
Graph(
let={
"_n": Const(2),
"x": MaxKDivides(target=Factorial(Const(222)), base=Ref("_n")),
"_c": Const(88),
"Q": Sum(Pow(Ref("x"), Const(2)), Mul(Const(49), Ref("x")), Ref("_c")),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | antilemma_v1_legendre | null | 3 | 0 | [
"V1"
] | 1 | 0.001 | 2026-02-08T13:44:37.310114Z | {
"verified": true,
"answer": 57328,
"timestamp": "2026-02-08T13:44:37.311406Z"
} | 8fb344 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 640
},
"timestamp": "2026-02-09T18:17:24.758Z",
"answer": 57328
},
{
"i... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"sta... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
b9b43d | lin_form_endings_v1_784195855_69 | Let $S$ be the set of integers $t$ with $126 \leq t \leq 6076$ for which there exist positive integers $a \leq 52$ and $b \leq 35$ such that $t = 98a + 28b$. Let $r$ be the number of elements in $S$. Compute the remainder when $5520 \cdot r$ is divided by $75282$. | 59,940 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=52)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:56:52.694973Z | {
"verified": true,
"answer": 59940,
"timestamp": "2026-02-08T02:56:52.695795Z"
} | 9836bc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 4612
},
"timestamp": "2026-02-10T11:55:24.038Z",
"answer": 65460
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": 2.55,
"mid": 3.99,
"hi": 5.3
} | ||
dafa47 | comb_sum_binomial_row_v1_1218484723_6980 | Let $M = \left|\left\{ (a, b) : 1 \leq a \leq b \leq 10,\ 2a^2 + 2b^2 - 4ab = 128 \right\}\right|^{14}$. Find the remainder when $67997M$ is divided by $86333$. | 21,816 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(14),
"result": Pow(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(10)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(10)), Leq(Var("a"), ... | COMB | null | SUM | sympy | POLY_ORBIT_HENSEL | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"POLY_ORBIT_HENSEL",
"QF_PSD_ORBIT"
] | 2 | 0.098 | 2026-02-25T08:24:28.631600Z | {
"verified": true,
"answer": 21816,
"timestamp": "2026-02-25T08:24:28.729223Z"
} | 1eff74 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1918
},
"timestamp": "2026-03-30T03:32:51.142Z",
"answer": 21816
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
834109 | nt_sum_gcd_range_mod_v1_1431428450_852 | Let $k = 504$ and $M = 11027$. Compute the sum
$$
\frac{4}{40} \sum_{n=1}^{1583} \sum_{j=1}^{10} \gcd(n, k),
$$
and let $\text{result}$ be the remainder when this sum is divided by $M$. Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 189$ and $t = 5a + 4b$ for some integers $a, b$ with $1 \leq a \leq 21... | 70,526 | graphs = [
Graph(
let={
"_n": Const(76280),
"k": Const(504),
"M": Const(11027),
"sum": Div(Mul(Const(4), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("n"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=C... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"SUM_INDEPENDENT"
] | ddec56 | nt_sum_gcd_range_mod_v1 | negation_mod | 6 | 0 | [
"LIN_FORM",
"SUM_INDEPENDENT"
] | 2 | 0.147 | 2026-02-08T13:44:41.434814Z | {
"verified": true,
"answer": 70526,
"timestamp": "2026-02-08T13:44:41.582074Z"
} | 662498 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 5917
},
"timestamp": "2026-02-15T20:00:53.032Z",
"answer": 70529
},... | 0 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"... | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
128558 | alg_poly3_count_v1_1218484723_3144 | Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \leq a, b, c \leq 43$ such that
$$
-204bc^2 + 60a^2c - 2a^3 - 180ac^2 - 12ab^2 - 12a^2b + 48b^2c - 4b^3 + 320c^3 + m \cdot abc = -85750,
$$
where $m = \min\{ x + y : x > 0, y > 0, xy = 2304 \}$. | 14 | graphs = [
Graph(
let={
"_n": Const(43),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(43)), Geq(Var("c"), Const(1)), Leq(Var("c... | ALG | null | COUNT | sympy | LIN_FORM | [
"B3"
] | 0cd20d | alg_poly3_count_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 1.907 | 2026-02-25T04:51:19.806949Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-25T04:51:21.713802Z"
} | 505579 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T08:43:31.920Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
70f1e3 | nt_count_with_divisor_count_v1_2080023795_93 | Let $p=73$ and $q=13$, and let $n_1=p^2q$. Let $\mu$ denote the Möbius function, and define
$$u=\mu(n_1)^2.$$
Let $n=1$, and let $f$ be the number of prime factors of $n$ counted with multiplicity.
Let $U=5184$. Let $d=6$, and let $R$ be the number of integers $t$ with $1\le t\le U$ such that $t$ has exactly $d$ posi... | 54,969 | graphs = [
Graph(
let={
"p": Const(73),
"q": Const(13),
"n1": Mul(Pow(Ref("p"), Const(2)), Ref("q")),
"u": Pow(MoebiusMu(n=Ref(name='n1')), Const(2)),
"n": Const(1),
"f": BigOmega(n=Ref(name='n')),
"upper": Const(5184),
... | NT | null | COUNT | sympy | B3 | [
"B3/MOBIUS_SQUAREFREE/BIG_OMEGA_ZERO"
] | 4b9d5f | nt_count_with_divisor_count_v1 | affine_mod | 6 | 2 | [
"B3",
"BIG_OMEGA_ZERO",
"MOBIUS_SQUAREFREE"
] | 3 | 0.223 | 2026-02-08T11:31:47.596216Z | {
"verified": true,
"answer": 54969,
"timestamp": "2026-02-08T11:31:47.819595Z"
} | 3d8cd3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 324,
"completion_tokens": 7177
},
"timestamp": "2026-02-10T05:12:18.459Z",
"answer": 54969
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
... | {
"lo": 1.94,
"mid": 5.23,
"hi": 8.52
} | ||
b5c857 | nt_count_gcd_equals_v1_458359167_3825 | Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 1171$. Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq \max(S)$ and $\gcd(n, 6) = 1$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 39204$ and $\gcd(n, k) = 391$. Compute the number of elements in $T$... | 100 | graphs = [
Graph(
let={
"upper": Const(39204),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1171)), IsPrime(Var("n")))))), Eq(... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/C4"
] | a99ef8 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 3.268 | 2026-02-08T11:22:48.622374Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T11:22:51.889907Z"
} | a57cd3 | 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": 1896
},
"timestamp": "2026-02-14T12:41:50.950Z",
"answer": 100
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
9e2c61 | antilemma_sum_primes_v1_1918700295_2711 | Compute the sum of all prime numbers $n$ such that $2 \le n \le 98$. | 1,060 | graphs = [
Graph(
let={
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(98)), IsPrime(Var("n"))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | SUM_PRIMES | [
"SUM_PRIMES"
] | 83231d | antilemma_sum_primes_v1 | null | 3 | 0 | [
"SUM_PRIMES"
] | 1 | 0.004 | 2026-02-08T08:10:39.886864Z | {
"verified": true,
"answer": 1060,
"timestamp": "2026-02-08T08:10:39.891057Z"
} | 81f582 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 733
},
"timestamp": "2026-02-20T10:55:40.134Z",
"answer": 1060
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
6d1307 | algebra_quadratic_discriminant_v1_458359167_3907 | Let $m = 2049$. Define $n$ to be the number of integers $j$ with $0 \leq j \leq 2049$ such that $\binom{2049}{j}$ is odd. Let $a = -1$, $b = -8$, and $c = -16$. Let $p$ range over the positive integers for which there exists an integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $r = b^k$, where $k$ is... | 38,416 | graphs = [
Graph(
let={
"_m": Const(2049),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2049)), Eq(Mod(value=Binom(n=Ref("_m"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"a"... | NT | null | COMPUTE | sympy | V8 | [
"V8/COPRIME_PAIRS"
] | cea98a | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.003 | 2026-02-08T11:25:58.379209Z | {
"verified": true,
"answer": 38416,
"timestamp": "2026-02-08T11:25:58.382387Z"
} | 139df8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1428
},
"timestamp": "2026-02-14T13:52:34.791Z",
"answer": 38416
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bdb9b6 | nt_count_phi_equals_v1_153355830_695 | Let $N = 22$. Let $u$ be the number of positive integers $k$ such that $1 \leq k \leq 110000$ and $N$ divides $k$. Let $k_0 = 4379$. Determine the number of positive integers $n$ such that $1 \leq n \leq u$ and $\phi(n) = k_0$, where $\phi$ denotes Euler's totient function. | 0 | graphs = [
Graph(
let={
"_n": Const(22),
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(110000)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"k": Const(4379),
"... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"C2"
] | 9685eb | nt_count_phi_equals_v1 | null | 7 | 0 | [
"C2",
"MAX_DIVISOR"
] | 2 | 2.69 | 2026-02-08T04:08:04.268223Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T04:08:06.957856Z"
} | 4ab363 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 742
},
"timestamp": "2026-02-10T15:30:24.021Z",
"answer": 0
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
37d892 | algebra_poly_eval_v1_1419126231_689 | Let $b = 20$. Let $e$ be the number of ordered pairs $(a, b1)$ with $1 \le a, b1 \le 10$ satisfying
$$
162a^4 + 216a^3b1 + 540a^2b1^2 + 312ab1^3 + 82b1^4 = 811296.
$$
Compute $5 \cdot b^e + \sum_{k=0}^{2} 2^k \cdot b + 4$. | 2,144 | graphs = [
Graph(
let={
"_n": Const(4),
"b": Const(20),
"result": Sum(Mul(Const(5), Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b1")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(10)), Geq(Var("b1"), Const(1)), Leq(Var("b... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT",
"SUM_GEOM"
] | 6419b7 | algebra_poly_eval_v1 | null | 4 | 0 | [
"POLY4_COUNT",
"SUM_GEOM"
] | 2 | 0.003 | 2026-02-25T10:09:37.903727Z | {
"verified": true,
"answer": 2144,
"timestamp": "2026-02-25T10:09:37.906752Z"
} | 5407e1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 31878
},
"timestamp": "2026-03-30T09:41:20.412Z",
"answer": 2144
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
49edbf | modular_modexp_compute_v1_458359167_79 | Let $a = 41$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1018081$. Define $e$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $m = 35721$. Compute the remainder when $a^e$ is divided by $m$. | 20,203 | graphs = [
Graph(
let={
"a": Const(41),
"e": 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(1018081)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T02:59:17.375909Z | {
"verified": true,
"answer": 20203,
"timestamp": "2026-02-08T02:59:17.378681Z"
} | 48327b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T20:41:23.494Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
eef9ee | comb_binomial_compute_v1_1218484723_2703 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 35$ such that $b^2 - 8ab + 16a^2 = 256$. Let $M = \binom{n}{5}$. Find the remainder when $62132M$ is divided by $53551$. | 48,726 | graphs = [
Graph(
let={
"_n": Const(35),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Eq(Sum(Pow(Var("b"), Const(2)), Mul(Const(-8), Var... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | comb_binomial_compute_v1 | null | 4 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.002 | 2026-02-25T04:26:04.207636Z | {
"verified": true,
"answer": 48726,
"timestamp": "2026-02-25T04:26:04.209959Z"
} | 6ca739 | 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": 2014
},
"timestamp": "2026-03-29T06:04:14.870Z",
"answer": 48726
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
9b36c8 | nt_count_primes_v1_1978505735_896 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $A$. Let $S$ be the set of all prime numbers $n$ such that $n \geq m$ and $n \leq 32768$. Let $r$ be the number of elements in $S$... | 2,678 | graphs = [
Graph(
let={
"upper": Const(32768),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.752 | 2026-02-08T15:40:08.809689Z | {
"verified": true,
"answer": 2678,
"timestamp": "2026-02-08T15:40:09.562173Z"
} | cf67e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1923
},
"timestamp": "2026-02-16T11:34:36.500Z",
"answer": 2678
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
026629 | geo_count_lattice_rect_v1_1520064083_9749 | Compute the number of lattice points $(x, y)$ with $0 \leq x \leq 222$ and $0 \leq y \leq 180$. Determine the value of this count. | 40,363 | graphs = [
Graph(
let={
"a": Const(222),
"b": Const(180),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T10:59:45.218650Z | {
"verified": true,
"answer": 40363,
"timestamp": "2026-02-08T10:59:45.219551Z"
} | cf14a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 260
},
"timestamp": "2026-02-24T12:35:31.141Z",
"answer": 40363
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
2c86e6 | alg_poly3_sum_v1_1218484723_1822 | Let $K = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 15,\ -2a_1b_1 + 13a_1^2 + 2b_1^2 \le 1832 \}\right|$. Find the remainder when $$\sum_{a=1}^{472} \sum_{b=1}^{472} \left( -133a^3 + K a^2 b - 84a b^2 + 16b^3 \right)$$ is divided by $85144$. | 74,072 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(472)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(472)))), expr=Sum(Mul(Const(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_sum_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.402 | 2026-02-25T03:29:22.902939Z | {
"verified": true,
"answer": 74072,
"timestamp": "2026-02-25T03:29:23.304923Z"
} | 6be21c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 5537
},
"timestamp": "2026-03-29T01:32:22.794Z",
"answer": 18832
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
602bd4 | diophantine_fbi2_count_v1_1918700295_2004 | Let $k = 120$. Determine the number of positive integers $d$ such that $3 \leq d \leq 109$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 110$. | 11 | graphs = [
Graph(
let={
"k": Const(120),
"a": Const(2),
"b": Const(3),
"upper": Const(107),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(109)), Divides(divisor=Var("d"), dividend=R... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"C4"
] | 1 | 0.049 | 2026-02-08T07:36:45.297964Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T07:36:45.346793Z"
} | 713404 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 878
},
"timestamp": "2026-02-13T11:26:41.275Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
73eda1 | nt_count_with_divisor_count_v1_124444284_10344 | Let $\mathcal{P}$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9000000$. Let $s$ be the minimum value of $x + y$ over all pairs $(x, y) \in \mathcal{P}$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq s$ and $n$ has exactly 15 positive divisors. Compute the valu... | 4,108 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(9000000)))), expr=Sum(Var("x"), Var("y")... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 2.644 | 2026-02-08T12:59:10.823558Z | {
"verified": true,
"answer": 4108,
"timestamp": "2026-02-08T12:59:13.467612Z"
} | da7c67 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2881
},
"timestamp": "2026-02-15T08:59:57.891Z",
"answer": 4108
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
28473c | modular_min_modexp_v1_1520064083_4979 | Let $m = 191$. Let $T$ be the set of all integers $t$ such that $15 \leq t \leq 113$ and there exist integers $a$ and $b$ with $1 \leq a \leq 17$, $1 \leq b \leq 10$, and $t = 5a + 2b + 8$. Let $u$ be the number of elements in $T$. Find the smallest positive integer $x$ such that $1 \leq x \leq u$ and $3^x \equiv 147 \... | 28,010 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(147),
"m": Const(191),
"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)), L... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_modexp_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-08T06:32:28.213794Z | {
"verified": true,
"answer": 28010,
"timestamp": "2026-02-08T06:32:28.221699Z"
} | 126fe8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 4255
},
"timestamp": "2026-02-13T02:01:53.366Z",
"answer": 28010
},
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
164912 | modular_sum_quadratic_residues_v1_1742523217_577 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$. Define $m = 2$ and let $n$ be the minimum value of $x + y$ over all such pairs in $T$. Let $p$ be the smallest divisor of $1751722385533$ that is at least $m$. Compute $\frac{p(p-1)}{n}$. | 19,113 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(4)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B1 | [
"B1/MIN_PRIME_FACTOR"
] | 37b65c | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T03:07:40.233955Z | {
"verified": true,
"answer": 19113,
"timestamp": "2026-02-08T03:07:40.236531Z"
} | d8844d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 13060
},
"timestamp": "2026-02-23T16:42:39.206Z",
"answer": 19113
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemm... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
b7ea15 | alg_poly3_sum_v1_601307018_8733 | Find the remainder when $$\sum_{\substack{a=1 \\ b=1 \\ c=1}}^{30} \left( -396a b^2 - 136a^3 - 8c^3 - 36b c^2 - 54b^2 c - 24a^2 c - 120a c^2 - 432a b c - 27b^3 \right)$$ is divided by $66272$, where the upper limit for $c$ is $$\left| \left\{ (a_1, b_1) \mid 1 \le a_1, b_1 \le 30,\ 16 b_1^2 = \left| \left\{ (a_2, b_2) ... | 65,080 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_COUNT"
] | 831c70 | alg_poly3_sum_v1 | null | 6 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.13 | 2026-03-10T09:11:11.900796Z | {
"verified": true,
"answer": 65080,
"timestamp": "2026-03-10T09:11:12.031171Z"
} | a09069 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 338,
"completion_tokens": 7990
},
"timestamp": "2026-04-19T09:40:53.081Z",
"answer": 65080
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
5f874c | comb_count_surjections_v1_1978505735_2118 | Let $k$ be the number of ordered pairs $(i, j)$ of integers such that $i + j = 8$, $1 \leq i \leq 6$, and $1 \leq j \leq 7$. Compute $k! \cdot S(6, k)$, where $S(6, k)$ denotes the Stirling number of the second kind. | 720 | graphs = [
Graph(
let={
"_n": Const(8),
"n": Const(6),
"k": 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(6)), right=IntegerRang... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.017 | 2026-02-08T16:40:18.588033Z | {
"verified": true,
"answer": 720,
"timestamp": "2026-02-08T16:40:18.604603Z"
} | 664302 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 979
},
"timestamp": "2026-02-24T21:46:13.046Z",
"answer": 720
},
{
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
2e3f71 | diophantine_product_count_v1_717093673_1898 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 8100$. Define $k$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $T$ be the set of all positive integers $x_1$ such that $1 \leq x_1 \leq 162$, $x_1$ divides $k$, and $\frac{k}{x_1} \leq 162$. Compute the number o... | 16 | 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(8100)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(162... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 3.424 | 2026-02-08T16:23:08.057890Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T16:23:11.481493Z"
} | b54dc8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1280
},
"timestamp": "2026-02-17T01:34:26.726Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c66963 | comb_sum_binomial_row_v1_168721529_447 | Let $n_1 = 0$ and $n_2 = 0$. Define
$$
v = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}
\quad\text{and}\quad
m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n$ be the number of integers $t$ such that $7 \leq t \leq 26$ and there exist integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 2$, and $t = 2a + 5b$.
Let... | 2,621 | graphs = [
Graph(
let={
"_n": Const(44121),
"n2": Const(0),
"m": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"v": Summation(var="k", start=Const(0), end=Ref(... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | comb_sum_binomial_row_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T13:03:39.298892Z | {
"verified": true,
"answer": 2621,
"timestamp": "2026-02-08T13:03:39.303215Z"
} | 69a362 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 324,
"completion_tokens": 4746
},
"timestamp": "2026-02-09T05:05:27.528Z",
"answer": 2621
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -1.2,
"mid": 1.93,
"hi": 4.95
} | ||
3b83a0 | diophantine_fbi2_count_v1_1439011603_2889 | Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq 2204$ and $\gcd(n, 21) = 1$. Determine the number of positive integers $d$ such that $3 \leq d \leq 171$, $d$ divides $k$, and the quotient $k/d$ is an integer between $4$ and $172$, inclusive. | 22 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2204)), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.021 | 2026-02-08T17:03:18.731617Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T17:03:18.752552Z"
} | ba545d | 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": 1832
},
"timestamp": "2026-02-17T17:51:50.082Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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