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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1a235e | antilemma_k2_v1_1874849503_35 | Let $S$ be the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 356$ and $1 \leq j \leq 8$. Define $x = \frac{6}{48} \sum_{(k,j) \in S} \varphi(k) \left\lfloor \frac{356}{k} \right\rfloor$. Let $d_i$ denote the $i$-th decimal digit of $|x|$, starting from the units digit as $i=0$. Compute... | 35,234 | graphs = [
Graph(
let={
"_n": Const(48),
"x": Div(Mul(Const(6), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(356)), right=IntegerRange(start=Const(1), end=... | NT | COMB | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/K2",
"IDENTITY_POW_ZERO",
"K2"
] | 6fbc40 | antilemma_k2_v1 | null | 4 | 0 | [
"IDENTITY_POW_ZERO",
"K2",
"SUM_INDEPENDENT"
] | 3 | 0.004 | 2026-02-08T12:46:19.125438Z | {
"verified": true,
"answer": 35234,
"timestamp": "2026-02-08T12:46:19.129782Z"
} | a8820c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 1616
},
"timestamp": "2026-02-10T02:00:49.883Z",
"answer": 35234
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{... | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
c22c22 | nt_min_coprime_above_v1_124444284_9101 | Let $m=2$ and $n_0=16779$. Let $d_0$ be the smallest integer $d$ with $d\ge 2$ such that $d$ divides $229210813$.
Let $K$ be the number of integers $n$ with $1\le n\le M_0$ such that
$$n\equiv \left\lfloor\frac{n}{2}\right\rfloor \pmod{11}$$
and $d_0$ divides the $n$th Fibonacci number $F_n$, where
$$M_0=\#\{n:\,1\le ... | 13,478 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(16779),
"start": Const(81225),
"upper": Const(81452),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COUNT_FIB_DIVISIBLE/L3C"
] | 933348 | nt_min_coprime_above_v1 | null | 8 | 0 | [
"COUNT_FIB_DIVISIBLE",
"L3C",
"MIN_PRIME_FACTOR"
] | 3 | 0.086 | 2026-02-08T12:13:30.076415Z | {
"verified": true,
"answer": 13478,
"timestamp": "2026-02-08T12:13:30.162229Z"
} | 5eedbd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 3261
},
"timestamp": "2026-02-14T23:22:04.495Z",
"answer": 13478
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "L3c",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
795b0b | nt_sum_gcd_range_mod_v1_1978505735_7607 | Let $k = 180$ and $M = 11597$. Define
$$
S = \left\{ (n, j) \mid 1 \leq n \leq 4900,\ 1 \leq j \leq 5 \right\}.
$$
Let
$$
\sigma = \frac{3}{15} \sum_{(n,j) \in S} \gcd(n, k).
$$
Let $r = \sigma \bmod M$, the unique integer such that $0 \leq r < M$ and $r \equiv \sigma \pmod{M}$.
Let $c$ be the sum of all real solution... | 17,481 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(15),
"k": Const(180),
"M": Const(11597),
"sum": Div(Mul(Const(3), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("n"), Var("_j")]), condition=Const(1), domain=CartesianProduct(... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"SUM_INDEPENDENT"
] | 28e0c7 | nt_sum_gcd_range_mod_v1 | quadratic_mod | 6 | 0 | [
"SUM_INDEPENDENT",
"VIETA_SUM"
] | 2 | 0.621 | 2026-02-08T20:21:47.012921Z | {
"verified": true,
"answer": 17481,
"timestamp": "2026-02-08T20:21:47.633533Z"
} | 5b630e | CC BY 4.0 | [
{
"id": 11,
"model": "google/gemma-2-9b-it",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 311,
"completion_tokens": 594
},
"timestamp": "2026-02-13T01:21:08.092Z",
"answer": null
}
] | 0 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
... | {
"lo": -7.07,
"mid": 1.24,
"hi": 9.56
} | ||
3ac654 | nt_min_phi_inverse_v1_1874849503_1183 | Let $n = 20$. Define $\text{upper}$ to be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 20$. Define $k$ to be the number of integers $t$ with $27 \leq t \leq 114$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 12$, $1 \leq b \leq 2$, and $t = 6a + 21b$. ... | 35 | graphs = [
Graph(
let={
"_n": Const(20),
"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")))), expr=Mul(Var("x"), Var("y")))),... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"B1"
] | 2f9b70 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.01 | 2026-02-08T13:39:33.013170Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T13:39:33.023493Z"
} | 929b58 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 5207
},
"timestamp": "2026-02-10T02:18:29.719Z",
"answer": 35
},
{
"id"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
9d37d9 | diophantine_fbi2_min_v1_458359167_3176 | Let $k = 15$ and $\text{upper} = 25$. Consider the set of all integers $d$ such that $4 \leq d \leq 25$, $d$ divides $k$, and $$
\frac{k}{d} \geq \sum_{k=1}^{2} \varphi(k) \left\lfloor \frac{2}{k} \right\rfloor.
$$ Determine the value of the smallest such $d$. | 5 | graphs = [
Graph(
let={
"k": Const(15),
"upper": Const(25),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Summation(var="k"... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"K2"
] | 6897ab | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.06 | 2026-02-08T07:00:48.546842Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T07:00:48.606471Z"
} | 4db42c | 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": 789
},
"timestamp": "2026-02-13T07:04:44.665Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
6b8b2a | nt_count_coprime_and_v1_798873815_123 | Let $m = 2$. Let $n$ be the number of integers $t$ with $10 \le t \le 36$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 4$, $1 \le b \le 3$, and $t = 6a + 4b$. Let $k_2$ be the largest prime number that is at least $m$ and at most $n$. Compute the number of positive integers $n$ at most $30... | 62,671 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(n... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 4ef32e | nt_count_coprime_and_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 3 | 2.851 | 2026-02-08T02:26:26.287530Z | {
"verified": true,
"answer": 62671,
"timestamp": "2026-02-08T02:26:29.138857Z"
} | 8feed3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 4877
},
"timestamp": "2026-02-08T19:02:47.857Z",
"answer": 62671
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
... | {
"lo": -1.89,
"mid": 1.79,
"hi": 4.93
} | ||
50997a | comb_count_partitions_v1_1520064083_7846 | Let $n$ be the number of integers $t$ with $20 \leq t \leq 120$ such that there exist positive integers $a \leq 13$ and $b \leq 3$ satisfying $t = 6a + 14b$. Let $\mathrm{result}$ be the number of integer partitions of $n$. Compute the remainder when $62347 \cdot \mathrm{result}$ is divided by $56139$. | 29,208 | 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=13)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T09:20:38.129246Z | {
"verified": true,
"answer": 29208,
"timestamp": "2026-02-08T09:20:38.131207Z"
} | 321500 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 3573
},
"timestamp": "2026-02-24T11:07:27.898Z",
"answer": 29208
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
7b54fb | modular_sum_quadratic_residues_v1_458359167_4045 | Let $p$ be the smallest integer greater than or equal to 2 that divides 1822577. Define
$$
r = \frac{p(p-1)}{4}.
$$
Find the remainder when $44121 \cdot r$ is divided by 60131. | 34,793 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1822577))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(valu... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T11:29:19.533696Z | {
"verified": true,
"answer": 34793,
"timestamp": "2026-02-08T11:29:19.535059Z"
} | 145e07 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 2378
},
"timestamp": "2026-02-14T15:23:37.525Z",
"answer": 34793
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
78ccf2 | comb_count_derangements_v1_1915831931_1217 | Let $\_d=48640$ and let $m$ be the number of nonnegative integers $j$ with $0\le j\le 48640$ such that the binomial coefficient $\binom{48640}{j}$ is odd, plus $13$.
Let $c=77$. Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ satisfying all of the following:
\begin{itemize}... | 1,854 | graphs = [
Graph(
let={
"_d": Const(48640),
"_c": Const(77),
"_m": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(48640)), Eq(Mod(value=Binom(n=Ref("_d"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonne... | NT | COMB | COUNT | sympy | V8 | [
"V8/SUM_DIVISIBLE/MIN_PRIME_FACTOR",
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | e8b7e6 | comb_count_derangements_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE",
"V8"
] | 4 | 0.01 | 2026-02-08T15:57:13.978549Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T15:57:13.989030Z"
} | 9072eb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 2082
},
"timestamp": "2026-02-16T17:26:51.852Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CON... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
581a88 | comb_count_surjections_v1_153355830_765 | Let $n$ be the number of ordered pairs $(i,j)$ where $i \in \{1,2\}$ and $j \in \{1,2\}$. Let $k = 2$. Compute the remainder when $33915 \cdot k! \cdot S(n, k)$ is divided by $77948$, where $S(n, k)$ denotes the Stirling number of the second kind. | 7,122 | graphs = [
Graph(
let={
"_n": Const(77948),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(2)))),
"k": Const(2),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'),... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:09:53.367801Z | {
"verified": true,
"answer": 7122,
"timestamp": "2026-02-08T04:09:53.369111Z"
} | 2d2fd0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 876
},
"timestamp": "2026-02-23T23:39:56.806Z",
"answer": 7122
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
e7203b | nt_sum_gcd_range_mod_v1_1520064083_8659 | Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 94$. Let $k = 60$ and $M = 11071$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Find the remainder when $\text{sum}$ is divided by $M$. | 2,150 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(94)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(60),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.198 | 2026-02-08T10:17:36.222453Z | {
"verified": true,
"answer": 2150,
"timestamp": "2026-02-08T10:17:36.420721Z"
} | ffae8a | 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": 2363
},
"timestamp": "2026-02-14T07:01:13.624Z",
"answer": 2150
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d0a394 | comb_count_permutations_fixed_v1_124444284_3880 | Let $n = 10$ and $k = 6$. Define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $d_0$ be the smallest integer $d \geq 2$ that divides $1573$. Compute the value of the Bell number $B_m$, where $m$ is the remainder when $|\text{result}|$ is divided by $d_... | 21,147 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(10),
"k": Const(6),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | comb_count_permutations_fixed_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.059 | 2026-02-08T05:39:22.970990Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T05:39:23.029864Z"
} | 3f20bd | 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": 974
},
"timestamp": "2026-02-12T11:53:26.464Z",
"answer": 21147
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e2a6a9 | nt_min_with_divisor_count_v1_1915831931_3039 | Let $r$ be the smallest positive integer $n$ such that $1 \le n \le 9801$ and $n$ has exactly three positive divisors.
Let $d_{\text{min}}$ be the smallest divisor of 8998611773 that is at least 2.
Compute the value of
$$
r \bmod d_{\text{min}} + 3001 \cdot (r \bmod 317).
$$ | 12,008 | graphs = [
Graph(
let={
"_n": Const(317),
"upper": Const(9801),
"div_count": Const(3),
"result": MinOverSet(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"))))),
... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | nt_min_with_divisor_count_v1 | two_moduli | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.432 | 2026-02-08T17:19:07.339356Z | {
"verified": true,
"answer": 12008,
"timestamp": "2026-02-08T17:19:07.771144Z"
} | d9ef9e | 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": 2427
},
"timestamp": "2026-02-17T23:56:22.074Z",
"answer": 12008
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f174eb | diophantine_product_count_v1_1915831931_276 | Let $k = 60$ and $u = 41$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $60$, and $\frac{60}{x} \leq 41$. Let $r$ be the number of elements in $S$.
Compute the remainder when the Bell number $B_{|r| \bmod 11}$ is divided by $67267$. | 48,708 | graphs = [
Graph(
let={
"k": Const(60),
"upper": Const(41),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))))... | NT | COMB | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"MAX_PRIME_BELOW",
"B3"
] | 3199d3 | diophantine_product_count_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | 3 | 0.041 | 2026-02-08T15:19:05.762927Z | {
"verified": true,
"answer": 48708,
"timestamp": "2026-02-08T15:19:05.804341Z"
} | 4accf3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1315
},
"timestamp": "2026-02-16T04:05:43.758Z",
"answer": 48708
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4c2612 | alg_qf_psd_min_v1_601307018_1955 | Find the minimum value of $17595c^2 + 1725b^2 + 3450ab + 6210bc + 6210ac + 1725a^2$ over all ordered triples $(a, b, c)$ of positive integers with $1 \le a, b, c \le 41$. | 36,915 | graphs = [
Graph(
let={
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(41)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(41)), Geq(Var("c"), Const(1)), Leq(Var("c"), Const(41))))... | ALG | null | COMPUTE | sympy | SUM_AP | [
"SUM_AP"
] | ff6f57 | alg_qf_psd_min_v1 | null | 5 | null | [
"SUM_AP"
] | 1 | 0.306 | 2026-03-10T02:42:28.477267Z | {
"verified": true,
"answer": 36915,
"timestamp": "2026-03-10T02:42:28.782774Z"
} | 51b76b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1076
},
"timestamp": "2026-03-29T03:55:51.647Z",
"answer": 36915
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_AP",
"status": "ok"
}
] | {
"lo": -2.48,
"mid": 1.07,
"hi": 4.5
} | ||
afaa36 | nt_max_prime_below_v1_677425708_325 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Determine the largest prime number $n$ such that $m \leq n \leq 11681$. Let $Q$ be the remainder when $89821$ times this prime is divided by $71755$. Compute $Q$. | 69,246 | graphs = [
Graph(
let={
"upper": Const(11681),
"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 | 0.267 | 2026-02-08T03:13:22.363461Z | {
"verified": true,
"answer": 69246,
"timestamp": "2026-02-08T03:13:22.630558Z"
} | 125e5b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 7047
},
"timestamp": "2026-02-08T20:27:51.407Z",
"answer": 69246
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
deb361 | modular_sum_quadratic_residues_v1_784195855_7205 | Let $p = 401$. Consider the set of all ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 4$, $1 \leq j \leq 5$, and $i + j = 5$. Compute the value of $\frac{p(p-1)}{\text{the number of elements in that set}}$. | 40,100 | graphs = [
Graph(
let={
"p": Const(401),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(5)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(... | NT | null | SUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T09:08:45.607849Z | {
"verified": true,
"answer": 40100,
"timestamp": "2026-02-08T09:08:45.618898Z"
} | 385248 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 340
},
"timestamp": "2026-02-15T20:34:07.769Z",
"answer": 40100
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"statu... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
5c20a1 | alg_qf_psd_min_v1_1218484723_6706 | Let $d_{\min}$ be the smallest divisor of $131753$ that is at least $2$. Find the minimum value of $40730a^2 - 73314ab + 52949b^2$ over all positive integers $a, b$ with $1 \le a \le d_{\min}$ and $1 \le b \le 359$. | 20,365 | graphs = [
Graph(
let={
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.53 | 2026-02-25T08:13:11.950025Z | {
"verified": true,
"answer": 20365,
"timestamp": "2026-02-25T08:13:12.479701Z"
} | a0e047 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 12345
},
"timestamp": "2026-03-30T02:39:55.059Z",
"answer": 20365
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
64ca5c | comb_count_surjections_v1_784195855_9123 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 6$ and $1 \leq j \leq 7$ such that $i + j = 7$. Compute the value of $k! \cdot S(7, k)$, where $S(n, k)$ denotes the Stirling number of the second ... | 15,120 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | null | COUNT | sympy | LIN_FORM | [
"COMB1/COUNT_SUM_EQUALS"
] | 4d9cac | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.045 | 2026-02-08T16:33:18.970977Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-08T16:33:19.015513Z"
} | 57232a | 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": 882
},
"timestamp": "2026-02-17T07:29:09.047Z",
"answer": 15120
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "V8",
"st... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
e549ee | nt_gcd_compute_v1_1440796553_1478 | Let $a = 254440$ and $b = 559768$. Let $g = \gcd(a, b)$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 93025$. Find the remainder when $s - g$ is divided by $73934$. | 23,656 | graphs = [
Graph(
let={
"_n": Const(93025),
"a": Const(254440),
"b": Const(559768),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(n... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_gcd_compute_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T14:01:47.569608Z | {
"verified": true,
"answer": 23656,
"timestamp": "2026-02-08T14:01:47.571122Z"
} | 32eea8 | 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": 1169
},
"timestamp": "2026-02-15T23:00:47.026Z",
"answer": 23656
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
50bbe0 | geo_count_lattice_rect_v1_784195855_4318 | Let $a = 377$ and $b = 119$. Define $\mathcal{R}$ as the set of all lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $N$ be the number of points in $\mathcal{R}$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $N + 2$. Find the value of $k$. | 17,499 | graphs = [
Graph(
let={
"a": Const(377),
"b": Const(119),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 5 | 0 | null | null | 0.002 | 2026-02-08T06:59:56.958513Z | {
"verified": true,
"answer": 17499,
"timestamp": "2026-02-08T06:59:56.960540Z"
} | a51a98 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T07:34:28.875Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
76850d_l | comb_count_partitions_v1_677425708_1984 | Let $S$ be the set of all ordered pairs $(k,j)$ where $k$ is an integer from 1 to 9, inclusive, and $j$ is an integer from 1 to 6, inclusive. Let $T$ be the set of all values $k$ such that $(k,j) \in S$. Define $n$ to be $\frac{7 \times (\text{sum of all elements in } T)}{42}$. Compute the number of integer partitions ... | 15 | COMB | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"SUM_ARITHMETIC"
] | 9f7183 | comb_count_partitions_v1 | null | 6 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 0.002 | 2026-02-08T04:42:08.667258Z | {
"verified": false,
"answer": 89134,
"timestamp": "2026-02-08T04:42:08.668932Z"
} | fa6528 | 76850d | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 7069
},
"timestamp": "2026-02-10T04:03:54.521Z",
"answer": 15
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | |
615e2c | geo_count_lattice_rect_v1_48377204_1330 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 256$ and $0 \leq y \leq 215$. | 55,512 | graphs = [
Graph(
let={
"a": Const(256),
"b": Const(215),
"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 | 0.004 | 2026-02-08T16:01:53.323400Z | {
"verified": true,
"answer": 55512,
"timestamp": "2026-02-08T16:01:53.327806Z"
} | c03a16 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 239
},
"timestamp": "2026-02-24T19:43:13.871Z",
"answer": 55512
},
{
"... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||||
2ee74d | comb_count_derangements_v1_717093673_4092 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 21000$, $\gcd(p, q) = 1$, and $p < q$. Let $!n$ denote the number of derangements of $n$ elements. Compute the remainder when $71566 \cdot (!n)$ is divided by $90949$. | 72,699 | graphs = [
Graph(
let={
"_n": Const(71566),
"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=21000)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T18:02:10.972449Z | {
"verified": true,
"answer": 72699,
"timestamp": "2026-02-08T18:02:10.975288Z"
} | 8dc51c | 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": 3180
},
"timestamp": "2026-02-18T12:25:58.407Z",
"answer": 72699
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
81c128 | algebra_poly_eval_v1_1520064083_7395 | Let $m = 40$. Define $n$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 8836$. Let $a = 11$. Compute the value of $$\frac{40 \cdot 11^4 + n \cdot 11^3 - 384 \cdot 11^2 - 784 \cdot 11 - 140}{t},$$ where $t$ is the number of integers in the range $5 \leq t \leq 381... | 205 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(8836)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/LIN_FORM"
] | 9cebb8 | algebra_poly_eval_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T09:00:35.546028Z | {
"verified": true,
"answer": 205,
"timestamp": "2026-02-08T09:00:35.549982Z"
} | 0e1b5f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 5405
},
"timestamp": "2026-02-13T23:35:40.014Z",
"answer": 205
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
41ae1d | nt_euler_phi_compute_v1_677425708_1740 | Let $g = 9$, $n_2 = 7$, and $p = 7$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $15$. Define $a = g \cdot d_{\text{min}}$ and $b = g \cdot n_2$. Let $h = \sum_{d \mid \gcd(a,b)} \mu(d)$, where $\mu$ is the Möbius function. Define $n_1 = p^{1+h}$ and let $e$ be the number of distinct prime fact... | 27,648 | graphs = [
Graph(
let={
"_n": Const(2),
"g": Const(9),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(15))))),
"n2": Const(7),
"a": Mul(Ref("g"), Ref("m")),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_COPRIME",
"OMEGA_ONE"
] | 4999b1 | nt_euler_phi_compute_v1 | null | 6 | 2 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME",
"OMEGA_ONE"
] | 3 | 0.004 | 2026-02-08T04:24:36.841281Z | {
"verified": true,
"answer": 27648,
"timestamp": "2026-02-08T04:24:36.845235Z"
} | 5c3ea6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 741
},
"timestamp": "2026-02-10T00:09:55.763Z",
"answer": 27648
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
05809b | comb_bell_compute_v1_655260480_4113 | Let $m = 404$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $n_0 = |S|$.
Let $k$ be the largest positive integer such that $n_0^k \leq m$. Compute the Bell number $B_k$. | 4,140 | graphs = [
Graph(
let={
"_m": Const(404),
"_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=... | NT | COMB | COMPUTE | sympy | LTE_SUM | [
"COPRIME_PAIRS/MAX_VAL"
] | aa93c6 | comb_bell_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"LTE_SUM",
"MAX_VAL"
] | 3 | 0.016 | 2026-02-08T17:43:36.166450Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T17:43:36.182351Z"
} | eefc63 | 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": 1488
},
"timestamp": "2026-02-18T07:45:00.202Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bb4381 | comb_count_partitions_v1_1978505735_3081 | Let $t = \sum_{k=0}^{5} (-1)^k \binom{5}{k}$ and $u = 1$. Define $n_1 = u + 1$ and $h = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}$. Let $n = 45 + t + h$. Compute the number of integer partitions of $n$. | 89,134 | graphs = [
Graph(
let={
"n2": Const(5),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(1),
"n1": Sum(Ref("u"), Const(1)),
"h": Summation(var="k1", start=Const(0... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_partitions_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T17:19:11.520913Z | {
"verified": true,
"answer": 89134,
"timestamp": "2026-02-08T17:19:11.522455Z"
} | 62a003 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 583
},
"timestamp": "2026-02-18T00:36:26.796Z",
"answer": 89134
},
{... | 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": "V8",... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
2693d4 | antilemma_k3_v1_397696148_1054 | Let $n = 85168$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 85,168 | graphs = [
Graph(
let={
"_n": Const(85168),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T12:19:47.814380Z | {
"verified": true,
"answer": 85168,
"timestamp": "2026-02-08T12:19:47.815084Z"
} | bf06ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 805
},
"timestamp": "2026-02-14T23:50:59.913Z",
"answer": 85168
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6f6d6d | modular_count_residue_v1_717093673_1538 | Let $m$ be the number of positive integers $n$ with $1 \leq n \leq 360$ such that $15$ divides the $n$th Fibonacci number. Let $U = 34225$ and $r = 13$. Define $S$ as the set of all integers $n_1$ such that $1 \leq n_1 \leq U$ and
$$
n_1 \equiv 13 \pmod{m}.
$$
Let $k$ be the number of elements in $S$. Let $Q$ be the ... | 870 | graphs = [
Graph(
let={
"upper": Const(34225),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(360)), Divides(divisor=Const(15), dividend=Fibonacci(arg=Var(name='n')))))),
"r": Const(13),
"result": Co... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | modular_count_residue_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 1.143 | 2026-02-08T16:09:23.963953Z | {
"verified": true,
"answer": 870,
"timestamp": "2026-02-08T16:09:25.106685Z"
} | 6a5db5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2744
},
"timestamp": "2026-02-16T22:00:10.602Z",
"answer": 870
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
502fd6 | nt_count_divisible_and_v1_1440796553_1526 | Let $d_1 = 12$. Let $d_2$ be the sum
$$
\sum_{k=1}^{d_{\text{min}}} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,
$$
where $d_{\text{min}}$ is the smallest integer $d \geq 2$ that divides $21175$, and $\phi$ denotes Euler's totient function. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 9186... | 72,291 | graphs = [
Graph(
let={
"upper": Const(91860),
"d1": Const(12),
"d2": Summation(var="k", start=Const(1), end=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(21175))))), expr=Mul(EulerPhi(n=Var("k"))... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2"
] | 352a97 | nt_count_divisible_and_v1 | null | 7 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 3.091 | 2026-02-08T14:02:13.818683Z | {
"verified": true,
"answer": 72291,
"timestamp": "2026-02-08T14:02:16.909564Z"
} | 95fcf6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1814
},
"timestamp": "2026-02-15T23:18:53.428Z",
"answer": 72291
},
... | 1 | [
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "n... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1f8275 | nt_gcd_compute_v1_1874849503_876 | Let $m = 54535$. Let $n$ be the number of positive integers $p$ for which there exists an integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $a = 556075$ and $b = 898275$. Define $r = \gcd(a, b)$. Let $S$ be the set of all positive divisors $d$ of $170867$ such that $d \geq n$. Let $t$ be the mi... | 11,777 | graphs = [
Graph(
let={
"_m": Const(54535),
"_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(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 902529 | nt_gcd_compute_v1 | negation_mod | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T13:23:14.953607Z | {
"verified": true,
"answer": 11777,
"timestamp": "2026-02-08T13:23:14.959076Z"
} | 34859b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 2720
},
"timestamp": "2026-02-09T22:02:18.755Z",
"answer": 11777
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"s... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
bb6edf | nt_lcm_compute_v1_168721529_1686 | Let $a = 1144$. Let $b$ be the sum of all real solutions $x$ to the equation $x^2 - 1408x + 23647 = 0$. Compute the least common multiple of $a$ and $b$. | 18,304 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1144),
"b": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-1408), Var("x")), Const(23647)), Const(0)))),
"result": LCM(a=Ref("a"), b=Ref("b")),
},
... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"VIETA_SUM"
] | b33a7a | nt_lcm_compute_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"VIETA_SUM"
] | 2 | 0.013 | 2026-02-08T13:50:46.104221Z | {
"verified": true,
"answer": 18304,
"timestamp": "2026-02-08T13:50:46.117251Z"
} | ed980f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 906
},
"timestamp": "2026-02-09T20:24:07.995Z",
"answer": 18304
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
d6dd36 | comb_factorial_compute_v1_1218484723_203 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that $$
17a^4 + 17b^4 + 68ab^3 + 68a^3b + 102a^2b^2 = 15699857.
$$ Let $n$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1 \le M$, $1 \le b_1 \le 30$ such that $$
27b_1^3 + 108a_1b_1^2 + 1... | 23,808 | graphs = [
Graph(
let={
"_m": Const(68),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Mul(Const(17), Pow(Var("a"), Const(4))), M... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/POLY3_COUNT"
] | 6c2b6f | comb_factorial_compute_v1 | null | 5 | 0 | [
"POLY3_COUNT",
"POLY4_COUNT"
] | 2 | 0.006 | 2026-02-25T01:53:38.332103Z | {
"verified": true,
"answer": 23808,
"timestamp": "2026-02-25T01:53:38.338073Z"
} | 70c051 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 300,
"completion_tokens": 6339
},
"timestamp": "2026-03-10T08:49:06.455Z",
"answer": 23808
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"s... | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
5c2718 | nt_count_divisible_v1_655260480_1453 | Let $\phi(k)$ denote Euler's totient function. Define $d = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$. Let $C$ be the number of positive integers $n$ less than or equal to $69751$ such that $n$ is divisible by $d$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy =... | 4,350 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(69751),
"divisor": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq... | NT | null | COUNT | sympy | B3 | [
"B3",
"K2"
] | 35ca5b | nt_count_divisible_v1 | negation_mod | 7 | 0 | [
"B3",
"K2"
] | 2 | 2.442 | 2026-02-08T16:08:52.310665Z | {
"verified": true,
"answer": 4350,
"timestamp": "2026-02-08T16:08:54.752390Z"
} | a5ecd8 | 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": 1255
},
"timestamp": "2026-02-16T21:34:23.520Z",
"answer": 4350
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DI... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8fa3dc | modular_count_residue_v1_1520064083_1161 | Let $m = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n \leq 44521$ such that $n \equiv 14 \pmod{m}$.\n\nCompute this number. | 2,968 | graphs = [
Graph(
let={
"upper": Const(44521),
"m": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"r": Const(14),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | modular_count_residue_v1 | null | 4 | 0 | [
"K2"
] | 1 | 1.491 | 2026-02-08T03:49:00.295977Z | {
"verified": true,
"answer": 2968,
"timestamp": "2026-02-08T03:49:01.787152Z"
} | 428285 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 808
},
"timestamp": "2026-02-10T15:47:11.398Z",
"answer": 2968
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
cd4270 | comb_count_derangements_v1_124444284_2309 | Let $n$ be the smallest divisor of $91091$ that is greater than or equal to $2$. Compute the subfactorial $!n$. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(91091))))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T04:35:39.148229Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T04:35:39.149153Z"
} | b2dbab | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 860
},
"timestamp": "2026-02-10T17:15:16.242Z",
"answer": 1854
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
1de458 | nt_count_with_divisor_count_v1_2051736721_2972 | Let $n$ be a positive integer such that $1 \leq n \leq 50400$ and the number of positive divisors of $n$ is exactly 7. Let $r$ be the number of such integers $n$. Let $d$ be the smallest divisor of 65007371 that is at least 2. Compute the Bell number $B_k$, where $k$ is the remainder when $|r|$ is divided by $d$. Deter... | 5 | graphs = [
Graph(
let={
"upper": Const(50400),
"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"))))),
"Q": Bell(Mod(valu... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_with_divisor_count_v1 | bell_mod | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.1 | 2026-02-08T17:02:12.443287Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T17:02:14.542937Z"
} | 9a4722 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 836
},
"timestamp": "2026-02-17T18:04:08.291Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
858bfe | modular_count_residue_v1_458359167_350 | Let $m$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 169$. Let $r$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 4$. Compute the number of positive integers $n$ with $1 \leq n \leq 53361$ such that $n \equiv r... | 2,053 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(53361),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(169)))), ... | NT | null | COUNT | sympy | B1 | [
"B1",
"B3"
] | 655d51 | modular_count_residue_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 1.737 | 2026-02-08T03:13:41.678575Z | {
"verified": true,
"answer": 2053,
"timestamp": "2026-02-08T03:13:43.416024Z"
} | 200c2e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1112
},
"timestamp": "2026-02-10T13:39:13.236Z",
"answer": 2053
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
bc3c09 | algebra_quadratic_discriminant_v1_2051736721_3872 | Let $a = 2$, $b = -12$, and let $c$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 9222$ and $\binom{9222}{j}$ is odd. Define $d = b^2 - 4ac$. Compute the value of $15129 - d$. | 15,113 | graphs = [
Graph(
let={
"_n": Const(15129),
"a": Const(2),
"b": Const(-12),
"c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(9222)), Eq(Mod(value=Binom(n=Const(9222), k=Var("j")), modulus=Const(2)), Co... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.004 | 2026-02-08T17:36:39.620738Z | {
"verified": true,
"answer": 15113,
"timestamp": "2026-02-08T17:36:39.624344Z"
} | e8eb12 | 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": 1754
},
"timestamp": "2026-02-18T04:57:39.448Z",
"answer": 15113
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
efc8e5 | comb_count_surjections_v1_124444284_8834 | Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$. Let $n = 4$. Compute the value of $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 24 | graphs = [
Graph(
let={
"_n": Const(8),
"n": Const(4),
"k": 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... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T11:56:10.846922Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T11:56:10.848801Z"
} | d12061 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 632
},
"timestamp": "2026-02-24T14:59:56.424Z",
"answer": 24
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
da6fb3 | modular_count_residue_v1_124444284_8243 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Let $n$ be the minimum value of $x + y$ over all such pairs. Define $m = \sum_{k=1}^{n} k$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 59536$ and $n \equiv 0 \pmod{m}$. Compute the number of elements ... | 5,953 | graphs = [
Graph(
let={
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(4)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(59536... | NT | null | COUNT | sympy | B3 | [
"B3/SUM_ARITHMETIC"
] | b6a880 | modular_count_residue_v1 | null | 4 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 4.358 | 2026-02-08T09:36:51.796664Z | {
"verified": true,
"answer": 5953,
"timestamp": "2026-02-08T09:36:56.154929Z"
} | d2455f | 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": 561
},
"timestamp": "2026-02-14T05:12:59.055Z",
"answer": 5953
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lem... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ed5e50 | diophantine_fbi2_min_v1_677425708_1050 | Let $A$ be the set of all ordered pairs of positive integers $(a, b)$ such that $1 \leq a \leq 24$, $1 \leq b \leq 43$, and the quantity $t = 7a + 3b$ satisfies $10 \leq t \leq 297$. Let $T$ be the set of all such values $t$. Let $N$ be the number of positive integers $n \leq |T|$ such that $8$ divides the $n$-th Fibon... | 42,773 | graphs = [
Graph(
let={
"_n": Const(59746),
"k": Const(36),
"upper": 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(n... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/COUNT_FIB_DIVISIBLE"
] | 95eec8 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T03:58:51.614871Z | {
"verified": true,
"answer": 42773,
"timestamp": "2026-02-08T03:58:51.621186Z"
} | 3278bd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 3447
},
"timestamp": "2026-02-09T15:12:50.854Z",
"answer": 42773
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"stat... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
ca6d30 | comb_catalan_compute_v1_865884756_2383 | Let $n = 10$. Define $C_n$ to be the $n$th Catalan number. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $m$ be the number of elements in $S$. Compute the remainder when the Bell number $B_{|C_n| \bmod m}$ is divided by $68734$.
Find the value of this exp... | 47,241 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=V... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | d93ba8 | comb_catalan_compute_v1 | bell_mod | 3 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T16:43:41.178349Z | {
"verified": true,
"answer": 47241,
"timestamp": "2026-02-08T16:43:41.181385Z"
} | 87dd62 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1230
},
"timestamp": "2026-02-17T11:00:56.135Z",
"answer": 47241
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
441d93 | alg_telescope_v1_1218484723_3052 | Let $T = \{ t \in \mathbb{Z} : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 1025,\ 1 \leq b \leq 686 \text{ such that } t = 2a + 5b,\ 7 \leq t \leq 5480 \}$. Let $M = \left( \sum_{k=0}^{54} (3k^2 + 3k + 1) \right) \bmod |T|$. Compute $|M|.$ | 2,275 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(54), expr=Sum(Mul(Ref("_n"), Pow(Var("k"), Const(2))), Mul(Const(3), Var("k")), Const(1))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'),... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_telescope_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-25T04:49:00.197704Z | {
"verified": true,
"answer": 2275,
"timestamp": "2026-02-25T04:49:00.205511Z"
} | a7a48c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 7515
},
"timestamp": "2026-03-29T08:06:04.255Z",
"answer": 2215
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
c56f8d | comb_bell_compute_v1_601307018_7711 | Let $n$ be the number of integers $t$ with $5 \le t \le 14$ that can be written as $t = 3a + 2b$ for integers $a, b$ satisfying $1 \le a \le 2$ and $1 \le b \le 4$. Let $M = B_n$, where $B_n$ is the $n$-th Bell number. Find the remainder when $44121M$ is divided by $56311$. | 44,367 | graphs = [
Graph(
let={
"_n": Const(56311),
"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_bell_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-03-10T08:18:08.384782Z | {
"verified": true,
"answer": 44367,
"timestamp": "2026-03-10T08:18:08.387658Z"
} | 8622d1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 921
},
"timestamp": "2026-04-19T07:19:01.977Z",
"answer": 44367
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
5f68c9 | nt_sum_divisors_mod_v1_124444284_7871 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 8100$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $93397 \cdot \sigma$ is divided by $78725$. | 59,687 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(8100)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10631),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T09:24:09.880253Z | {
"verified": true,
"answer": 59687,
"timestamp": "2026-02-08T09:24:09.881421Z"
} | a9ed5a | 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": 1910
},
"timestamp": "2026-02-14T03:44:05.413Z",
"answer": 59687
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e46467_l | comb_count_surjections_v1_1439011603_2825 | Let $u = 1$ and $n_2 = u + \binom{7}{0}$. Define
$$
v = \sum_{k_1=0}^{n_2} (-1)^{k_1} \binom{n_2}{k_1}.
$$
Let $n_1 = v$ and
$$
c = \sum_{k_2 = \binom{12}{12} - 1}^{n_1} (-1)^{k_2} \binom{n_1}{k_2}.
$$
Let $n = 6 \cdot c$ and $k = 5$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a... | 0 | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N",
"ONE_BINOM_0"
] | cc0bf5 | comb_count_surjections_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_0",
"ZERO_BINOM_N"
] | 3 | 0.005 | 2026-02-08T17:01:12.582531Z | {
"verified": false,
"answer": 1800,
"timestamp": "2026-02-08T17:01:12.587637Z"
} | a81851 | e46467 | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 873
},
"timestamp": "2026-02-17T17:43:12.350Z",
"answer": 1800
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemm... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | |
392565 | alg_qf_psd_min_v1_601307018_4490 | Let $M$ be the largest prime number $n$ with $2 \le n \le 3797$. Let $R$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 8976016$. Let $S$ be the number of ordered pairs $(a_1, b_1)$ with $1 \le a_1, b_1 \le 30$ satisfying $10a_1^2 - 18a_1b_1 + 25b_1^2 \le M$. Let $Q... | 73,402 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(3797)), IsPrime(Var("n"))))),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), cond... | NT | null | COMPUTE | sympy | SUM_GEOM | [
"MAX_PRIME_BELOW/B3/QF_PSD_COUNT_LEQ"
] | 444b01 | alg_qf_psd_min_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"QF_PSD_COUNT_LEQ",
"SUM_GEOM"
] | 4 | 0.347 | 2026-03-10T05:06:33.227098Z | {
"verified": true,
"answer": 73402,
"timestamp": "2026-03-10T05:06:33.573823Z"
} | 4bc999 | 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": 19556
},
"timestamp": "2026-03-29T12:30:47.835Z",
"answer": 73402
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
d83837 | geo_count_lattice_rect_v1_458359167_1462 | Let $a = 225$ and $b = 56$. Define the set of lattice points in the rectangle $[0, a] \times [0, b]$ as the set of all ordered pairs $(x, y)$ of integers such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the number of such lattice points. | 12,882 | graphs = [
Graph(
let={
"a": Const(225),
"b": Const(56),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.003 | 2026-02-08T04:37:12.041039Z | {
"verified": true,
"answer": 12882,
"timestamp": "2026-02-08T04:37:12.043938Z"
} | a19f1f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 268
},
"timestamp": "2026-02-24T01:17:46.599Z",
"answer": 12882
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||||
20583e | modular_count_residue_v1_124444284_5419 | Let $T$ be the set of all ordered pairs $(k, \_j)$ such that $1 \le k \le 2$ and $1 \le \_j \le 5$. Define
$$
r = \frac{3}{15} \sum_{(k,\_j) \in T} k.
$$
Let $\mathcal{N}$ be the set of all positive integers $n$ such that $1 \le n \le 42025$ and $n \equiv r \pmod{5}$. Compute the number of elements in $\mathcal{N}$. | 8,405 | graphs = [
Graph(
let={
"upper": Const(42025),
"m": Const(5),
"r": Div(Mul(Const(3), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=In... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | modular_count_residue_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 1.411 | 2026-02-08T06:34:52.932113Z | {
"verified": true,
"answer": 8405,
"timestamp": "2026-02-08T06:34:54.343145Z"
} | 217def | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 756
},
"timestamp": "2026-02-15T17:37:18.438Z",
"answer": 8405
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
2cff56 | nt_sum_totient_over_divisors_v1_124444284_4256 | Let $n$ be the number of positive integers at most $31809$ that are divisible by $3$ and relatively prime to $10$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 4,242 | graphs = [
Graph(
let={
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(31809)), Divides(divisor=Ref("_n"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"result": SumOverDivi... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.004 | 2026-02-08T05:53:08.368203Z | {
"verified": true,
"answer": 4242,
"timestamp": "2026-02-08T05:53:08.372048Z"
} | 52561f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 1038
},
"timestamp": "2026-02-12T16:30:40.694Z",
"answer": 4242
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d57abc | modular_mod_compute_v1_458359167_3191 | Let $a = -8649$ and $m = 73441$. Define $r$ to be the remainder when $a$ is divided by $m$, so that $0 \leq r < m$ and $r \equiv a \pmod{m}$. Let $k = r + 2$. Compute the smallest positive integer $n$ such that the $n$th Fibonacci number is divisible by $k$. | 64,788 | graphs = [
Graph(
let={
"a": Const(-8649),
"m": Const(73441),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.02 | 2026-02-08T07:02:31.251428Z | {
"verified": true,
"answer": 64788,
"timestamp": "2026-02-08T07:02:31.271847Z"
} | 314757 | 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": 3457
},
"timestamp": "2026-02-13T07:11:20.643Z",
"answer": 64788
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
1e26ec | antilemma_k3_v1_865884756_7098 | Let $n = 96710$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $c = 27053$. Compute the remainder when $c \cdot x$ is divided by $80280$. | 50,710 | graphs = [
Graph(
let={
"_n": Const(96710),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(27053),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(80280)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T19:37:20.684758Z | {
"verified": true,
"answer": 50710,
"timestamp": "2026-02-08T19:37:20.685460Z"
} | 5f36ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1754
},
"timestamp": "2026-02-18T22:52:09.712Z",
"answer": 50710
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
74ebc6 | lin_form_endings_v1_349078426_1306 | Let $a = 21$ and $b = 14$. Compute $\gcd(a, b)$, and let $k = 64$. Let $d = \gcd(k, \gcd(a, b))$. Define $s = \left\lfloor \frac{k}{d} \right\rfloor$. Multiply $s$ by $17284$, and let the result be $t$. Find the remainder when $t$ is divided by $50960$. | 36,016 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(14),
"k_val": Const(64),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(17... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:33:10.399536Z | {
"verified": true,
"answer": 36016,
"timestamp": "2026-02-08T13:33:10.400432Z"
} | c34de8 | 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": 867
},
"timestamp": "2026-02-15T17:52:33.456Z",
"answer": 36016
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
4ecd28 | modular_count_residue_v1_971394319_498 | Let $m = \sum_{k=1}^{4} k$ and $r = 5$. Compute the number of positive integers $n$ such that $1 \leq n \leq 48400$ and $n \equiv r \pmod{m}$. | 4,840 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(48400),
"m": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"r": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Va... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_count_residue_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 1.8 | 2026-02-08T13:07:50.465778Z | {
"verified": true,
"answer": 4840,
"timestamp": "2026-02-08T13:07:52.265872Z"
} | a32167 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 488
},
"timestamp": "2026-02-15T09:46:34.223Z",
"answer": 4840
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
c5d7ea | nt_count_coprime_v1_124444284_2670 | Let $n = 289$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $k$ be the minimum value of $x + y$ over all such pairs. Let $S$ be the set of all positive integers $m$ such that $1 \leq m \leq 11881$ and $\gcd(m, k) = 1$. Determine the number of elements in $S$. | 5,592 | graphs = [
Graph(
let={
"_n": Const(289),
"upper": Const(11881),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 3.666 | 2026-02-08T04:52:16.563298Z | {
"verified": true,
"answer": 5592,
"timestamp": "2026-02-08T04:52:20.229351Z"
} | 4e4f22 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 951
},
"timestamp": "2026-02-11T22:18:22.423Z",
"answer": 5592
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
740b9e | comb_count_derangements_v1_1440796553_853 | Let $n$ be the number of integers $t$ such that $20 \leq t \leq 38$ and there exist positive integers $a \leq 2$ and $b \leq 4$ for which $t = 6a + 4b + 10$.
Compute the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_derangements_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:01:25.899345Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T12:01:25.900231Z"
} | fc64c6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 930
},
"timestamp": "2026-02-24T15:07:44.495Z",
"answer": 14833
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
645d25_n | alg_qf_psd_orbit_v1_1419126231_1040 | On a coordinate grid, points $(a,b)$ are plotted where $a$ and $b$ are positive integers from $1$ to $168$, and $a \leq b$. A point is special if it satisfies $17a^2 - 16ab + 17b^2 = 235625$. How many such special points are there? | 5 | ALG | null | COUNT | sympy | V8 | [
"B3"
] | 0cd20d | alg_qf_psd_orbit_v1 | null | 5 | null | [
"B3",
"V8"
] | 2 | 2.551 | 2026-02-25T10:32:52.464507Z | null | 392f0d | 645d25 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T04:19:52.618Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
988e59 | nt_sum_divisors_mod_v1_1915831931_1249 | Let $n$ be the number of positive integers at most $4041$ that are divisible by $9$ and relatively prime to $10$. Let $M = 11717$. Compute the remainder when the sum of the positive divisors of $n$ is divided by $M$. | 546 | graphs = [
Graph(
let={
"_n": Const(10),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(4041)), Divides(divisor=Const(9), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Ref("_n")), Const(1))))),
"M": Const(11717)... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T15:58:04.779064Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T15:58:04.780664Z"
} | 9dceab | 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": 878
},
"timestamp": "2026-02-16T17:24:11.895Z",
"answer": 546
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
455da0 | nt_count_with_divisor_count_v1_1248542787_460 | Let $A$ be the number of positive integers $n \leq 65536$ that have exactly two positive divisors. Let $B$ be the number of unordered pairs of coprime positive integers $(p, q)$ with $p < q$ such that $pq = 2397137350007400$. Compute the remainder when $B - A$ is divided by $59048$. | 52,762 | graphs = [
Graph(
let={
"upper": Const(65536),
"div_count": Const(2),
"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"))))),
"_c": CountOverSet... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | c90628 | nt_count_with_divisor_count_v1 | negation_mod | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.947 | 2026-02-08T03:10:01.986598Z | {
"verified": true,
"answer": 52762,
"timestamp": "2026-02-08T03:10:04.933831Z"
} | b80e83 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 8716
},
"timestamp": "2026-02-23T17:11:23.766Z",
"answer": 52762
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
8717f5 | diophantine_fbi2_count_v1_1470522791_1334 | Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 720$. Let $T$ be the set of all positive integers $t$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 11$, and $t = 21a + 9b$, and such that $30 \leq t \leq 225$. Let $r$ be the number o... | 33,552 | graphs = [
Graph(
let={
"_n": Const(44121),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"COMB1"
] | 3d1461 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.014 | 2026-02-08T13:35:29.314511Z | {
"verified": true,
"answer": 33552,
"timestamp": "2026-02-08T13:35:29.328966Z"
} | eed80f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 3798
},
"timestamp": "2026-02-15T18:18:18.340Z",
"answer": 33552
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma":... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
92cbf6 | algebra_vieta_sum_v1_1978505735_917 | Let $r$ be the sum of all solutions $x$ to the equation $-x^2 + 10x - 21 = 0$. Let $c$ be the largest prime number $n$ such that $2 \leq n \leq 33$. Compute $r^2 + 36r + c$. | 491 | graphs = [
Graph(
let={
"_n": Const(2),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Const(-1), Pow(Var("x"), Const(2))), Mul(Const(10), Var("x")), Const(-21)), Const(0)))),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 65166f | algebra_vieta_sum_v1 | quadratic_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.007 | 2026-02-08T15:41:01.762876Z | {
"verified": true,
"answer": 491,
"timestamp": "2026-02-08T15:41:01.770070Z"
} | 1de027 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 370
},
"timestamp": "2026-02-16T06:16:11.882Z",
"answer": 491
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
904ae6 | diophantine_fbi2_min_v1_124444284_9660 | Let $k = 360$. Let the upper bound be the number of positive integers $j$ such that $1 \le j \le 370$ and $j^3 \le 50653000$. Let $d$ be a positive integer satisfying $2 \le d \le \text{upper}$, $d$ divides $k$, and $\frac{k}{d} \ge 3$. Determine the value of the smallest such $d$. Let $Q$ be the smallest positive inte... | 6 | graphs = [
Graph(
let={
"k": Const(360),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(370)), Leq(Pow(Var("j"), Const(3)), Const(50653000))), domain='positive_integers')),
"result": MinOverSet(set=Solutions... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"C3"
] | 8a214c | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"C3",
"COUNT_CARTESIAN"
] | 2 | 0.033 | 2026-02-08T12:36:53.330176Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T12:36:53.363060Z"
} | 2fd759 | 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": 918
},
"timestamp": "2026-02-15T02:42:11.762Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b5df9e | nt_sum_phi_v1_1918700295_306 | Let
$$U = \sum_{k=1}^{\sum_{k=1}^{7} \varphi(k)\left\lfloor\frac{7}{k}\right\rfloor} \varphi(k)\left\lfloor\frac{28}{k}\right\rfloor,$$
where $\varphi$ denotes Euler's totient function.
Let $T$ be the set of all integers $n$ such that $1 \le n \le U$. Define
$$R = \sum_{n \in T} \varphi(n).$$
Compute $R$. | 50,154 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": Const(28),
"upper": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(7), Var("k"))))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), ... | NT | null | SUM | sympy | B3 | [
"K2/K2"
] | ddede2 | nt_sum_phi_v1 | null | 8 | 0 | [
"B3",
"K2"
] | 2 | 0.352 | 2026-02-08T03:09:24.412757Z | {
"verified": true,
"answer": 50154,
"timestamp": "2026-02-08T03:09:24.764657Z"
} | 29fcf1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 15939
},
"timestamp": "2026-02-23T16:55:17.819Z",
"answer": 50166
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 3.78,
"mid": 6.08,
"hi": 9.16
} | ||
35ce6b | comb_bell_compute_v1_809748730_435 | Let $n$ be the number of positive integers less than 30 that are relatively prime to 30. Define $B_n$ to be the $n$-th Bell number, which counts the number of partitions of a set of size $n$. Let $S$ be the sum of the squares of the positions (starting from 1) of each digit in the decimal representation of $|B_n|$, wei... | 585 | graphs = [
Graph(
let={
"_n": Const(30),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(29)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"result": Bell(Ref("n")),
"Q": Sum(Summation(var="i", star... | NT | COMB | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | comb_bell_compute_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.002 | 2026-02-08T11:30:58.115140Z | {
"verified": true,
"answer": 585,
"timestamp": "2026-02-08T11:30:58.117057Z"
} | 5733cf | 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": 684
},
"timestamp": "2026-02-14T15:29:46.372Z",
"answer": 585
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d74497 | nt_lcm_compute_v1_1439011603_754 | Let $a$ be the number of positive integers $n$ such that $n \le 1633$ and $\gcd(n, 6) = 1$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 986049$, and let $b$ be the minimum value of $x + y$ over all such pairs. Define $L = \mathrm{lcm}(a, b)$. Find the remainder when $L$ is divi... | 52,119 | graphs = [
Graph(
let={
"_m": Const(1633),
"_n": Const(60603),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
"b": MinOverSet(set=MapOverSet(set=So... | NT | null | COMPUTE | sympy | B3 | [
"B3",
"C4"
] | 8d18b3 | nt_lcm_compute_v1 | null | 6 | 0 | [
"B3",
"C4"
] | 2 | 0.004 | 2026-02-08T15:41:53.218486Z | {
"verified": true,
"answer": 52119,
"timestamp": "2026-02-08T15:41:53.222732Z"
} | dbb1fd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 5384
},
"timestamp": "2026-02-16T11:12:12.742Z",
"answer": 52119
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f2b018 | antilemma_k2_v1_153355830_278 | Compute
$$
\sum_{k=1}^{221} \phi(k) \left\lfloor \frac{221}{k} \right\rfloor,
$$
and denote this value by $x$. Let $d_i$ be the $i$-th decimal digit of $|x|$, where $i = 0$ corresponds to the units digit. Let $\ell$ be the number of digits in $|x|$. Compute
$$
\sum_{i=0}^{\ell-1} d_i (i+1)^2 + 4900.
$$ | 5,072 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(221), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(221), Var("k"))))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=R... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T03:00:14.405128Z | {
"verified": true,
"answer": 5072,
"timestamp": "2026-02-08T03:00:14.405834Z"
} | b87df6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 683
},
"timestamp": "2026-02-10T12:26:19.180Z",
"answer": 5072
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -1.87,
"mid": 0.73,
"hi": 2.96
} | ||
eb98ca | nt_count_coprime_v1_2051736721_3869 | Let $m = 225$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 562500$. Let $d$ be the minimum value of $x_1 + y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = m$. Let $k$ be the number of positive integers $n$ such that $1 \... | 23,329 | graphs = [
Graph(
let={
"_m": Const(225),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(562500)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | nt_count_coprime_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 2.294 | 2026-02-08T17:36:33.245735Z | {
"verified": true,
"answer": 23329,
"timestamp": "2026-02-08T17:36:35.539307Z"
} | 9a6c13 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 2004
},
"timestamp": "2026-02-18T04:31:42.089Z",
"answer": 23329
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
18d74d | nt_count_gcd_equals_v1_1431428450_176 | Let $S$ be the set of all nonnegative integers $j$ such that $0 \le j \le 31231$ and $\binom{31231}{j}$ is odd. Let $u$ be the number of elements in $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 13689$. Let $k$ be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Fin... | 210 | graphs = [
Graph(
let={
"_n": Const(31231),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(31231), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | COUNT | sympy | V8 | [
"V8",
"B3"
] | 5b3848 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"V8"
] | 2 | 0.663 | 2026-02-08T13:17:17.155905Z | {
"verified": true,
"answer": 210,
"timestamp": "2026-02-08T13:17:17.818858Z"
} | e8530f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 3051
},
"timestamp": "2026-02-15T12:04:15.801Z",
"answer": 210
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1c6749 | antilemma_k2_v1_1520064083_3934 | Let $n = 51995$. Define
$$
x = \sum_{k=1}^{351} \varphi(k) \left\lfloor \frac{\sum_{k=1}^{26} k}{k} \right\rfloor.
$$
Compute the remainder when $55934 \cdot x$ is divided by $n$. | 51,059 | graphs = [
Graph(
let={
"_n": Const(51995),
"x": Summation(var="k", start=Const(1), end=Const(351), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=Const(26), expr=Var("k")), Var("k"))))),
"Q": Mod(value=Mul(Const(55934), Ref("x")), modulus... | NT | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2",
"K2"
] | ec0b42 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.001 | 2026-02-08T05:59:20.761335Z | {
"verified": true,
"answer": 51059,
"timestamp": "2026-02-08T05:59:20.762222Z"
} | e590de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 1353
},
"timestamp": "2026-02-12T17:55:46.380Z",
"answer": 51059
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"sta... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
631d63 | modular_mod_compute_v1_458359167_3797 | Let $a = 4181$. Let $m$ be the number of integers $t$ such that $9 \leq t \leq 7589$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 586$, $1 \leq b \leq 1049$, and $t = 4a + 5b$. Compute the remainder when $a$ is divided by $m$. | 4,181 | graphs = [
Graph(
let={
"a": Const(4181),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=586)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T11:22:35.485134Z | {
"verified": true,
"answer": 4181,
"timestamp": "2026-02-08T11:22:35.487741Z"
} | bb1028 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 6104
},
"timestamp": "2026-02-14T12:46:41.669Z",
"answer": 4181
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1dd138 | comb_count_surjections_v1_1125832087_1044 | Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 10$. Let $k$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 4$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ is the number of ways to partition a set of $n$ elem... | 30 | graphs = [
Graph(
let={
"_n": Const(4),
"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")), Con... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T03:29:16.214649Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T03:29:16.218113Z"
} | 759a39 | 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": 885
},
"timestamp": "2026-02-10T14:30:36.091Z",
"answer": 30
},
{
"id":... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
4f1516 | nt_sum_divisors_mod_v1_1520064083_9399 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 396900$. For each such pair, compute $x + y$, and let $n$ be the smallest value of $x + y$ over all such pairs. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $11083... | 36,141 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11083... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.012 | 2026-02-08T10:43:18.542852Z | {
"verified": true,
"answer": 36141,
"timestamp": "2026-02-08T10:43:18.554471Z"
} | 1b9ce8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 4640
},
"timestamp": "2026-02-14T08:15:28.787Z",
"answer": 36141
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dcb0a4 | modular_mod_compute_v1_1125832087_2199 | Let $m$ be the number of integers $t$ such that $8 \le t \le 4504$ and there exist positive integers $a \le 506$ and $b \le 658$ satisfying $t = 5a + 3b$. Let $r$ be the remainder when $7$ is divided by $m$. Compute the remainder when $66371 \cdot r$ is divided by $74508$. | 17,549 | graphs = [
Graph(
let={
"a": Const(7),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=506)), Geq(left=Var(n... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:24:08.250119Z | {
"verified": true,
"answer": 17549,
"timestamp": "2026-02-08T04:24:08.252189Z"
} | e422ed | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 2125
},
"timestamp": "2026-02-10T16:43:42.512Z",
"answer": 17549
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
bba262_n | modular_sum_quadratic_residues_v1_601307018_4397 | A botanist observes that a certain plant species produces a number of seeds in month $n$ equal to the $n$-th Fibonacci number $F_n$. She records a 'bloom event' whenever the seed count is divisible by $14$. Over the first $12984$ months, she counts $p$ such bloom events. She then calculates the number of unique pairs o... | 73,035 | NT | null | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | modular_sum_quadratic_residues_v1 | null | 5 | null | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.003 | 2026-03-10T04:57:28.847174Z | null | 345d4d | bba262 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 3389
},
"timestamp": "2026-03-29T18:40:37.770Z",
"answer": 73035
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
... | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
080cc2 | modular_sum_quadratic_residues_v1_1978505735_4236 | Let $p = 109$. Let $s$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 2809$. Let $t$ be the minimum value of $x + y$ as $(x, y)$ ranges over $s$. Let $u$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = t$. Let $v$ be the maximum value of $x \cdot y$... | 76,466 | graphs = [
Graph(
let={
"_n": Const(4),
"p": Const(109),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(... | NT | null | SUM | sympy | B3 | [
"B3/B1"
] | 6cdf3d | modular_sum_quadratic_residues_v1 | negation_mod | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.006 | 2026-02-08T18:05:07.319528Z | {
"verified": true,
"answer": 76466,
"timestamp": "2026-02-08T18:05:07.325046Z"
} | f4401c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 869
},
"timestamp": "2026-02-18T13:51:39.731Z",
"answer": 76466
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7a53b4 | comb_sum_binomial_row_v1_1218484723_5688 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 20$ such that $32a^2 + 32b^2 - 64ab = 800$. Compute $59049 - 2^n$. | 26,281 | graphs = [
Graph(
let={
"_n": Const(20),
"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(20)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(32), Pow... | COMB | null | SUM | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.002 | 2026-02-25T07:12:43.433822Z | {
"verified": true,
"answer": 26281,
"timestamp": "2026-02-25T07:12:43.435566Z"
} | 91690c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 681
},
"timestamp": "2026-03-29T22:18:11.368Z",
"answer": 26281
},
{
"i... | 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": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
cfea4c | nt_count_divisible_and_v1_2051736721_2449 | Let $d_2$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 11$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 57540$, $n$ is divisible by $12$, and the remainder when $n$ is divided by $d_2$ is $\sum_{k=0}^{1} (-1)^k \binom{1}{k}$. Comput... | 959 | graphs = [
Graph(
let={
"_n": Const(11),
"upper": Const(57540),
"d1": Const(12),
"d2": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | e741ba | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 2.143 | 2026-02-08T16:41:03.329056Z | {
"verified": true,
"answer": 959,
"timestamp": "2026-02-08T16:41:05.472006Z"
} | 342e0e | 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": 711
},
"timestamp": "2026-02-17T10:27:58.536Z",
"answer": 959
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
c76122 | sequence_count_fib_divisible_v1_168721529_1962 | Let $d$ be the smallest divisor of $2458739$ that is at least $2$. Let $S$ be the set of all positive integers $n \leq d$ such that $8$ divides $F_n$, where $F_n$ denotes the $n$-th Fibonacci number. Compute $\sum_{k=1}^{|S|} \tau(k)$, where $\tau(k)$ denotes the number of positive divisors of $k$. | 70 | graphs = [
Graph(
let={
"upper": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2458739))))),
"d": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.011 | 2026-02-08T14:02:09.374314Z | {
"verified": true,
"answer": 70,
"timestamp": "2026-02-08T14:02:09.385487Z"
} | 1132e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 2449
},
"timestamp": "2026-02-15T23:03:53.778Z",
"answer": 70
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
129332 | modular_mod_compute_v1_153355830_1677 | Let $ a = 3249 $. Let $ S $ be the set of all ordered pairs of positive odd integers $ (x_1, x_2) $ such that $ x_1 + x_2 = 11858 $. Let $ m $ be the number of elements in $ S $. Define $ r $ to be the remainder when $ a $ is divided by $ m $. Let $ Q $ be the remainder when $ 44121 \cdot r $ is divided by 95246. Deter... | 3,899 | graphs = [
Graph(
let={
"_n": Const(95246),
"a": Const(3249),
"m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')),... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_mod_compute_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T06:33:13.995471Z | {
"verified": true,
"answer": 3899,
"timestamp": "2026-02-08T06:33:13.997432Z"
} | 5c37c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 912
},
"timestamp": "2026-02-13T01:45:08.266Z",
"answer": 3899
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
203e81_l | comb_factorial_compute_v1_124444284_2460 | Define
\[s = \sum_{k=A}^{2} (-1)^k \binom{2}{k},\]
where
\[A = \sum_{k=0}^{8} (-1)^k \binom{8}{k}.\]
Define
\[t = \sum_{k=0}^{0} (-1)^k \binom{0}{k}.\]
Let $N_0$ be the number of integers $t'$ for which there exist integers $a$ and $b$ satisfying
\[1 \le a \le 2, \quad 1 \le b \le 4, \quad 15 \le t' \le 42, \quad t' =... | 0 | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING",
"ONE_BINOM_0"
] | 9959fb | comb_factorial_compute_v1 | null | 8 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM",
"ONE_BINOM_0"
] | 3 | 2.64 | 2026-02-08T04:42:03.088842Z | {
"verified": false,
"answer": 19378,
"timestamp": "2026-02-08T04:42:05.728579Z"
} | ff593d | 203e81 | legacy_text | CC BY 4.0 | [
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028f7f | comb_bell_compute_v1_865884756_6699 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 1260$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. Determine the rema... | 27,666 | graphs = [
Graph(
let={
"_n": Const(98001),
"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=1260)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T19:21:22.358056Z | {
"verified": true,
"answer": 27666,
"timestamp": "2026-02-08T19:21:22.360142Z"
} | ec51a0 | CC BY 4.0 | [
{
"id": 5,
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"score": 3,
"correct": {
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"usage": {
"prompt_tokens": 160,
"completion_tokens": 2918
},
"timestamp": "2026-02-18T22:03:59.541Z",
"answer": 27666
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
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{
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"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
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} | ||
d8f3be | alg_qf_psd_sum_v1_1218484723_3068 | Find the remainder when
$$
\sum_{a=1}^{13} \sum_{b=1}^{13} \sum_{c=1}^{13} \sum_{d=1}^{13} \left( 7a^2 + 24bc -14ac + 61b^2 + 18cd -26ad + 57c^2 -26bd -2ab + \sum_{k=1}^7 k \cdot d^2 \right)
$$
is divided by $87272$. | 49,301 | graphs = [
Graph(
let={
"_n": Const(13),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(13)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Ge... | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | alg_qf_psd_sum_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.101 | 2026-02-25T04:49:19.449384Z | {
"verified": true,
"answer": 49301,
"timestamp": "2026-02-25T04:49:19.550603Z"
} | 3f49af | CC BY 4.0 | [
{
"id": 1,
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"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 2370
},
"timestamp": "2026-03-29T08:09:45.999Z",
"answer": 49301
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
4f2520 | nt_count_divisible_v1_1520064083_9469 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 80656$ and $n$ is congruent modulo $2$ to $\sum_{k=0}^{1} (-1)^k \binom{1}{k}$. Compute the number of elements in $S$. | 40,328 | graphs = [
Graph(
let={
"upper": Const(80656),
"divisor": Const(2),
"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")), Summation(var="k", start=Const(0),... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_v1 | null | 2 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 4.221 | 2026-02-08T10:46:49.316579Z | {
"verified": true,
"answer": 40328,
"timestamp": "2026-02-08T10:46:53.537670Z"
} | 390b63 | CC BY 4.0 | [
{
"id": 1,
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"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 605
},
"timestamp": "2026-02-24T12:18:40.521Z",
"answer": 40328
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
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},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
7110fe | algebra_poly_eval_v1_898971024_2227 | Let $a$ be the smallest divisor of $667$ that is greater than $1$. Compute the value of $$\frac{2a^3 - 7a^2 - 5a + c}{41},$$ where $c$ is the number of integers $t$ such that $11 \leq t \leq 43$ and there exist positive integers $a' \leq 5$, $b' \leq 5$ satisfying $t = 3a' + 5b' + 3$. | 501 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(667))))),
"result": Div(Sum(Mul(Ref("_n"), Pow(Ref("a"), Const(3))), Mul(Cons... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | algebra_poly_eval_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T16:36:42.269830Z | {
"verified": true,
"answer": 501,
"timestamp": "2026-02-08T16:36:42.275215Z"
} | 8143d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
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"completion_tokens": 2690
},
"timestamp": "2026-02-17T07:51:18.449Z",
"answer": 501
},
{
... | 1 | [
{
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{
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},
{
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{
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"status": "no"
},
{
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"status": "ok"
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{
"lemma": "MOD_MUL",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9568d2 | comb_count_derangements_v1_1470522791_704 | Let $T$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 2$, $1 \leq b \leq 5$, $5 \leq t \leq 16$, and $t = 3a + 2b$. Let $\_n$ be the number of elements in $T$. Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p... | 1,854 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"LIN_FORM/MAX_PRIME_BELOW"
] | d6bd1c | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.01 | 2026-02-08T13:12:16.056901Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T13:12:16.067241Z"
} | ebb234 | 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": 2033
},
"timestamp": "2026-02-15T10:29:14.781Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
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},
{
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},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"l... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3800a0 | diophantine_fbi2_count_v1_458359167_5757 | Let $m = 69$. Let $A$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq 8193$ and $\binom{8193}{j}$ is odd. Let $n$ be the number of elements in $A$. Let $k = 240$. Let $B$ be the set of all positive integers $d$ such that $n \leq d \leq m$, $d$ divides $k$, $\frac{k}{d} \geq 3$, and $\frac{k}{d} \leq... | 14 | graphs = [
Graph(
let={
"_m": Const(69),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(8193)), Eq(Mod(value=Binom(n=Const(8193), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"k"... | NT | null | COUNT | sympy | C2 | [
"B3/B3",
"V8/B3"
] | afea9a | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"C2",
"V8"
] | 3 | 0.425 | 2026-02-08T12:40:52.895767Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T12:40:53.321086Z"
} | 176e16 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 2107
},
"timestamp": "2026-02-15T03:55:33.222Z",
"answer": 14
},
{
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{
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{
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"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
038d9b | nt_min_phi_inverse_v1_50713871_77 | Let $n = 606$. Let $\text{result}$ be the smallest positive integer $k$ such that $1 \leq k \leq 10$ and $\phi(k) = 1$, where $\phi$ is Euler's totient function. Let $Q = v_2(n!) - \text{result}$, where $v_2(n!)$ denotes the largest power of 2 that divides $n!$.
Find the value of $Q$. | 599 | graphs = [
Graph(
let={
"_n": Const(606),
"upper": Const(10),
"k": Const(1),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"Q": Sub(Max... | NT | null | EXTREMUM | sympy | V1 | [
"V1"
] | 574795 | nt_min_phi_inverse_v1 | negation_mod | 4 | 0 | [
"V1"
] | 1 | 0.003 | 2026-02-08T02:44:23.819344Z | {
"verified": true,
"answer": 599,
"timestamp": "2026-02-08T02:44:23.822495Z"
} | cf6775 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 716
},
"timestamp": "2026-02-08T19:47:29.965Z",
"answer": 599
},
{
"id"... | 1 | [
{
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{
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{
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{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
a7919c | nt_count_divisors_in_range_v1_1915831931_3771 | Let $n = 166320$. Let $a$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 8$ and $1 \leq j \leq 9$. Let $b = 41584$. Define $D$ to be the set of all positive divisors $d$ of $n$ such that $a \leq d \leq b$. Compute the number of elements in $D$. \n\nFind this number. | 119 | graphs = [
Graph(
let={
"n": Const(166320),
"a": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(9)))),
"b": Const(41584),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), con... | NT | null | COUNT | sympy | C4 | [
"COUNT_CARTESIAN"
] | 409d7d | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"C4",
"COUNT_CARTESIAN"
] | 2 | 0.447 | 2026-02-08T17:54:19.741174Z | {
"verified": true,
"answer": 119,
"timestamp": "2026-02-08T17:54:20.188506Z"
} | 95559d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 3430
},
"timestamp": "2026-02-18T09:30:25.123Z",
"answer": 119
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "DS2",
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},
{
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{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b50112 | modular_product_range_v1_1520064083_346 | Let $m = 12$. Define $S$ as the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 12168$. Let $n$ be the number of elements in $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $s$ be the minimum value of $x + y$ as $(x, y)$ ranges ove... | 3,283 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), C... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1/B3"
] | 014cfb | modular_product_range_v1 | null | 5 | 0 | [
"B3",
"COMB1"
] | 2 | 0.005 | 2026-02-08T03:16:54.116621Z | {
"verified": true,
"answer": 3283,
"timestamp": "2026-02-08T03:16:54.121542Z"
} | bd090b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 13455
},
"timestamp": "2026-02-23T18:04:56.031Z",
"answer": 3283
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
b14ac4 | antilemma_cartesian_v1_1125832087_1928 | Compute the number of ordered pairs $(a, b)$ such that $1 \le a \le 17$ and $1 \le b \le 23$. | 391 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Const(23)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:14:47.010799Z | {
"verified": true,
"answer": 391,
"timestamp": "2026-02-08T04:14:47.011340Z"
} | ff6b8a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 115
},
"timestamp": "2026-02-23T23:51:56.480Z",
"answer": 391
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
39cea3 | nt_gcd_compute_v1_1742523217_2527 | Let $a = 184485$ and $b = 342615$. Define $d = \gcd(a, b)$. Let $r$ be the remainder when $|d|$ is divided by $11$, and let $B_r$ denote the $r$-th Bell number. Compute the remainder when $B_r$ is divided by $55849$. | 4,277 | graphs = [
Graph(
let={
"a": Const(184485),
"b": Const(342615),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))), modulus=Const(55849)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | nt_gcd_compute_v1 | bell_mod | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.012 | 2026-02-08T04:50:05.923683Z | {
"verified": true,
"answer": 4277,
"timestamp": "2026-02-08T04:50:05.935330Z"
} | d8514d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 591
},
"timestamp": "2026-02-11T22:05:47.099Z",
"answer": 4277
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
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},
{
"lemma": "K18",
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},
{
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},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
834313 | comb_count_surjections_v1_1439011603_1027 | Let $n = 6$ and $k = 2$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ is the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets. Let $T$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $m$ be the number of elements in... | 877 | graphs = [
Graph(
let={
"_n": Const(22),
"n": Const(6),
"k": Const(2),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Tuple... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | d93ba8 | comb_count_surjections_v1 | bell_mod | 5 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T15:52:41.322501Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T15:52:41.325482Z"
} | 75a70e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 787
},
"timestamp": "2026-02-24T18:53:44.413Z",
"answer": 877
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
3dd6cd | alg_poly3_min_v1_601307018_2875 | Let $A = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 30,\ 13a_1^2 - 2a_1b_1 + 2b_1^2 \leq 1373 \}\right|$ and $B = \left|\{ t : t = 21a + 6b\ \text{for some}\ 1 \leq a \leq 56,\ 1 \leq b \leq 33,\ 27 \leq t \leq 1374 \}\right|$. Find the remainder when $$\min_{\substack{1 \leq a, b, c \leq 57}} \left( -92a^3 + 336b c^2 ... | 33,452 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(57)), Geq(Var("b"), Const(1)), Leq(Var("b"... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"LIN_FORM"
] | 74f7c5 | alg_poly3_min_v1 | null | 6 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.672 | 2026-03-10T03:29:53.884904Z | {
"verified": true,
"answer": 33452,
"timestamp": "2026-03-10T03:29:54.556985Z"
} | 584fb6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 351,
"completion_tokens": 9046
},
"timestamp": "2026-03-29T06:48:34.711Z",
"answer": 33452
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
f355f4 | nt_sum_totient_over_divisors_v1_865884756_1898 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 19731364$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 8,884 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(19731364)))), expr=Sum(Var("x"), Var("y")))),
"result": SumO... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T16:22:10.946927Z | {
"verified": true,
"answer": 8884,
"timestamp": "2026-02-08T16:22:10.950353Z"
} | 0553db | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 1397
},
"timestamp": "2026-02-17T01:53:56.638Z",
"answer": 8884
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
48857a | comb_count_permutations_fixed_v1_349078426_1063 | Let $n = 6$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Define $c = 56266$ and let $Q$ be the remainder when $c \cdot \binom{n}{k} \cdot !{(n - k)}$ is divided by $57139$. Find the value of $Q$. | 53,562 | graphs = [
Graph(
let={
"n": Const(6),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=12)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T13:23:34.966067Z | {
"verified": true,
"answer": 53562,
"timestamp": "2026-02-08T13:23:34.970389Z"
} | a96ba6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1885
},
"timestamp": "2026-02-15T14:33:28.488Z",
"answer": 53562
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
721239 | nt_count_intersection_v1_151522320_1372 | Let $a$ be the largest prime number less than or equal to $\sum_{k=1}^{3} k$. Determine the number of positive integers $n$ such that $1 \leq n \leq 20000$, $a$ divides $n$, and $\gcd(n, 6) = 1$. | 1,333 | graphs = [
Graph(
let={
"_n": Const(3),
"N": Const(20000),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k"))), IsPrime(Var("n"))))),
"b": Const(6... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/MAX_PRIME_BELOW"
] | bde608 | nt_count_intersection_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.989 | 2026-02-08T03:55:14.052943Z | {
"verified": true,
"answer": 1333,
"timestamp": "2026-02-08T03:55:15.042208Z"
} | 8c7520 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 759
},
"timestamp": "2026-02-10T16:21:04.306Z",
"answer": 1333
},
{
"id... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
0657b7 | diophantine_product_count_v1_1520064083_441 | Let $k = 360$ and $u = 309$. Let $S$ be the set of all integers $x$ such that $x \geq \sum_{d\mid \gcd(9,14)} \mu(d)$, $x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Compute the number of elements in $S$. | 22 | graphs = [
Graph(
let={
"k": Const(360),
"upper": Const(309),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), SumOverDivisors(n=GCD(a=Const(value=9), b=Const(value=14)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("x"), Ref("upper... | NT | null | COUNT | sympy | B3 | [
"MOBIUS_COPRIME"
] | ac54ac | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 2.814 | 2026-02-08T03:21:30.214591Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T03:21:33.028216Z"
} | f8bff3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 800
},
"timestamp": "2026-02-18T00:19:28.901Z",
"answer": 22
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
}
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
d32d64 | comb_count_derangements_v1_124444284_8135 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 185220$, and $\gcd(p, q) = 1$. Let $n$ be the number of elements in $S$. Let $D_n$ denote the number of derangements of $n$ elements. Compute the remainder when $89433 \cdot D_n$ is divided by $67910$. | 5,749 | graphs = [
Graph(
let={
"_n": Const(67910),
"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=185220)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T09:34:34.108680Z | {
"verified": true,
"answer": 5749,
"timestamp": "2026-02-08T09:34:34.109949Z"
} | 21378c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 3263
},
"timestamp": "2026-02-14T04:50:56.093Z",
"answer": 5749
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} |
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