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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ff4bc4 | diophantine_sum_product_min_v1_1742523217_5330 | Let $A$ be the set of all pairs of positive integers $(p, q)$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of such pairs. Let $B$ be the set of all prime numbers $n$ such that $m \leq n \leq 79$. Define $N$ to be the number of elements in $B$. Let $S = 23$. Let $P$ be the number of ... | 4 | graphs = [
Graph(
let={
"_m": Const(79),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COUNT_PRIMES/LIN_FORM"
] | 87b6ce | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"COUNT_PRIMES",
"LIN_FORM"
] | 3 | 0.008 | 2026-02-08T10:55:28.281073Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T10:55:28.289075Z"
} | 25edf5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 3886
},
"timestamp": "2026-02-14T09:39:50.440Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3e8805 | nt_sum_divisors_compute_v1_1978505735_4437 | Let $n = 23005$. Compute the sum of all positive divisors of $n$. | 28,512 | graphs = [
Graph(
let={
"n": Const(23005),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MOBIUS_SQUAREFREE | [
"MOBIUS_SQUAREFREE"
] | 6fcd31 | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"MOBIUS_SQUAREFREE"
] | 1 | 0.003 | 2026-02-08T18:14:42.121207Z | {
"verified": true,
"answer": 28512,
"timestamp": "2026-02-08T18:14:42.123799Z"
} | 4d7da3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 66,
"completion_tokens": 1335
},
"timestamp": "2026-02-18T15:34:35.044Z",
"answer": 28512
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cd75f1 | nt_min_coprime_above_v1_865884756_4307 | Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = 396900$. Let $r$ be the smallest integer $n$ such that $s < n \leq 1731$ and $\gcd(n, 461) = 1$. Compute $r$. | 1,261 | graphs = [
Graph(
let={
"start": 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")))),
"upper": Con... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.067 | 2026-02-08T17:53:05.478200Z | {
"verified": true,
"answer": 1261,
"timestamp": "2026-02-08T17:53:05.545156Z"
} | b6564c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 902
},
"timestamp": "2026-02-18T09:04:25.654Z",
"answer": 1261
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fead14 | geo_count_lattice_rect_v1_677425708_517 | Compute the number of lattice points in the rectangle $[0, 225] \times [0, 293]$. | 66,444 | graphs = [
Graph(
let={
"a": Const(225),
"b": Const(293),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T03:35:15.789143Z | {
"verified": true,
"answer": 66444,
"timestamp": "2026-02-08T03:35:15.789876Z"
} | 493f5d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 318
},
"timestamp": "2026-02-08T20:41:41.214Z",
"answer": 66444
},
{
"i... | 1 | [] | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||||
174b75 | comb_factorial_compute_v1_601307018_9249 | Let $n$ be the minimum value of $37a^3 - 15a^2b - 33ab^2 + 19b^3$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 14$. Let $M = n!$. Find the remainder when $44121M$ is divided by $65491$. | 26,687 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(14)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(14)))), expr=Sum(Mul(Const(-33), Var("a"), P... | COMB | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | comb_factorial_compute_v1 | null | 4 | 0 | [
"POLY3_MIN"
] | 1 | 0.002 | 2026-03-10T09:38:13.587350Z | {
"verified": true,
"answer": 26687,
"timestamp": "2026-03-10T09:38:13.589354Z"
} | d851ad | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 3116
},
"timestamp": "2026-04-19T10:56:31.724Z",
"answer": 26687
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "n... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
547f8b | modular_sum_quadratic_residues_v1_1742523217_1231 | Let $A$ be the set of positive integers $n$ such that $1 \leq n \leq 238$ and $n \equiv 0 \pmod{119}$. Let $N$ be the sum of all elements in $A$. Let $p$ be the largest prime number satisfying $2 \leq p \leq N$. Compute $\frac{p(p-1)}{4}$. | 31,064 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(238)), Eq(Mod(value=Var("n"), modulus=Cons... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"SUM_DIVISIBLE/MAX_PRIME_BELOW"
] | caf344 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 3 | 0.003 | 2026-02-08T03:34:21.322229Z | {
"verified": true,
"answer": 31064,
"timestamp": "2026-02-08T03:34:21.325631Z"
} | 4fcb69 | 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": 707
},
"timestamp": "2026-02-10T05:23:58.983Z",
"answer": 31064
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status":... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
8618f7 | antilemma_sum_equals_v1_1918700295_2612 | Let $m = 126$ and let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = m$. Let $x$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 62$ and $1 \le j \le 63$ such that $i + j = n$. Compute the value of $$\sum_{k=\binom{15}{0}}^{|x|} \phi(k),$$ where $\phi$ denotes ... | 1,192 | graphs = [
Graph(
let={
"_m": Const(126),
"_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")), ... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 862178 | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 3 | 0.013 | 2026-02-08T08:08:03.352046Z | {
"verified": true,
"answer": 1192,
"timestamp": "2026-02-08T08:08:03.365369Z"
} | 1ca78c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 3859
},
"timestamp": "2026-02-24T08:51:38.186Z",
"answer": 1192
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
1b1c60 | nt_num_divisors_compute_v1_784195855_3790 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 109999$ and
$$
k \equiv \left\lfloor \frac{k}{2} \right\rfloor \pmod{11}.
$$
Determine the value of the number of positive divisors of $n$. | 12 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(109999)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
"result": NumDivisors(n=Re... | NT | null | COMPUTE | sympy | K2 | [
"L3C"
] | 73f8b0 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"K2",
"L3C"
] | 2 | 0.011 | 2026-02-08T06:38:58.932488Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T06:38:58.943529Z"
} | 9a632b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1023
},
"timestamp": "2026-02-13T02:49:03.124Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
84d323 | alg_poly4_count_v1_1218484723_6574 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ with $1 \leq a_1, b_1 \leq 20$ such that $$16a_1b_1 + 17b_1^2 + 25a_1^2 = v$$ for some integer $v$ in $[58, 1450]$. Let $T = |S|$. Define $U$ to be the number of ordered pairs $(a_1, b_1)$ with $1 \leq a_1 \leq 20$, $1 \leq b_1 \leq 20$, satisfying $$T b_1^2 + 10a_1^2 - ... | 10 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(20),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(253)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSe... | ALG | null | COUNT | sympy | SUM_SQUARES_IDENTITY | [
"QF_PSD_DISTINCT/QF_PSD_COUNT_LEQ"
] | b3c180 | alg_poly4_count_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT",
"SUM_SQUARES_IDENTITY"
] | 3 | 5.041 | 2026-02-25T08:07:26.642228Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-25T08:07:31.682844Z"
} | b2a56d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 369,
"completion_tokens": 8948
},
"timestamp": "2026-03-30T02:15:34.477Z",
"answer": 10
},
{
"id"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
9af8b2 | modular_modexp_compute_v1_397696148_1507 | Let $a = 19$. Let $e$ be the number of positive integers $j$ such that $1 \le j \le 9999$ and $j^2 \le 99980001$. Compute the remainder when $a^e$ is divided by $90000$. | 61,579 | graphs = [
Graph(
let={
"_n": Const(9999),
"a": Const(19),
"e": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(2)), Const(99980001))), domain='positive_integers')),
"m": Cons... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | modular_modexp_compute_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T12:35:45.665061Z | {
"verified": true,
"answer": 61579,
"timestamp": "2026-02-08T12:35:45.666189Z"
} | 3e0d28 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 2551
},
"timestamp": "2026-02-15T03:05:01.891Z",
"answer": 61579
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d970da | diophantine_fbi2_min_v1_784195855_9126 | Let $k$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 8$ and $1 \leq j \leq 12$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Find the smallest integer $d$ such that $6 \leq d \leq 106$, $d$ divides $k$, and $\frac{k}{d} \geq s$. | 6 | graphs = [
Graph(
let={
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(12)))),
"upper": Const(106),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(... | NT | null | EXTREMUM | sympy | B3 | [
"COUNT_CARTESIAN",
"B3"
] | 0ad34f | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B3",
"COUNT_CARTESIAN"
] | 2 | 0.021 | 2026-02-08T16:33:23.723669Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T16:33:23.744821Z"
} | 6687db | 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": 741
},
"timestamp": "2026-02-17T07:26:28.894Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cb82d6 | antilemma_k3_v1_784195855_2781 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $81740$, where $\phi$ denotes Euler's totient function. | 81,740 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=81740), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T06:02:51.852039Z | {
"verified": true,
"answer": 81740,
"timestamp": "2026-02-08T06:02:51.852375Z"
} | 6b3261 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 866
},
"timestamp": "2026-02-12T18:45:18.430Z",
"answer": 81740
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
53e155 | nt_count_coprime_v1_809748730_354 | Let $k$ be the smallest integer greater than $1$ that divides $146969$. Determine the number of positive integers $n \leq 61776$ such that $\gcd(n, k) = 1$. Let this number be $A$.
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Let $B$ be the minimum value of $x + y$ ove... | 22,166 | graphs = [
Graph(
let={
"upper": Const(61776),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(146969))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Con... | NT | null | COUNT | sympy | B3 | [
"B3",
"MIN_PRIME_FACTOR"
] | 58c683 | nt_count_coprime_v1 | negation_mod | 6 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 4.709 | 2026-02-08T11:29:09.183880Z | {
"verified": true,
"answer": 22166,
"timestamp": "2026-02-08T11:29:13.893318Z"
} | 13ed66 | 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": 1549
},
"timestamp": "2026-02-14T14:55:24.630Z",
"answer": 22166
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"le... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7a1ef3 | nt_count_gcd_equals_v1_784195855_10062 | Let $n = 90$. Let $U$ be the number of positive integers $k$ such that $1 \leq k \leq 696960$ and $n$ divides $k$. Let $d = 1$ and $k = 359$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq U$ and $\gcd(n, k) = d$. Let $t = |S|$. Compute $t + \phi(t+1) + \tau(t+1)$, where $\phi$ denotes Euler's... | 11,589 | graphs = [
Graph(
let={
"_n": Const(90),
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(696960)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"k": Const(359),
"d... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"C2"
] | 1 | 1.148 | 2026-02-08T17:25:06.961924Z | {
"verified": true,
"answer": 11589,
"timestamp": "2026-02-08T17:25:08.109765Z"
} | 32eaeb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1724
},
"timestamp": "2026-02-18T01:46:26.913Z",
"answer": 11589
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eadee1 | nt_lcm_compute_v1_124444284_3053 | Let $n$ be a positive integer such that $1 \leq n \leq 14096$, $8$ divides $n$, and $\gcd(n, 21) = 1$. Let $b$ denote the number of such integers $n$. Let $a = 508$. Define $c = \text{lcm}(a, b)$. Compute the remainder when $44 - c$ is divided by $54619$. | 34,678 | graphs = [
Graph(
let={
"_n": Const(14096),
"a": Const(508),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(8), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | nt_lcm_compute_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.003 | 2026-02-08T05:10:26.509901Z | {
"verified": true,
"answer": 34678,
"timestamp": "2026-02-08T05:10:26.512434Z"
} | 3a2589 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1329
},
"timestamp": "2026-02-11T23:06:38.102Z",
"answer": 34678
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ee8f75 | diophantine_fbi2_count_v1_1439011603_1441 | Let $n$ be a positive integer such that $1 \leq n \leq 1574$, $n$ is even, and $\gcd(n, 15) = 1$. Let $k$ be the number of such integers $n$. Now consider the set of all positive integers $d$ such that $4 \leq d \leq 53$, $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 54$. Let $r$ be the number of such integers $d$. Com... | 8,653 | graphs = [
Graph(
let={
"_n": Const(4),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1574)), Divides(divisor=Const(2), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(15)), Const(1))))),
"result": CountOverSet(... | NT | null | COUNT | sympy | K3 | [
"K3",
"C5"
] | 2f75ac | diophantine_fbi2_count_v1 | digits_weighted_mod | 6 | 0 | [
"C5",
"K3"
] | 2 | 0.022 | 2026-02-08T16:06:07.108799Z | {
"verified": true,
"answer": 8653,
"timestamp": "2026-02-08T16:06:07.130624Z"
} | f576f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 1780
},
"timestamp": "2026-02-16T21:24:14.704Z",
"answer": 8653
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ba2153 | comb_count_permutations_fixed_v1_151522320_611 | Let $\mathcal{P}$ be the set of all prime numbers $n$ such that $2 \le n \le 7$. Let $k$ be the largest element of $\mathcal{P}$. Let $n = 11$. Compute
$$
\binom{n}{k} \cdot !(n - k),
$$
where $!m$ denotes the number of derangements of $m$ elements. | 2,970 | graphs = [
Graph(
let={
"_n": Const(7),
"n": Const(11),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T03:25:41.030354Z | {
"verified": true,
"answer": 2970,
"timestamp": "2026-02-08T03:25:41.031912Z"
} | 92facd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 417
},
"timestamp": "2026-02-10T14:17:33.772Z",
"answer": 2970
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
b2d947_n | alg_qf_psd_orbit_v1_601307018_564 | An architect designs triangular frames where side lengths $a$, $b$, and $c$ are integers satisfying $1 \le a \le b \le c \le 55$. A frame is stable if the expression $50a^2 + 50b^2 + 50c^2 - 34ab - 34ac - 34bc$ equals $86330$. How many stable triangular frames are possible? | 6 | ALG | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | alg_qf_psd_orbit_v1 | null | 5 | null | [
"MOBIUS_COPRIME"
] | 1 | 1.231 | 2026-03-10T01:05:43.121640Z | null | c78baa | b2d947 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T14:13:28.808Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
586818 | geo_count_lattice_triangle_v1_1520064083_3565 | Let $A = (0,0)$, $B = (169,23)$, and $C = (128,100)$. The quantity $2 \times \text{area}$ of triangle $ABC$ is given by
$$
|169 \cdot 100 + 128 \cdot (-23)|.
$$
The number of lattice points on the boundary of triangle $ABC$ is
$$
\gcd(169, 23) + \gcd(|128 - 169|, |100 - 23|) + \gcd(128, 100).
$$
Using Pick's Theorem, t... | 6,976 | graphs = [
Graph(
let={
"_n": Const(169),
"area_2x": Abs(arg=Sum(Mul(Const(value=169), Const(value=100)), Mul(Const(value=128), Sub(left=Const(value=0), right=Const(value=23))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=169)), b=Abs(arg=Const(value=23))), GCD(a=Abs(arg=... | ALG | NT | COUNT | sympy | L3B | [
"L3B"
] | cc148f | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"L3B"
] | 1 | 0.005 | 2026-02-08T05:44:29.434608Z | {
"verified": true,
"answer": 6976,
"timestamp": "2026-02-08T05:44:29.439411Z"
} | fba07e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 2962
},
"timestamp": "2026-02-12T13:51:26.447Z",
"answer": 6976
},
{... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
c6a441 | lin_form_endings_v1_1116507919_323 | Let $a = 18$ and $b = 27$. Compute the remainder when $6773 \cdot \left\lfloor \frac{27}{\gcd(a,b)} \right\rfloor$ is divided by $91051$. | 20,319 | graphs = [
Graph(
let={
"a_coeff": Const(18),
"b_coeff": Const(27),
"_inner_result": Floor(Div(Const(27), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(6773),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T02:31:24.301696Z | {
"verified": true,
"answer": 20319,
"timestamp": "2026-02-08T02:31:24.302077Z"
} | 063a46 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 453
},
"timestamp": "2026-02-08T19:23:03.092Z",
"answer": 20319
},
{
"i... | 2 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.1,
"mid": -5.34,
"hi": -3.62
} | ||
5ada01 | antilemma_sum_equals_v1_397696148_617 | Let $m = 14697$. Let $n$ be the number of integers $t$ such that $18 \leq t \leq 63$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 11$, and $t = 5a + 3b + 10$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 36$ and $1 \leq j \leq 36$ such that $i + j = n$. ... | 3,060 | graphs = [
Graph(
let={
"_m": Const(14697),
"_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=V... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.009 | 2026-02-08T11:37:42.253808Z | {
"verified": true,
"answer": 3060,
"timestamp": "2026-02-08T11:37:42.262379Z"
} | 84ae78 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T14:26:03.336Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
e512ed | diophantine_fbi2_count_v1_717093673_3012 | Let $k = 1260$. Let $D$ be the set of all positive integers $d$ such that $3 \leq d \leq 91$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Furthermore, suppose $\frac{k}{d} \leq N$, where $N$ is the number of integers $t$ with $10 \leq t \leq 194$ for which there exist positive integers $a \in [1,8]$ and $b \in [1,27]$ s... | 34 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(1260),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(91)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.174 | 2026-02-08T17:20:09.073647Z | {
"verified": true,
"answer": 34,
"timestamp": "2026-02-08T17:20:09.248082Z"
} | ebc0c1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 3212
},
"timestamp": "2026-02-18T00:24:12.900Z",
"answer": 34
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
88ed13 | modular_sum_quadratic_residues_v1_601307018_7263 | Let $p = 109$. Compute the remainder when $44121M$ is divided by $69404$, where $M = \frac{p(p - 1)}{\max\{ xy : x > 0, y > 0,\ x + y = 4 \}}$. | 62,623 | graphs = [
Graph(
let={
"_n": Const(69404),
"p": Const(109),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y'... | NT | null | SUM | sympy | B1 | [
"B1"
] | 5b950e | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"B1"
] | 1 | 0.003 | 2026-03-10T07:50:24.839475Z | {
"verified": true,
"answer": 62623,
"timestamp": "2026-03-10T07:50:24.842684Z"
} | 9d0255 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1286
},
"timestamp": "2026-04-19T06:16:11.571Z",
"answer": 62623
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
fb772a | geo_count_lattice_triangle_v1_865884756_3419 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 8100$. Let $m = \min\{x + y \mid (x, y) \in S\}$.
Define
$$
A = \left| 289 \cdot 121 + 289 \cdot (0 - m) \right|.
$$
Let $B_1 = \gcd(289, 180)$,
$$
B_2 = \gcd\left( \left| \max\{x y \mid x, y \in \mathbb{Z}^+,\ x + y = 34\} - 289 \r... | 82,507 | graphs = [
Graph(
let={
"_m": Const(180),
"_n": Const(180),
"area_2x": Abs(arg=Sum(Mul(Const(value=289), Const(value=121)), Mul(Const(value=289), Sub(left=Const(value=0), right=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), ... | NT | null | COUNT | sympy | B1 | [
"B1",
"B3"
] | 655d51 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.009 | 2026-02-08T17:22:28.600125Z | {
"verified": true,
"answer": 82507,
"timestamp": "2026-02-08T17:22:28.608922Z"
} | 40629c | 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": 1533
},
"timestamp": "2026-02-18T02:19:17.015Z",
"answer": 82507
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fda3ee | comb_count_surjections_v1_677425708_1975 | Let $n$ be the number of integers $t$ with $15 \leq t \leq 42$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 6a + 9b$. Let $k = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ labeled elements into $k$ nonempty un... | 40,824 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:41:08.568101Z | {
"verified": true,
"answer": 40824,
"timestamp": "2026-02-08T04:41:08.569486Z"
} | a4e0c5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1734
},
"timestamp": "2026-02-10T03:58:28.031Z",
"answer": 40824
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
c09469 | v1_endings_v1_1742523217_415 | Let $n = 41588$. Let $v_7(n!)$ denote the largest integer $k$ such that $7^k$ divides $n!$, and let $v_2(n!)$ denote the largest integer $k$ such that $2^k$ divides $n!$. Let $r = \frac{99999 \cdot v_7(n!)}{v_7(n!) + v_2(n!)}$. Compute $\lfloor r \rfloor$. | 14,283 | graphs = [
Graph(
let={
"n_val": Const(41588),
"p_val": Const(7),
"q_val": Const(2),
"n_fact": Factorial(Ref("n_val")),
"vp": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
"vq": MaxKDivides(target=Ref("n_fact"), base=Ref("q_val"... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 5 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T03:01:52.337880Z | {
"verified": true,
"answer": 14283,
"timestamp": "2026-02-08T03:01:52.339015Z"
} | 6a55ca | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 3249
},
"timestamp": "2026-02-09T17:38:42.668Z",
"answer": 14291
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"st... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
d0ee5d | antilemma_k2_v1_1520064083_6069 | Compute the value of $$
\sum_{k=1}^{345} \phi(k) \left\lfloor \frac{345}{k} \right\rfloor.
$$ Let $x$ denote this sum. Compute the remainder when $69919 \cdot x$ is divided by $70394$. | 18,407 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(345), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(345), Var("k"))))),
"_c": Const(69919),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(70394)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K13",
"K2"
] | 2 | 0.003 | 2026-02-08T07:50:03.308563Z | {
"verified": true,
"answer": 18407,
"timestamp": "2026-02-08T07:50:03.311080Z"
} | 157b0b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 7260
},
"timestamp": "2026-02-13T13:00:14.852Z",
"answer": 18407
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4faecc | lin_form_endings_v1_1520064083_1079 | Let $a = 25$ and $b = 20$. Let $k = 17$ and define $s = \gcd(a, b)$. Let $r = \left\lfloor \frac{k}{\gcd(k, s)} \right\rfloor$. Let $x = (19393 \cdot r) \bmod 89500$. Compute $x$. | 61,181 | graphs = [
Graph(
let={
"a_coeff": Const(25),
"b_coeff": Const(20),
"k_val": Const(17),
"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(19... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:46:39.333114Z | {
"verified": true,
"answer": 61181,
"timestamp": "2026-02-08T03:46:39.333699Z"
} | 149978 | 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": 530
},
"timestamp": "2026-02-10T15:43:55.434Z",
"answer": 61181
},
{
"i... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
efe463 | modular_sum_quadratic_residues_v1_2051736721_4811 | Let $p$ be the largest prime number such that $2 \leq p \leq 160$. Compute $\frac{p(p-1)}{4}$, and let this value be $r$. Let $c = 42827$. Find the remainder when $c \cdot r$ is divided by $83406$. | 1,257 | graphs = [
Graph(
let={
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(160)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": Const(42827),
"Q": Mod(value=M... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T18:10:33.908079Z | {
"verified": true,
"answer": 1257,
"timestamp": "2026-02-08T18:10:33.910314Z"
} | d069c0 | 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": 5878
},
"timestamp": "2026-02-18T15:14:39.504Z",
"answer": 1257
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
27e9d0 | algebra_poly_eval_v1_124444284_1952 | Let $n = 9$ and $m = 7$. Define
$$
\text{result} = n \cdot m^4 - 8m^3 + 6m^2 - 5m - 5.
$$
Let
$$
c = \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Compute the remainder when $\text{result}^2 + 11 \cdot \text{result} + c$ is divided by $69192$. | 66,870 | graphs = [
Graph(
let={
"_n": Const(9),
"m": Const(7),
"result": Sum(Mul(Ref("_n"), Pow(Ref("m"), Const(4))), Mul(Const(-8), Pow(Ref("m"), Const(3))), Mul(Const(6), Pow(Ref("m"), Const(2))), Mul(Const(-5), Ref("m")), Const(-5)),
"_c": Summation(var="k", start=... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 598070 | algebra_poly_eval_v1 | quadratic_mod | 4 | 0 | [
"K2"
] | 1 | 0.005 | 2026-02-08T04:13:19.557593Z | {
"verified": true,
"answer": 66870,
"timestamp": "2026-02-08T04:13:19.562103Z"
} | 12b2c7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 2145
},
"timestamp": "2026-02-10T15:57:24.204Z",
"answer": 66870
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
525ac4 | alg_qf_psd_count_v1_1419126231_1238 | Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \le a, b, c \le 30$ such that $8a^2 + 26c^2 + 72b^2 + 32ab + 32bc + 24ac = 84808$. | 10 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Geq(Var("c"), Const(1)), Leq(Var("c"), Const(30)), Eq(Sum(Mul(Co... | ALG | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | alg_qf_psd_count_v1 | null | 3 | null | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.24 | 2026-02-25T10:42:14.149001Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-25T10:42:14.388645Z"
} | 308850 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 23352
},
"timestamp": "2026-03-30T11:56:34.467Z",
"answer": 10
},
{
"id... | 1 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
7172d6 | nt_lcm_compute_v1_717093673_1849 | Let $a = 1620$ and $b = 1044$. Define $\text{result} = \text{lcm}(a, b)$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 754$. Let $c$ be the number of elements in $S$. Compute the remainder when $\text{result}^2 + 30 \cdot \text{result} + c$ is divided by $77429$. | 22,810 | graphs = [
Graph(
let={
"a": Const(1620),
"b": Const(1044),
"result": LCM(a=Ref("a"), b=Ref("b")),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsO... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 0a3d6e | nt_lcm_compute_v1 | quadratic_mod | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T16:22:27.617291Z | {
"verified": true,
"answer": 22810,
"timestamp": "2026-02-08T16:22:27.619767Z"
} | 86ab45 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1606
},
"timestamp": "2026-02-17T01:32:27.599Z",
"answer": 22810
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
aa5004 | nt_count_coprime_v1_2051736721_5303 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 40000$. For each such pair, compute $x + y$, and let $s_{\min}$ be the minimum value of $x + y$ over all pairs in $T$. Now, let $U$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = s_{\min}$. For each such... | 18,490 | graphs = [
Graph(
let={
"_n": Const(40000),
"upper": Const(46225),
"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")), MinOverSet(... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | nt_count_coprime_v1 | null | 6 | 0 | [
"B3"
] | 1 | 3.257 | 2026-02-08T18:28:42.253739Z | {
"verified": true,
"answer": 18490,
"timestamp": "2026-02-08T18:28:45.510358Z"
} | 9fc9f9 | 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": 1832
},
"timestamp": "2026-02-18T17:22:56.658Z",
"answer": 18490
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
684be6 | diophantine_fbi2_count_v1_809748730_1731 | Let $k$ be the number of positive integers that are divisible by $225$ and do not exceed $283500$. Let $D$ be the set of all integers $d$ such that $4 \leq d \leq 193$, $d$ divides $k$, and the quotient $k/d$ is between $2$ and $191$, inclusive. Compute the number of elements in $D$. | 24 | graphs = [
Graph(
let={
"_n": Const(191),
"k": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(283500)), Divides(divisor=Const(225), dividend=Var("k"))), domain='positive_integers')),
"result": CountOverSet(set=Soluti... | NT | null | COUNT | sympy | LIN_FORM | [
"C2"
] | 9685eb | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 0.093 | 2026-02-08T12:39:23.098557Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T12:39:23.191268Z"
} | ca1dfb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 2173
},
"timestamp": "2026-02-15T03:48:34.529Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9310f2 | modular_sum_quadratic_residues_v1_1520064083_2763 | Let $t$ be an integer satisfying $7 \leq t \leq 553$. A pair of positive integers $(a, b)$ with $1 \leq a \leq 70$ and $1 \leq b \leq 91$ is called good if $t = 4a + 3b$. Let $p$ be the number of distinct values of $t$ for which there exists at least one good pair $(a, b)$. Compute $\frac{p(p-1)}{4}$. | 73,035 | graphs = [
Graph(
let={
"_n": Const(4),
"p": 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=70)), Geq(left=Var(n... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:59:48.600367Z | {
"verified": true,
"answer": 73035,
"timestamp": "2026-02-08T04:59:48.602101Z"
} | 5dd015 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 6109
},
"timestamp": "2026-02-11T22:39:46.498Z",
"answer": 73035
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
bbf3e8 | nt_count_digit_sum_v1_124444284_3878 | Let $N = 9999$. Define $\text{upper} = \sum_{d \mid N} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $\mathcal{T}$ be the set of all positive integers $n$ such that $1 \leq n \leq \text{upper}$ and the sum of the decimal digits of $n$ is $23$. Let $\text{result}$ be the number of elements in $\mathcal{T}... | 10,134 | graphs = [
Graph(
let={
"_n": Const(98466),
"upper": SumOverDivisors(n=Const(value=9999), var='d', expr=EulerPhi(n=Var(name='d'))),
"target_sum": Const(23),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | nt_count_digit_sum_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.365 | 2026-02-08T05:39:22.179541Z | {
"verified": true,
"answer": 10134,
"timestamp": "2026-02-08T05:39:22.544262Z"
} | 35d0dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1613
},
"timestamp": "2026-02-12T11:52:50.967Z",
"answer": 10134
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
f24131 | antilemma_k3_v1_151522320_2344 | Let $x = \sum_{d \mid 63898} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the remainder when $44121 \cdot x$ is divided by $94823$. | 61,045 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=63898), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(94823)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T04:45:53.530633Z | {
"verified": true,
"answer": 61045,
"timestamp": "2026-02-08T04:45:53.531162Z"
} | eeb297 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 2021
},
"timestamp": "2026-02-11T21:55:38.947Z",
"answer": 61045
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
a16cc6 | comb_bell_compute_v1_1456120455_101 | Let $m = 2$. Define $s = \sum_{d\mid 18} \mu(d)$, where $\mu$ is the M\"obius function. Let $N$ be the number of integers $j$ such that $s \leq j \leq 10400$ and $\binom{10400}{j} \equiv 1 \pmod{m}$. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = N$. Compute the Bel... | 4,140 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), SumOverDivisors(n=Const(value=18), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("j"), Const(10400)), Eq(Mod(value=Binom(n=Const(10400), k=Var("j")), modulus=Re... | NT | COMB | COMPUTE | sympy | MOBIUS_SUM | [
"MOBIUS_SUM",
"V8/B3"
] | 383b44 | comb_bell_compute_v1 | null | 7 | 0 | [
"B3",
"MOBIUS_SUM",
"V8"
] | 3 | 0.003 | 2026-02-08T02:53:45.451671Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T02:53:45.454570Z"
} | 16f62a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 2497
},
"timestamp": "2026-02-08T20:02:39.064Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -6.51,
"mid": -0.53,
"hi": 4.75
} | ||
fbd2f0 | nt_count_coprime_and_v1_1918700295_1668 | Let $n = 55$. Let $k_1 = 3$, and let $k_2$ be the largest positive divisor of $55$ that is at most $5$. Determine the number of positive integers $n \leq 37261$ that are relatively prime to both $k_1$ and $k_2$. | 19,873 | graphs = [
Graph(
let={
"_n": Const(55),
"upper": Const(37261),
"k1": Const(3),
"k2": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(5)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"resul... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_count_coprime_and_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 25.372 | 2026-02-08T05:56:45.033122Z | {
"verified": true,
"answer": 19873,
"timestamp": "2026-02-08T05:57:10.405372Z"
} | 2b44f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1057
},
"timestamp": "2026-02-12T17:16:57.256Z",
"answer": 19873
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
20fc0c | antilemma_cartesian_v1_898971024_33 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 16$ and $1 \leq j \leq 21$. Let $c$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 7$, $1 \leq j \leq 8$, and $i + j = 8$. Define $Q$ to be the remainder when $c - x$ is divided by $79277$. Find the value of ... | 78,948 | graphs = [
Graph(
let={
"_n": Const(79277),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(21)))),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), conditio... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | f8dfda | antilemma_cartesian_v1 | negation_mod | 2 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.014 | 2026-02-08T15:09:31.289935Z | {
"verified": true,
"answer": 78948,
"timestamp": "2026-02-08T15:09:31.303499Z"
} | 524ad6 | 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": 685
},
"timestamp": "2026-02-24T20:01:33.778Z",
"answer": 78948
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
f34a7b | antilemma_k2_v1_1918700295_4118 | Let $n = \sum_{d \mid 297} \phi(d)$, where $\phi$ denotes Euler's totient function. Define $x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{297}{k} \right\rfloor$. Compute the remainder when $14161 - x$ is divided by $89836$. | 59,744 | graphs = [
Graph(
let={
"_n": Const(297),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(297), Var("k"))))),
"_c": Const(14161),
"Q": Mod(va... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T09:09:06.916487Z | {
"verified": true,
"answer": 59744,
"timestamp": "2026-02-08T09:09:06.917303Z"
} | 97b75d | 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": 4407
},
"timestamp": "2026-02-14T00:50:11.949Z",
"answer": 59744
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
f956ab | modular_count_residue_v1_809748730_1605 | Let $A$ be the set of all integers $t$ such that $21 \leq t \leq 38$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 3a + 4b + 14$. Let $r$ be the number of elements in $A$. Let $B$ be the set of all positive integers $n$ such that $n \leq 75025$ and $n \equiv r \pmod{17}$. Let ... | 4,420 | graphs = [
Graph(
let={
"upper": Const(75025),
"m": Const(17),
"r": 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'), rig... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_count_residue_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 2.445 | 2026-02-08T12:34:51.643247Z | {
"verified": true,
"answer": 4420,
"timestamp": "2026-02-08T12:34:54.088313Z"
} | b4864c | 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": 2690
},
"timestamp": "2026-02-15T02:49:19.705Z",
"answer": 4420
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
efcb78 | antilemma_cartesian_v1_677425708_1981 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 35$ and $1 \leq b \leq 49$. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $x + 2$. | 450 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(49)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T04:41:08.617540Z | {
"verified": true,
"answer": 450,
"timestamp": "2026-02-08T04:41:08.617918Z"
} | 224d94 | 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": 2379
},
"timestamp": "2026-02-10T03:59:48.077Z",
"answer": 450
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
619362 | diophantine_fbi2_min_v1_168721529_761 | Let $k$ be the smallest positive integer $n$ such that $13^2$ divides $n!$. Let $u$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 12$. Let $\text{result}$ be the smallest integer $d$ such that $3 \leq d \leq u$, $d$ divides $k$, and $k/d \geq 2$. Compute $\text{result}$. | 13 | graphs = [
Graph(
let={
"_n": Const(3),
"k": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(13)), Const(2)), domain='Z_{>0}')),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Va... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"ONE_PHI_2",
"V5",
"B1"
] | 8ff0c6 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B1",
"ONE_PHI_2",
"V5"
] | 3 | 0.01 | 2026-02-08T13:17:10.614605Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T13:17:10.624639Z"
} | 95047c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 602
},
"timestamp": "2026-02-09T08:49:26.787Z",
"answer": 13
},
{
"id":... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lem... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
6ee5cb | comb_catalan_compute_v1_677425708_1133 | Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3, 4, 5\}$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $\sum_{k=1}^{C_n} \tau(k)$ is divided by $62753$, where $\tau(k)$ is the number of positive divisors of $k$. | 40,489 | graphs = [
Graph(
let={
"_n": Const(62753),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"Q": Mod(value=Summation(var="n", start=Const(1... | COMB | NT | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T04:00:35.059451Z | {
"verified": true,
"answer": 40489,
"timestamp": "2026-02-08T04:00:35.061876Z"
} | 365da3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 10337
},
"timestamp": "2026-02-23T23:11:27.315Z",
"answer": 40481
},
{
... | 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",
"status": "no... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
04c7c9 | alg_poly3_min_v1_601307018_9878 | Find the minimum value of $$
275a^3 + 375a^2b + 225a^2c + 50b^3 -75ab^{\left|\{ k \in \mathbb{Z}^+ : 1 \le k \le 16,\, 8 \mid k \}\right|} + 150abc + 45ac^2 + 30bc^2
$$ over all ordered triples $(a, b, c)$ of positive integers with $1 \le a, b, c \le 30$. | 1,075 | graphs = [
Graph(
let={
"_n": Const(275),
"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(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Geq(Var("c"), Const(1... | ALG | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | alg_poly3_min_v1 | null | 6 | 0 | [
"C2"
] | 1 | 0.098 | 2026-03-10T10:16:16.677545Z | {
"verified": true,
"answer": 1075,
"timestamp": "2026-03-10T10:16:16.775279Z"
} | 697913 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 3590
},
"timestamp": "2026-04-19T12:21:00.127Z",
"answer": 1075
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
a75415 | nt_count_digit_sum_v1_1470522791_157 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 144$. Let $s$ be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Find the number of positive integers $n$ at most $99999$ such that the sum of the decimal digits of $n$ is $s$. | 5,875 | graphs = [
Graph(
let={
"_n": Const(144),
"upper": Const(99999),
"target_sum": 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(... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_digit_sum_v1 | null | 6 | 0 | [
"B3"
] | 1 | 3.829 | 2026-02-08T12:51:06.444948Z | {
"verified": true,
"answer": 5875,
"timestamp": "2026-02-08T12:51:10.273460Z"
} | 7801b8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 1411
},
"timestamp": "2026-02-15T07:06:20.047Z",
"answer": 5875
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
854a34 | nt_min_phi_inverse_v1_458359167_959 | Let $k$ be the number of integers $j$ with $0 \le j \le 98338$ such that $\binom{98338}{j}$ is odd. Let $n$ be the smallest positive integer at most $70$ such that $\phi(n) = k$, where $\phi$ denotes Euler's totient function. Let $Q$ be the remainder when $55369 \cdot n$ is divided by $88066$. Compute $Q$. | 60,613 | graphs = [
Graph(
let={
"_n": Const(88066),
"upper": Const(70),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(98338)), Eq(Mod(value=Binom(n=Const(98338), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonn... | NT | null | EXTREMUM | sympy | V8 | [
"V8"
] | 86348e | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.007 | 2026-02-08T04:12:15.384525Z | {
"verified": true,
"answer": 60613,
"timestamp": "2026-02-08T04:12:15.391941Z"
} | 132d6d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1212
},
"timestamp": "2026-02-10T15:52:22.887Z",
"answer": 60613
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
bb52b9 | nt_count_coprime_and_v1_1918700295_2514 | Let $T$ be the set of all integers $t$ such that $7 \le t \le 24$ and there exist positive integers $a$ and $b$ with $1 \le a \le 4$, $1 \le b \le 3$, and $t = 3a + 4b$. Let $m = 2$ and let $n = |T|$. Let $k_2$ be the largest prime number in the interval $[m, n]$. Compute the number of positive integers $n$ such that $... | 13,124 | 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"
] | 47006e | nt_count_coprime_and_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 9.316 | 2026-02-08T07:56:23.053654Z | {
"verified": true,
"answer": 13124,
"timestamp": "2026-02-08T07:56:32.369927Z"
} | 152a01 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 928
},
"timestamp": "2026-02-13T13:48:16.267Z",
"answer": 13124
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d394af | nt_num_divisors_compute_v1_784195855_929 | Let $n$ be the number of integers $t$ such that $9 \leq t \leq 645$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 13$, $1 \leq b \leq 145$, and $t = 5a + 4b$. Let $d(n)$ denote the number of positive divisors of $n$. Compute the remainder when $44121 \cdot d(n)$ is divided by $94414$. | 31,777 | graphs = [
Graph(
let={
"_n": Const(94414),
"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=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T04:42:31.481350Z | {
"verified": true,
"answer": 31777,
"timestamp": "2026-02-08T04:42:31.484090Z"
} | 5cfdd8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 4478
},
"timestamp": "2026-02-11T21:46:36.858Z",
"answer": 31777
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2b1559 | geo_visible_lattice_v1_1440796553_1067 | Let $n = 120$. A visible lattice point is a point $(x, y)$ in the coordinate plane with $1 \le x, y \le n$ such that $\gcd(x, y) = 1$. Let $L$ be the number of visible lattice points for this $n$. Compute the Bell number $B_r$, where $r$ is the remainder when $|L|$ is divided by $11$. | 15 | graphs = [
Graph(
let={
"n": Const(120),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.326 | 2026-02-08T12:10:02.036774Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T12:10:02.362692Z"
} | 357801 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T15:21:42.262Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
56be97 | alg_sum_powers_v1_1218484723_6619 | Let $T$ be the number of positive integers $n$ with $1 \leq n \leq 511$ such that the sum of the digits of $n$ in binary is odd. Let $R = \left(\sum_{k=1}^{T} k^3\right) \bmod 3073$. Find the remainder when $27815 \cdot R$ is divided by $91804$. | 76,758 | graphs = [
Graph(
let={
"_n": Const(511),
"result": Mod(value=Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))), expr=Pow... | ALG | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | alg_sum_powers_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.016 | 2026-02-25T08:09:41.612329Z | {
"verified": true,
"answer": 76758,
"timestamp": "2026-02-25T08:09:41.627919Z"
} | 626346 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 5639
},
"timestamp": "2026-03-30T02:28:25.397Z",
"answer": 45804
},
{
... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
bbaf57 | geo_count_lattice_rect_v1_458359167_2529 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 256$ and $0 \leq y \leq 114$. | 29,555 | graphs = [
Graph(
let={
"a": Const(256),
"b": Const(114),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.005 | 2026-02-08T06:18:46.204838Z | {
"verified": true,
"answer": 29555,
"timestamp": "2026-02-08T06:18:46.209399Z"
} | 0e50fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 120
},
"timestamp": "2026-02-24T05:58:11.465Z",
"answer": 29555
},
{
"i... | 1 | [] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||||
4d0752_l | comb_count_permutations_fixed_v1_601307018_1215 | Let $D_n$ denote the number of derangements of $n$ elements. Let $$
k = \frac{5 \cdot \sum_{k_1=1}^{4} (-1)^{k_1} \binom{4}{k_1}}{45}.
$$
Let $n = 8$ and $M = \binom{n}{k} \cdot D_{n - k}$. Find the remainder when $97131M$ is divided by $93925$. | 25,342 | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_INDEPENDENT/BINOMIAL_ALTERNATING"
] | e40483 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"POLY_ORBIT_LEGENDRE",
"SUM_INDEPENDENT"
] | 3 | 0.009 | 2026-03-10T01:53:39.827022Z | {
"verified": false,
"answer": 28548,
"timestamp": "2026-03-10T01:53:39.836119Z"
} | 364389 | 4d0752 | 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": 218,
"completion_tokens": 5536
},
"timestamp": "2026-03-29T01:33:03.668Z",
"answer": 29448
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma":... | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | |
25cdc1 | comb_binomial_compute_v1_1218484723_7483 | Let $M$ be the number of non-negative integers $j$ with $0 \le j \le 55900$ such that $\binom{55900}{j}$ is odd. Let $R = \binom{14}{6}$, and let $d(R)$ denote the number of positive divisors of $R$. Let $d_i(R)$ denote the $i$-th digit of $R$ in base 10, starting from the units digit (index $i=0$). Compute $\sum_{i=0}... | 563 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(14),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(55900)), Eq(Mod(value=Binom... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86b5fc | comb_binomial_compute_v1 | digits_weighted_mod | 5 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-25T08:54:34.781122Z | {
"verified": true,
"answer": 563,
"timestamp": "2026-02-25T08:54:34.783560Z"
} | ac7862 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 1423
},
"timestamp": "2026-03-30T04:44:07.277Z",
"answer": 563
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
4238cb | antilemma_k3_v1_2051736721_5300 | For each positive divisor $d$ of $9888$, let $\phi(d)$ denote Euler's totient function. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $9888$. Compute the remainder when $20803 \cdot x$ is divided by $95722$. | 89,208 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=9888), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(20803), Ref("x")), modulus=Const(95722)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T18:28:42.203549Z | {
"verified": true,
"answer": 89208,
"timestamp": "2026-02-08T18:28:42.203925Z"
} | 669422 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1595
},
"timestamp": "2026-02-18T17:22:33.544Z",
"answer": 89208
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3a4fd6 | comb_factorial_compute_v1_1218484723_2094 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 10$ such that $17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 69632$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(10)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(10)), Eq(Sum(Mul(Const(17), Pow(Var("a"), Const(4))), Mul... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_factorial_compute_v1 | null | 3 | 0 | [
"POLY4_COUNT"
] | 1 | 0.001 | 2026-02-25T03:47:55.006727Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T03:47:55.007941Z"
} | 3313e4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 626
},
"timestamp": "2026-03-29T02:57:47.150Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
ca45e9_n | comb_binomial_compute_v1_1419126231_806 | A game board has 15 red tokens and 15 blue tokens, each labeled from 1 to 15. A move is valid if the labels $a$ (red) and $b$ (blue) satisfy the energy equation $17a^4 + 102a^2b^2 + 68a^3b + 68ab^3 + 19b^4 = 22032$, where 19 is the smallest prime factor of 323. Let $k$ be the number of valid moves. The score is $\binom... | 792 | COMB | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"MIN_PRIME_FACTOR/POLY4_COUNT"
] | 8ab393 | comb_binomial_compute_v1 | null | 5 | null | [
"MIN_PRIME_FACTOR",
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 3 | 0.063 | 2026-02-25T10:18:04.443290Z | null | 68ec36 | ca45e9 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 10159
},
"timestamp": "2026-03-31T03:59:22.399Z",
"answer": 1
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "V7",
... | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
962e9c | modular_sum_quadratic_residues_v1_151522320_153 | Let $n = 14$ and $p = 509$. Compute the value of $\frac{p(p-1)}{k}$, where $k$ is the largest integer such that $13^k$ divides $n^{2197} - 1$. | 64,643 | graphs = [
Graph(
let={
"_n": Const(14),
"p": Const(509),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), MaxKDivides(target=Sub(Pow(Ref("_n"), Const(2197)), Const(1)), base=Const(13))),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"LTE_DIFF"
] | 1 | 0.002 | 2026-02-08T03:00:32.294481Z | {
"verified": true,
"answer": 64643,
"timestamp": "2026-02-08T03:00:32.296258Z"
} | ba4a84 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 694
},
"timestamp": "2026-02-08T23:56:59.184Z",
"answer": 64643
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
cf98bf | lin_form_endings_v1_784195855_3074 | Let $ a = 84 $ and $ b = 36 $. Let $ s = \gcd(a, b) $. Let $ k = 26 $, and let $ r = \gcd(k, s) $. Define $ n = \left\lfloor \frac{k}{r} \right\rfloor $. Compute the remainder when $ 16837 \cdot n $ is divided by $ 85183 $. | 48,515 | graphs = [
Graph(
let={
"a_coeff": Const(84),
"b_coeff": Const(36),
"k_val": Const(26),
"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(16... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:12:58.445370Z | {
"verified": true,
"answer": 48515,
"timestamp": "2026-02-08T06:12:58.446623Z"
} | 0d97c7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 507
},
"timestamp": "2026-02-19T02:55:28.129Z",
"answer": 49055
},
{
"id": 11... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
fc1c8f | modular_product_range_v1_48377204_1742 | Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 70$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 8$, and $t = 2a + 7b$. Let $k$ be the number of elements in $T$. Compute the product $P = 1 \cdot 2 \cdot 3 \cdots k$. Find the remainder when $P$ is divided by $10589... | 8,688 | graphs = [
Graph(
let={
"_n": Const(10589),
"prod": MathProduct(expr=Var("i"), var="i", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)),... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_product_range_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T16:22:30.214129Z | {
"verified": true,
"answer": 8688,
"timestamp": "2026-02-08T16:22:30.218425Z"
} | 5688c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 4518
},
"timestamp": "2026-02-17T02:55:18.449Z",
"answer": 8688
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f6af0 | lte_diff_endings_v1_260342960_212 | Let $a = 2511$ and $b = 11$. For each positive integer $k$, define $d_k = a^k - b^k$. Let $L_1 = \text{LCM}(d_1, d_5)$, $L_2 = \text{LCM}(L_1, d_9)$, $L_3 = \text{LCM}(L_2, d_{14})$, and $L_4 = \text{LCM}(L_3, d_{25})$. Let $e$ be the largest integer such that $5^e$ divides $L_4$. Compute the remainder when $9669e$ is ... | 58,014 | graphs = [
Graph(
let={
"a_val": Const(2511),
"b_val": Const(11),
"p_val": Const(5),
"ap_1": Ref("a_val"),
"bp_1": Ref("b_val"),
"d_1": Sub(Ref("ap_1"), Ref("bp_1")),
"ap_5": Pow(Ref("a_val"), Const(5)),
"bp_5": ... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 7 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T11:20:07.551345Z | {
"verified": true,
"answer": 58014,
"timestamp": "2026-02-08T11:20:07.552458Z"
} | 64ab72 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 1177
},
"timestamp": "2026-02-08T20:34:29.072Z",
"answer": 58014
},
{
"... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.76
} | ||
49b110 | algebra_poly_eval_v1_1520064083_7481 | Let $m = 1575$ and let $n$ be the smallest divisor of $m$ that is at least 2. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Define $s$ to be the minimum value of $x + y$ over all such pairs. Compute the absolute value of $$10 \cdot 7^4 + 10 \cdot 7^n + s \cdot 7^2 + 10 \cdot ... | 27,699 | graphs = [
Graph(
let={
"_m": Const(1575),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"t": Const(7),
"result": Sum(Mul(Const(10), Pow(Ref("t"), Const(4))), Mul(Const(... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/B3"
] | 5a1a4d | algebra_poly_eval_v1 | null | 4 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T09:03:56.784798Z | {
"verified": true,
"answer": 27699,
"timestamp": "2026-02-08T09:03:56.789440Z"
} | 15121f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 860
},
"timestamp": "2026-02-14T00:56:28.836Z",
"answer": 27699
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
bb9f4d | nt_count_divisible_and_v1_655260480_16 | Let $u = 89880$. Let $d_1 = 6$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Let $d_2$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Find the number of positive integers $n$ such that $1 \leq n \leq u$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$... | 2,996 | graphs = [
Graph(
let={
"upper": Const(89880),
"d1": Const(6),
"d2": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25)))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 3 | 0 | [
"B3"
] | 1 | 3.257 | 2026-02-08T15:08:06.227192Z | {
"verified": true,
"answer": 2996,
"timestamp": "2026-02-08T15:08:09.484376Z"
} | 031b7b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 673
},
"timestamp": "2026-02-16T00:25:12.950Z",
"answer": 2996
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a08337 | diophantine_sum_product_min_v1_1978505735_7144 | Find the smallest positive integer $x$ such that $1 \leq x \leq 93$ and $x(94 - x) = 840$. Let $d_i$ denote the $i$th decimal digit of this $x$ (starting from the units digit as $i=0$). Let $s$ be the sum
$$
\sum_{i=0}^{k-1} d_i (i+1)^2,
$$
where $k$ is the number of digits in $x$. Compute $s + 19$. | 23 | graphs = [
Graph(
let={
"S": Const(94),
"P": Const(840),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(93)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
"_c": Const(19),
... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"B3"
] | 233389 | diophantine_sum_product_min_v1 | null | 4 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 0.037 | 2026-02-08T20:05:38.331271Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T20:05:38.368032Z"
} | 943645 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 724
},
"timestamp": "2026-02-18T23:55:09.743Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ca5d6a | comb_binomial_compute_v1_1874849503_1174 | Let $m = 2$ and $n = 5$. Define
$$
S = \{ k \in \mathbb{Z}^+ \mid m \leq k \leq 6 \text{ and } k \text{ is prime} \}.
$$
Let $P$ be the maximum element of $S$. Compute
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{P}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $N$ be the value of this sum. Fi... | 6,435 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(5),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(6)), IsPrime(Var("... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T13:39:30.699997Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T13:39:30.702699Z"
} | 4dc6d1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 867
},
"timestamp": "2026-02-10T02:02:12.618Z",
"answer": 6435
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
1afa8b | modular_count_residue_v1_153355830_967 | Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 81$. Let $r = 1$ and $N = 68265$. Find the number of positive integers $n \leq N$ such that $n \equiv r \pmod{m}$. | 3,793 | graphs = [
Graph(
let={
"upper": Const(68265),
"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(81)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 3 | 0 | [
"B3"
] | 1 | 2.461 | 2026-02-08T04:20:14.503056Z | {
"verified": true,
"answer": 3793,
"timestamp": "2026-02-08T04:20:16.963716Z"
} | e8053d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 651
},
"timestamp": "2026-02-10T16:11:13.786Z",
"answer": 3793
},
{
"i... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
ff94a5 | geo_count_lattice_triangle_v1_1978505735_2152 | Let $m = 128$ and $n = 128$. Define the quantity
$$
\text{area}_{2x} = \left| 144m + 200 \cdot (0 - 4) \right|.
$$
Let $b_1 = \gcd(|144|, |4 - \sum_{k=0}^{2} (-1)^k \binom{2}{k}|)$,
$$
b_2 = \gcd\left(\left|200 - \text{the number of ordered pairs } (i,j) \text{ of positive integers such that } i+j=145\right|, \left|n -... | 8,809 | graphs = [
Graph(
let={
"_m": Const(128),
"_n": Const(128),
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Ref(name='_m')), Mul(Const(value=200), Sub(left=Const(value=0), right=Const(value=4))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Sub(le... | COMB | NT | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 9492c2 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.023 | 2026-02-08T16:41:06.448514Z | {
"verified": true,
"answer": 8809,
"timestamp": "2026-02-08T16:41:06.471920Z"
} | dcc0c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 4786
},
"timestamp": "2026-02-17T11:12:27.551Z",
"answer": 8809
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5de03c | antilemma_v8_lucas_548369836_39 | Determine the number of nonnegative integers $j$ such that $0 \leq j \leq 10718$ and
\[
\binom{10718}{j} \equiv \phi(2) \pmod{2},
\]
where $\phi$ denotes Euler's totient function. | 512 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(10718)), Eq(Mod(value=Binom(n=Const(10718), k=Var("j")), modulus=Const(2)), EulerPhi(n=Const(1)))), domain='nonnegative_integers')),
},
goal=Ref("x"... | NT | COMB | COMPUTE | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"V8"
] | 59ff2b | antilemma_v8_lucas | null | 4 | 0 | [
"ONE_PHI_1",
"V8"
] | 2 | 0.001 | 2026-02-08T02:43:25.043968Z | {
"verified": true,
"answer": 512,
"timestamp": "2026-02-08T02:43:25.045104Z"
} | 9f0045 | 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": 1331
},
"timestamp": "2026-02-08T19:44:11.930Z",
"answer": 512
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -1.93,
"mid": 1.65,
"hi": 4.55
} | ||
6b441e | nt_count_intersection_v1_1520064083_4108 | Let $N = 10000$, $a = 3$, and $b = 10$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq N$, $3$ divides $n$, and $\gcd(n, 10) = 1$. Let $m$ be the number of elements in $S$. Let $Q$ be the Bell number $B_k$, where $k$ is the remainder when $|m|$ is divided by $11$. Find the value of $Q$. | 5 | graphs = [
Graph(
let={
"N": Const(10000),
"a": Const(3),
"b": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=R... | NT | COMB | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_count_intersection_v1 | null | 3 | 0 | [
"ONE_PHI_2"
] | 1 | 3.923 | 2026-02-08T06:04:10.906112Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T06:04:14.829375Z"
} | 0ab552 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1194
},
"timestamp": "2026-02-12T19:15:48.740Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
664bdd | modular_sum_quadratic_residues_v1_601307018_10635 | Let $R$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 25$ such that $-189a^3 = -40824$. Let $m$ be the largest positive divisor of $21511043$ with $m^2 \leq 21511043$. Let $p$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1, b_1 \leq 30$ such that ... | 25,463 | graphs = [
Graph(
let={
"_c": Const(30),
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Mul(Const(-189), P... | NT | null | SUM | sympy | POLY3_COUNT | [
"POLY3_COUNT/QF_PSD_COUNT_LEQ",
"B3_CLOSEST/QF_PSD_COUNT_LEQ"
] | 9859e5 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"B3_CLOSEST",
"POLY3_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.008 | 2026-03-10T11:06:43.882386Z | {
"verified": true,
"answer": 25463,
"timestamp": "2026-03-10T11:06:43.889892Z"
} | eaa4b7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 13723
},
"timestamp": "2026-04-19T14:24:47.755Z",
"answer": 25463
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "V7",
"stat... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
2e3557 | geo_count_lattice_rect_v1_1218484723_2745 | Let $a = \sum_{k=0}^{4} 3^{k}$. Compute $38416 - M$, where $M$ is the number of lattice points $(x,y)$ with $0 \leq x \leq a$ and $0 \leq y \leq 157$. | 19,140 | graphs = [
Graph(
let={
"a": Summation(var="k", start=Const(0), end=Const(4), expr=Pow(Const(3), Var("k"))),
"b": Const(157),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(38416),
"Q": Sub(Ref("_c"), Ref("result")),
... | GEOM | GEOM | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | geo_count_lattice_rect_v1 | null | 2 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T04:27:32.926493Z | {
"verified": true,
"answer": 19140,
"timestamp": "2026-02-25T04:27:32.927491Z"
} | 4074a3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1275
},
"timestamp": "2026-03-29T06:19:02.669Z",
"answer": 19140
},
{
"... | 2 | [
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
a0ae87 | geo_count_lattice_rect_v1_458359167_371 | Let $a = 88$ and $b = 182$. Consider the rectangle in the coordinate plane with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Compute the number of points with integer coordinates that lie inside or on the boundary of this rectangle. Find the absolute value of this number. | 16,287 | graphs = [
Graph(
let={
"a": Const(88),
"b": Const(182),
"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 | 0.002 | 2026-02-08T03:14:40.766018Z | {
"verified": true,
"answer": 16287,
"timestamp": "2026-02-08T03:14:40.767574Z"
} | b2914e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 475
},
"timestamp": "2026-02-10T13:40:38.252Z",
"answer": 16287
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||||
87b207 | nt_count_coprime_v1_971394319_764 | Let $n = 240$. Let $k$ be the number of positive integers $d$ such that $d \le 6240$ and $d$ is divisible by $n$.
Let $R$ be the number of positive integers $m$ such that $1 \le m \le 10601$ and $\gcd(m, k) = 1$.
Find the value of $R$. | 4,893 | graphs = [
Graph(
let={
"_n": Const(240),
"upper": Const(10601),
"k": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(6240)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | nt_count_coprime_v1 | null | 5 | 0 | [
"C2"
] | 1 | 0.815 | 2026-02-08T13:17:39.851217Z | {
"verified": true,
"answer": 4893,
"timestamp": "2026-02-08T13:17:40.666424Z"
} | fcc7e4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 747
},
"timestamp": "2026-02-15T12:51:41.203Z",
"answer": 4893
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f76a41 | modular_count_residue_v1_124444284_1134 | Compute the number of integers $n$ such that $1 \leq n \leq 39204$ and $n \equiv 13 \pmod{20}$. | 1,960 | graphs = [
Graph(
let={
"upper": Const(39204),
"m": Const(20),
"r": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(1))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | modular_count_residue_v1 | null | 3 | 0 | [
"ONE_PHI_1"
] | 1 | 1.732 | 2026-02-08T03:42:19.347027Z | {
"verified": true,
"answer": 1960,
"timestamp": "2026-02-08T03:42:21.079358Z"
} | e35c15 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 412
},
"timestamp": "2026-02-10T03:11:53.875Z",
"answer": 1960
},
{
"id... | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
96b735 | comb_bell_compute_v1_1742523217_5187 | Let $n = 4$ and $a = 3$. Let $b$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = n$, where $1 \le i \le 3$ and $1 \le j \le 4$. Define $n_2 = a + b$. Compute
$$
e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $u = 3$ and define $n_1 = u + 1$. Compute
$$
h = \sum_{k=0}^{n_1} (-1)^k \bin... | 43,323 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(3),
"b": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRang... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_bell_compute_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T10:51:05.812969Z | {
"verified": true,
"answer": 43323,
"timestamp": "2026-02-08T10:51:05.825289Z"
} | 2270f3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 334,
"completion_tokens": 6206
},
"timestamp": "2026-02-24T12:23:40.731Z",
"answer": 43323
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
572ce0 | comb_sum_binomial_mod_v1_798873815_91 | Let $S$ be the set of all ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 332$. Define $t$ to be the number of elements in $S$. Compute the remainder when $\sum_{k=3}^{t} \binom{178}{k}$ is divided by $11243$. | 322 | graphs = [
Graph(
let={
"_n": Const(11243),
"sum": Summation(var="k", start=Const(3), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(n... | ALG | COMB | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_sum_binomial_mod_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.013 | 2026-02-08T02:26:06.544889Z | {
"verified": true,
"answer": 322,
"timestamp": "2026-02-08T02:26:06.558344Z"
} | 352aa6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:26:43.017Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 6.03,
"mid": 7.72,
"hi": 10
} | ||
013b75 | nt_min_with_divisor_count_v1_784195855_3967 | Let $m$ be the smallest integer $d \ge 2$ such that $d$ divides $3894467$. Let $p$ be the largest prime number with $2 \le p \le m$.
Let $U$ be the number of integers $t$ with $12 \le t \le 2053$ for which there exist integers $a$ and $b$ satisfying
$$1 \le a \le 94,\quad 1 \le b \le 279,\quad t = 7a + 5b.$$
Let $D =... | 5 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(3894467))))),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_c")), Le... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW/LIN_FORM"
] | 34e74e | nt_min_with_divisor_count_v1 | negation_mod | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 6.925 | 2026-02-08T06:43:34.484457Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T06:43:41.409816Z"
} | f41da4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 6284
},
"timestamp": "2026-02-13T03:53:23.984Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6dcd24 | antilemma_k2_v1_1470522791_1826 | Let $S$ be the set of all ordered pairs $(k, j)$ of positive integers with $1 \leq k \leq 18$ and $1 \leq j \leq 10$. Define $N = \frac{7}{70} \sum_{(k,j) \in S} \phi(k) \left\lfloor \frac{18}{k} \right\rfloor$. Compute $\sum_{k=1}^{N} \phi(k) \left\lfloor \frac{171}{k} \right\rfloor$. | 14,706 | graphs = [
Graph(
let={
"_c": Const(18),
"_n": Div(Mul(Const(7), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=... | NT | COMB | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"K2/K2",
"K2"
] | c37857 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.003 | 2026-02-08T14:00:24.136621Z | {
"verified": true,
"answer": 14706,
"timestamp": "2026-02-08T14:00:24.139758Z"
} | e1e7bd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1008
},
"timestamp": "2026-02-15T23:43:11.545Z",
"answer": 14706
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1c2764 | antilemma_k3_v1_1918700295_895 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $98251$, where $\phi$ denotes Euler's totient function. | 98,251 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=98251), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T05:23:12.454651Z | {
"verified": true,
"answer": 98251,
"timestamp": "2026-02-08T05:23:12.454944Z"
} | 4eb339 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 3441
},
"timestamp": "2026-02-12T07:50:46.574Z",
"answer": 98251
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2783d1 | geo_count_lattice_rect_v1_124444284_431 | Compute the number of lattice points in the rectangle $[0, 121] \times [0, 135]$. | 16,592 | graphs = [
Graph(
let={
"a": Const(121),
"b": Const(135),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T03:17:05.815552Z | {
"verified": true,
"answer": 16592,
"timestamp": "2026-02-08T03:17:05.816242Z"
} | c62b49 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 215
},
"timestamp": "2026-02-09T17:33:55.627Z",
"answer": 16592
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||||
90067d | nt_min_phi_inverse_v1_153355830_486 | Let $T$ be the set of all integers $t$ such that $11 \leq t \leq 128$ and there exist positive integers $a \leq 11$ and $b \leq 12$ satisfying $t = 4a + 7b$. Let $k$ be the number of elements in $T$. Find the smallest positive integer $n$ such that $1 \leq n \leq k$ and $\phi(n) = 24$, where $\phi$ is Euler's totient f... | 35 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(left=Var(name='b'), right=Const(va... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.01 | 2026-02-08T03:08:09.884966Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T03:08:09.894726Z"
} | a9a7fd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 4661
},
"timestamp": "2026-02-10T12:40:07.259Z",
"answer": 35
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.32
} | ||
5867d5 | nt_sum_divisors_range_v1_1248542787_371 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 194$ and there exist positive integers $a \leq 49$, $b \leq 32$ satisfying $t = 2a + 3b$. Let $n$ be the number of elements in $T$.\\
Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Define $u$ to be the maximum... | 81,662 | 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=49)), Geq(left=Var(name='b'), right=Const(value... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | nt_sum_divisors_range_v1 | null | 7 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.336 | 2026-02-08T03:05:05.563347Z | {
"verified": true,
"answer": 81662,
"timestamp": "2026-02-08T03:05:05.899501Z"
} | 5b27a8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 8124
},
"timestamp": "2026-02-09T15:39:13.434Z",
"answer": 81662
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"le... | {
"lo": 2.77,
"mid": 5.38,
"hi": 8.6
} | ||
33eeba | comb_count_partitions_v1_349078426_1083 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 5$ and $1 \leq j \leq 8$. Let $\text{result}$ be the number of integer partitions of $n$.
Compute the value of $\text{result}$. | 37,338 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(8)))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_partitions_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T13:24:13.863069Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T13:24:13.864474Z"
} | 0a0028 | 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": 850
},
"timestamp": "2026-02-24T18:21:55.575Z",
"answer": 37338
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
65171d | algebra_vieta_sum_v1_784195855_3963 | Let $S$ be the set of all real numbers $x$ such that $x^4 - 13x^3 + 29x^2 + 13x - 30 = 0$. Compute the sum of all elements of $S$. | 13 | graphs = [
Graph(
let={
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(4)), Mul(Const(-13), Pow(Var("x"), Const(3))), Mul(Const(29), Pow(Var("x"), Const(2))), Mul(Const(13), Var("x")), Const(-30)), Const(0)))),
},
goal=Ref("result"),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | algebra_vieta_sum_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.083 | 2026-02-08T06:43:00.177965Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T06:43:00.261277Z"
} | 96eb17 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 265
},
"timestamp": "2026-02-15T17:43:27.079Z",
"answer": 13
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
b02ef2 | antilemma_sum_equals_v1_1520064083_9182 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 13$ and $1 \leq i \leq 13$, $1 \leq j \leq 13$. Let $Q$ be the remainder when $44121 \cdot x$ is divided by $63610$. Find the value of $Q$. | 20,572 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(13)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(13))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.046 | 2026-02-08T10:35:14.735060Z | {
"verified": true,
"answer": 20572,
"timestamp": "2026-02-08T10:35:14.780643Z"
} | b2b49b | 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": 1053
},
"timestamp": "2026-02-24T12:09:11.429Z",
"answer": 20572
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
95f40f | diophantine_fbi2_min_v1_151522320_2322 | Let $A$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 9000$, $\gcd(p, q) = 1$, and $p < q$. Let $B$ be the sum of all integers $k$ in the range $1 \leq k \leq 8$ and all integers $j$ in the range $1 \leq j \leq 10$. Define $u = \frac{A \cdot B}{40}$. Determine the ... | 6 | graphs = [
Graph(
let={
"_n": Const(40),
"_m": Const(2),
"k": Const(26),
"upper": Div(Mul(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'))... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_INDEPENDENT",
"SUM_ARITHMETIC"
] | 7b31c7 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 3 | 0.008 | 2026-02-08T04:44:13.061244Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T04:44:13.068750Z"
} | a30c3f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 1796
},
"timestamp": "2026-02-11T21:55:03.005Z",
"answer": 6
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"le... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
1bfca1 | algebra_quadratic_discriminant_v1_1742523217_1555 | Let $a = 4$, $b = -1$, $c = 2$, and $n = 2$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$. Define $m$ to be the maximum value of $xy$ over all pairs $(x, y) \in S$. Compute the value of $Q$, where $Q$ is the smallest positive integer $k$ such that the $k$-th Fibonacci numb... | 20 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(4),
"b": Const(-1),
"c": Const(2),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(... | NT | null | COMPUTE | sympy | MAX_VAL | [
"B1"
] | 5b950e | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B1",
"MAX_VAL"
] | 2 | 0.015 | 2026-02-08T04:02:39.610211Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T04:02:39.625326Z"
} | b39ad2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 783
},
"timestamp": "2026-02-10T16:35:46.834Z",
"answer": 20
},
{
"id":... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
711d7b | geo_count_lattice_rect_v1_168721529_1558 | Let $a = 289$ and $b = 255$. A lattice point is a point in the plane with integer coordinates. The rectangle $R$ consists of all points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$.
Let $N$ be the number of lattice points contained in $R$. Compute $N$. | 74,240 | graphs = [
Graph(
let={
"a": Const(289),
"b": Const(255),
"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 | 3 | 0 | null | null | 0.001 | 2026-02-08T13:46:57.531858Z | {
"verified": true,
"answer": 74240,
"timestamp": "2026-02-08T13:46:57.532376Z"
} | 2d31b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 478
},
"timestamp": "2026-02-09T18:52:50.541Z",
"answer": 74240
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
52da15 | algebra_poly_eval_v1_397696148_1976 | Let $p$ and $q$ be positive integers such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such values of $p$.
Define $m = 5$, $t = 12$, and compute the value of $5 \cdot t^n - 7 \cdot t + m$. Let $c$ be the smallest divisor of $19343$ that is at least $2$.
Compute the remainder when $c - (5 \... | 95,727 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 24b358 | algebra_poly_eval_v1 | negation_mod | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T12:52:53.194716Z | {
"verified": true,
"answer": 95727,
"timestamp": "2026-02-08T12:52:53.198656Z"
} | a36f6c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1140
},
"timestamp": "2026-02-15T06:40:56.177Z",
"answer": 95727
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cd4dae | modular_min_linear_v1_1439011603_2877 | Let $a = 37726$. Let $b$ be the number of integers $t$ such that $16 \leq t \leq 9720$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 47$, $1 \leq b' \leq 4784$, and $t = 3a' + 2b' + 11$. Let $m = 42465$. Define $S$ as the set of all integers $x$ such that $1 \leq x \leq m$ and $ax \equiv b \pmod{... | 34,918 | graphs = [
Graph(
let={
"a": Const(37726),
"b": 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=47)), Geq(left=Va... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_linear_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 1.817 | 2026-02-08T17:03:11.979640Z | {
"verified": true,
"answer": 34918,
"timestamp": "2026-02-08T17:03:13.797009Z"
} | a55d01 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 6321
},
"timestamp": "2026-02-17T17:52:03.675Z",
"answer": 34918
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
298a79 | sequence_lucas_compute_v1_717093673_2152 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 266$, $7$ divides $k$, and $\gcd(k, 15) = 1$. Compute the $n$-th Lucas number. | 24,476 | graphs = [
Graph(
let={
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(266)), Divides(divisor=Ref("_n"), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Const(15)), Const(1))))),
"result": Lucas(ar... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T16:35:48.584593Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T16:35:48.586161Z"
} | a88f0b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 1025
},
"timestamp": "2026-02-17T08:13:40.814Z",
"answer": 24476
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c35cf | antilemma_sum_equals_v1_2051736721_2603 | Let $S$ be the set of all integers $t$ such that $12 \le t \le 178$ and there exist positive integers $a$ and $b$ with $1 \le a \le 14$, $1 \le b \le 16$, and $t = 7a + 5b$. Let $c$ be the number of elements in $S$. Let $T$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \le i, j \le 141$ and... | 67 | graphs = [
Graph(
let={
"_c": 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=14)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS/COMB1/COUNT_SUM_EQUALS",
"LIN_FORM/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | a1fd80 | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.046 | 2026-02-08T16:48:48.836280Z | {
"verified": true,
"answer": 67,
"timestamp": "2026-02-08T16:48:48.881891Z"
} | 362acb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 4703
},
"timestamp": "2026-02-17T12:04:12.395Z",
"answer": 67
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM"... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
a7c019 | geo_visible_lattice_v1_2051736721_3614 | Let $n = 55$. Define a visible lattice point as a point $(x, y)$ with $1 \leq x, y \leq n$ such that $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points in the $n \times n$ grid. Compute the remainder when $28 - R$ is divided by $95501$. | 93,650 | graphs = [
Graph(
let={
"n": Const(55),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Sub(Const(28), Ref("result")), modulus=Const(95501)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.457 | 2026-02-08T17:25:58.154395Z | {
"verified": true,
"answer": 93650,
"timestamp": "2026-02-08T17:25:58.611584Z"
} | ceefe2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 3692
},
"timestamp": "2026-02-18T01:30:57.315Z",
"answer": 93650
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
ca4dfa | comb_count_surjections_v1_655260480_3983 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 7$, $1 \leq i \leq 5$, and $1 \leq j \leq 6$. Let $k = 2$. Compute the remainder when $84851 \cdot k! \cdot S(n, k)$ is divided by 62382, where $S(n, k)$ denotes the Stirling number of the second kind. | 50,250 | graphs = [
Graph(
let={
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T17:38:45.354723Z | {
"verified": true,
"answer": 50250,
"timestamp": "2026-02-08T17:38:45.366685Z"
} | e45495 | 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": 674
},
"timestamp": "2026-02-18T05:12:13.441Z",
"answer": 50250
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
fef37a | antilemma_sum_equals_v1_784195855_6317 | Let $A$ be the set of all ordered pairs of positive integers $(i, j)$ such that $i + j = 32$, $1 \le i \le 30$, and $1 \le j \le 31$. Let $x$ be the number of elements in $A$. Let $B$ be the Cartesian product $\{1, 2, \dots, 62\} \times \{1, 2, \dots, 62\}$, and let $y$ be the number of elements in $B$. Compute $y - x$... | 3,814 | graphs = [
Graph(
let={
"_n": Const(32),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(30)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | b5abab | antilemma_sum_equals_v1 | negation_mod | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T08:34:42.369594Z | {
"verified": true,
"answer": 3814,
"timestamp": "2026-02-08T08:34:42.381046Z"
} | 2ab707 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 791
},
"timestamp": "2026-02-24T09:40:47.496Z",
"answer": 3814
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
8ec958 | nt_count_gcd_equals_v1_655260480_2297 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 20831$ and $\gcd(n, 30) = 1$. Let $d = 169$. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \leq N$ and $\gcd(n_1, 169) = d$. Multiply this count by $24179$, then compute the remainder when the product is divided by $91909$. | 38,456 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(20831)), Eq(GCD(a=Var("n"), b=Const(30)), Const(1))))),
"k": Const(169),
"d": Const(169),
"result": CountOverSet(set=Solutio... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.447 | 2026-02-08T16:39:50.807062Z | {
"verified": true,
"answer": 38456,
"timestamp": "2026-02-08T16:39:51.254543Z"
} | b01312 | 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": 2255
},
"timestamp": "2026-02-17T08:28:50.915Z",
"answer": 38456
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ae0e6f | sequence_fibonacci_compute_v1_1520064083_4438 | Let $n = 24$. Define $F_n$ to be the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $C$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 62$ and $1 \leq j \leq 140$ such that $\gcd(i,j) = 1$. Compute the remainder when $C \cdot F_n$ is divided... | 55,204 | graphs = [
Graph(
let={
"n": Const(24),
"result": Fibonacci(arg=Ref(name='n')),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 53d469 | sequence_fibonacci_compute_v1 | affine_mod | 4 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T06:16:14.495364Z | {
"verified": true,
"answer": 55204,
"timestamp": "2026-02-08T06:16:14.496150Z"
} | 6dab1a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 3722
},
"timestamp": "2026-02-12T22:11:17.473Z",
"answer": 55204
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
6b7436_n | alg_sym_quad_system_v1_1218484723_6733 | An engineer analyzes vibration modes in a triangular framework. Each mode is described by positive integers $(a, b, c)$ representing three stiffness parameters, which must satisfy
$$a^{2} + b^{2} + c^{2} = ab + bc + ca$$
and
$$9a + 8b + 4c = K,$$
where $K$ is the number of distinct loads $t$ that can be produced in the... | 39,291 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sym_quad_system_v1 | null | 7 | null | [
"LIN_FORM"
] | 1 | 0.014 | 2026-02-25T08:14:57.639811Z | null | 938dac | 6b7436 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 328,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T01:48:12.799Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
80c557 | comb_count_surjections_v1_1440796553_145 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 7$, $1 \leq j \leq 8$, and $i + j = 9$. Compute $6! \cdot S(n, 6)$, where $S(n, 6)$ is the Stirling number of the second kind. | 15,120 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(9)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(8))))),
"k": Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T11:37:03.287023Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-08T11:37:03.299776Z"
} | bf2dab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 980
},
"timestamp": "2026-02-24T14:22:47.044Z",
"answer": 15120
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} |
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