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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5f9b7f | modular_min_linear_v1_1439011603_305 | Let $a = 5447$. Let $b$ be the number of positive integers $k$ such that $1 \leq k \leq 199410$ and $289$ divides $k$. Let $m = 10454$. Consider the set of all positive integers $x$ such that $1 \leq x \leq m$ and
$$
5447x \equiv b \pmod{10454}.
$$
Let $r$ be the smallest such $x$. Compute $r$. | 8,794 | graphs = [
Graph(
let={
"a": Const(5447),
"b": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(199410)), Divides(divisor=Const(289), dividend=Var("k"))), domain='positive_integers')),
"m": Const(10454),
"r... | ALG | NT | EXTREMUM | sympy | C2 | [
"C2"
] | 9685eb | modular_min_linear_v1 | null | 5 | 0 | [
"C2"
] | 1 | 0.425 | 2026-02-08T15:24:21.576215Z | {
"verified": true,
"answer": 8794,
"timestamp": "2026-02-08T15:24:22.001126Z"
} | 7571bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 2530
},
"timestamp": "2026-02-16T05:24:24.361Z",
"answer": 8794
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1bc817 | nt_count_coprime_v1_784195855_5137 | Let $k = 19$ and $n$ be a positive integer such that $1 \leq n \leq 43681$. Determine the number of such integers $n$ for which $\gcd(n, k) = \phi(1)$, where $\phi$ denotes Euler's totient function. | 41,382 | graphs = [
Graph(
let={
"upper": Const(43681),
"k": Const(19),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), EulerPhi(n=Const(1)))))),
},
goal=Ref("... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_coprime_v1 | null | 4 | 0 | [
"ONE_PHI_1"
] | 1 | 3.681 | 2026-02-08T07:41:51.658492Z | {
"verified": true,
"answer": 41382,
"timestamp": "2026-02-08T07:41:55.339242Z"
} | 84181a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 466
},
"timestamp": "2026-02-20T04:48:19.214Z",
"answer": 41382
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "n... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
c8b2ee | nt_min_crt_v1_865884756_6583 | Let $m = 7$ and $k = 8$. Find the smallest positive integer $n$ such that $1 \leq n \leq 56$, $n \equiv 3 \pmod{7}$, and $n \equiv 5 \pmod{8}$. Let $F_j$ denote the Fibonacci sequence defined by $F_1 = 1$, $F_2 = 1$, and $F_j = F_{j-1} + F_{j-2}$ for $j \geq 3$. Determine the smallest positive index $j$ such that $F_j$... | 16 | graphs = [
Graph(
let={
"m": Const(7),
"k": Const(8),
"a": Const(3),
"b": Const(5),
"upper": Const(56),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"V1"
] | dae96f | nt_min_crt_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR",
"V1"
] | 2 | 0.114 | 2026-02-08T19:18:14.455556Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T19:18:14.569440Z"
} | 228d34 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 2011
},
"timestamp": "2026-02-18T21:50:20.270Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
06c074 | nt_sum_divisors_mod_v1_784195855_3653 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 32400$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11579$. | 1,170 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11579)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T06:34:02.958164Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T06:34:02.959267Z"
} | e189b4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 299
},
"timestamp": "2026-02-15T17:35:37.893Z",
"answer": 3600
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
b8b223_n | alg_sum_powers_v1_1218484723_3425 | A game assigns points using cubes: on turn $k$, a player gains $k^3$ points, for $k = 1$ to $186$. The total score is reduced modulo $m$, where $m$ is the number of distinct point totals $t$ between $9$ and $4540$ that can be formed as $t = 2a + 7b$ with $1 \le a \le 1045$ and $1 \le b \le 350$. What is $48400$ minus t... | 46,943 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sum_powers_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.009 | 2026-02-25T05:07:55.128434Z | null | 2c5d38 | b8b223 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 6976
},
"timestamp": "2026-03-30T20:03:34.208Z",
"answer": 46943
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
7e7324 | antilemma_k2_v1_1742523217_127 | Compute
$$
\sum_{k=1}^{212} \phi(k) \left\lfloor \frac{212}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. | 22,578 | graphs = [
Graph(
let={
"_n": Const(212),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(212), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T02:53:17.837965Z | {
"verified": true,
"answer": 22578,
"timestamp": "2026-02-08T02:53:17.838497Z"
} | 069bee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 500
},
"timestamp": "2026-02-09T13:56:22.737Z",
"answer": 22578
},
{
"i... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -0.58,
"mid": 1.54,
"hi": 3.31
} | ||
f02f0c | nt_count_gcd_equals_v1_124444284_1108 | Let $ A $ be the number of integers $ t $ such that $ 19 \leq t \leq 141 $ and there exist positive integers $ a $ and $ b $ with $ 1 \leq a \leq 9 $, $ 1 \leq b \leq 34 $, and $ t = 7a + 2b + 10 $. Let $ B $ be the number of integers $ t $ such that $ 12 \leq t \leq 152 $ and there exist positive integers $ a $ and $ ... | 295 | graphs = [
Graph(
let={
"upper": Const(34596),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 2.72 | 2026-02-08T03:41:06.668465Z | {
"verified": true,
"answer": 295,
"timestamp": "2026-02-08T03:41:09.388805Z"
} | e4cbec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 5798
},
"timestamp": "2026-02-10T02:54:04.068Z",
"answer": 295
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
55f7ea | comb_catalan_compute_v1_1918700295_489 | Let $T$ be the set of all integers $t$ such that $22 \leq t \leq 61$ and there exist integers $a \in \{1,2\}$, $b \in \{1,2,3,4,5\}$ satisfying $t = 15a + 6b + 1$. Let $n$ be the number of elements in $T$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:17:26.358802Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:17:26.360277Z"
} | b92d54 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 848
},
"timestamp": "2026-02-10T13:44:49.150Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
d0440c | modular_inverse_v1_124444284_8804 | Let $x$ be a positive integer such that $1 \leq x \leq 336$ and
$$
33x \equiv 1 \pmod{337}.
$$
Determine the value of $x$. | 143 | graphs = [
Graph(
let={
"a": Const(33),
"m": Const(337),
"upper": Const(336),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Const... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_inverse_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.074 | 2026-02-08T11:55:05.123272Z | {
"verified": true,
"answer": 143,
"timestamp": "2026-02-08T11:55:05.197335Z"
} | 2532f5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 464
},
"timestamp": "2026-02-16T03:26:53.427Z",
"answer": 53
},
{
"id": 11,
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
46b51f | nt_num_divisors_compute_v1_1978505735_1911 | Let $n$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 160$. Compute the number of positive divisors of $n$. | 27 | graphs = [
Graph(
let={
"_n": Const(160),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T16:31:23.955186Z | {
"verified": true,
"answer": 27,
"timestamp": "2026-02-08T16:31:23.958013Z"
} | 32687a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 526
},
"timestamp": "2026-02-17T05:03:07.656Z",
"answer": 27
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2310c8 | nt_sum_divisors_compute_v1_124444284_876 | Let $p = 11$ and $t = (10! + 1) \mod p$. Let $n_1$ be the number of integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 181$, $1 \leq b \leq 63$, $7 \leq t \leq 913$, and $t = 4a + 3b$. Define $u = \sum_{d \mid n_1} \phi(d) - n_1$, where $\phi$ is Euler's totient function. Let $n = 3459... | 21,195 | graphs = [
Graph(
let={
"p": Const(11),
"t": Mod(value=Sum(Factorial(Sub(Ref("p"), Const(1))), Const(1)), modulus=Ref("p")),
"n1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/EULER_TOTIENT_SUM",
"WILSON"
] | 78be44 | nt_sum_divisors_compute_v1 | null | 7 | 2 | [
"EULER_TOTIENT_SUM",
"LIN_FORM",
"WILSON"
] | 3 | 0.006 | 2026-02-08T03:33:25.680706Z | {
"verified": true,
"answer": 21195,
"timestamp": "2026-02-08T03:33:25.686965Z"
} | b5a7a4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 308,
"completion_tokens": 3046
},
"timestamp": "2026-02-09T07:00:44.810Z",
"answer": 21195
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
35d113 | geo_count_lattice_rect_v1_655260480_1984 | Let $a = 196$ and $b = 62$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Find the remainder when $39983$ times this number is divided by 76398. | 24,003 | graphs = [
Graph(
let={
"a": Const(196),
"b": Const(62),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(39983),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(76398)),
},
goal=Ref("Q"),
)... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.003 | 2026-02-08T16:30:06.628483Z | {
"verified": true,
"answer": 24003,
"timestamp": "2026-02-08T16:30:06.631749Z"
} | 8dec19 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1520
},
"timestamp": "2026-02-24T21:10:39.569Z",
"answer": 24003
},
{
... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
d62122 | diophantine_fbi2_count_v1_865884756_925 | Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1156$. Let $T$ be the set of all integers $d$ such that $5 \leq d \leq m$, $d$ divides $1260$, and $4 \leq \frac{1260}{d} \leq 67$. Compute the remainder when $36825$ multiplied by the number of elements in $T$ is divid... | 23,995 | graphs = [
Graph(
let={
"_n": Const(67),
"k": Const(1260),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.036 | 2026-02-08T15:41:21.908177Z | {
"verified": true,
"answer": 23995,
"timestamp": "2026-02-08T15:41:21.944581Z"
} | 21307b | 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": 1623
},
"timestamp": "2026-02-16T10:56:35.336Z",
"answer": 23995
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c5e89a | antilemma_k3_v1_717093673_628 | Let $n = 45978$. Define $x$ to be the sum
$$
\sum_{d \mid n} \phi(d),
$$
where the sum is over all positive divisors $d$ of $n$ and $\phi$ denotes Euler's totient function. Compute the remainder when $44121 \cdot x$ is divided by 56752. | 51,850 | graphs = [
Graph(
let={
"_n": Const(45978),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(56752)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:34:34.026106Z | {
"verified": true,
"answer": 51850,
"timestamp": "2026-02-08T15:34:34.026644Z"
} | 65f095 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 2101
},
"timestamp": "2026-02-16T08:28:54.972Z",
"answer": 51850
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2e7bb1 | sequence_fibonacci_compute_v1_784195855_9296 | Let $n$ be the number of integers $t$ with $20 \leq t \leq 84$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 7$, and $t = 14a + 6b$. Compute the $n$-th Fibonacci number. | 10,946 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:40:50.196640Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T16:40:50.198218Z"
} | 3a5a5a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1500
},
"timestamp": "2026-02-17T09:27:40.924Z",
"answer": 10946
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6d889e | nt_count_gcd_equals_v1_1439011603_2501 | Let $p_0$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $pq = 216$ and $\gcd(p, q) = 1$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 20250000$. Let $k$ be the smallest divisor of $194477$ that is at least $p_0$. Com... | 20 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=216)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR",
"B3"
] | f8b22e | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 3 | 0.848 | 2026-02-08T16:50:17.261959Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T16:50:18.110057Z"
} | 4c62bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 2543
},
"timestamp": "2026-02-17T13:31:20.918Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
23f4b2 | comb_bell_compute_v1_677425708_3201 | Let $n$ be the number of integers $t$ with $8 \leq t \leq 18$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 2a + 3b + 3$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. Let $Q$ be the remainder when ... | 62,722 | graphs = [
Graph(
let={
"_n": Const(73945),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:32:16.568430Z | {
"verified": true,
"answer": 62722,
"timestamp": "2026-02-08T05:32:16.569579Z"
} | fa28b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 2495
},
"timestamp": "2026-02-24T04:05:30.858Z",
"answer": 62722
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
7999ec | algebra_quadratic_discriminant_v1_1742523217_3037 | Let $a = 2$, $b = -20$, and let $c$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 625$. Define $\Delta = b^2 - 4ac$. Compute $44121 \cdot \Delta$. | 0 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": Const(2),
"b": Const(-20),
"c": 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"), V... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T05:30:27.882982Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T05:30:27.884234Z"
} | 3646ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 554
},
"timestamp": "2026-02-12T11:44:09.386Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
ca6ac2 | geo_count_lattice_triangle_v1_153355830_1996 | Let
$$A = \left|180\cdot 144 + 43\left(0 - \sum_{k=1}^{17} \varphi(k)\left\lfloor\frac{17}{k}\right\rfloor\right)\right|,$$
where $\varphi$ is Euler's totient function.
Let $U$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 8100$, and let $m$ be the minimum value of $x+y$ over all $(x,y)$... | 9,666 | graphs = [
Graph(
let={
"_c": Const(17),
"_m": Const(2),
"_n": Const(153),
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=144)), Mul(Const(value=43), Sub(left=Const(value=0), right=Summation(expr=Mul(EulerPhi(n=Var(name='k')), Floor(arg=Div(left=Cons... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"B3",
"K2"
] | b81c9e | geo_count_lattice_triangle_v1 | null | 8 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"K2"
] | 3 | 0.014 | 2026-02-08T06:50:46.725864Z | {
"verified": true,
"answer": 9666,
"timestamp": "2026-02-08T06:50:46.740106Z"
} | d6b190 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 1953
},
"timestamp": "2026-02-13T05:17:05.056Z",
"answer": 9666
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
59ce85 | comb_count_surjections_v1_784195855_5679 | Let $n_1 = 0$ and $n_2 = 0$. Define $u = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$ and $w = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n = 7u$ and $k = 3w$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. | 1,806 | graphs = [
Graph(
let={
"n2": Const(0),
"w": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"u": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_surjections_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T08:02:15.237025Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T08:02:15.238099Z"
} | 257f7f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 774
},
"timestamp": "2026-02-24T08:43:51.811Z",
"answer": 1806
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
ee3a3d | comb_binomial_compute_v1_677425708_3143 | Let $n = 15$ and let $k = \sum_{i=1}^{3} i$. Compute $\binom{n}{k}$. | 5,005 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(15),
"k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_binomial_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T05:30:25.722456Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-02-08T05:30:25.724163Z"
} | 99b5bd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 487
},
"timestamp": "2026-02-24T03:49:13.900Z",
"answer": 5005
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
d16b1d | comb_binomial_compute_v1_971394319_547 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 2286900$. Compute $\binom{n}{9}$. | 11,440 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=2286900)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_binomial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T13:10:03.924333Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T13:10:03.925665Z"
} | 248dcd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1392
},
"timestamp": "2026-02-15T10:46:21.652Z",
"answer": 11440
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
22ad01 | comb_count_surjections_v1_1520064083_9656 | Let $n = 6$. Consider all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 6$ and $1 \leq j \leq 6$ such that $i + j = 6$. Let $k$ be the number of such pairs. Define $R = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the remainder when $89093 \cdot R$ is divided by $7001... | 44,500 | graphs = [
Graph(
let={
"n": Const(6),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T10:57:14.227513Z | {
"verified": true,
"answer": 44500,
"timestamp": "2026-02-08T10:57:14.238196Z"
} | 7b1889 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 1565
},
"timestamp": "2026-02-24T12:30:24.482Z",
"answer": 44500
},
{
"... | 1 | [
{
"lemma": "C2",
"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",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
9c0345 | nt_min_phi_inverse_v1_168721529_896 | Find the smallest positive integer $n \leq 50$ such that $\phi(n) = 12$. | 13 | graphs = [
Graph(
let={
"upper": Const(50),
"k": Const(12),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
},
goal=Ref("result"),
)
] | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"LTE_SUM/MAX_PRIME_BELOW/MAX_VAL"
] | b866a6 | nt_min_phi_inverse_v1 | null | 4 | 0 | [
"LTE_SUM",
"MAX_PRIME_BELOW",
"MAX_VAL",
"MOBIUS_COPRIME"
] | 4 | 0.119 | 2026-02-08T13:20:36.402346Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T13:20:36.520924Z"
} | dba975 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1281
},
"timestamp": "2026-02-09T10:28:37.701Z",
"answer": 13
},
{
"id"... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -1.93,
"mid": 2.14,
"hi": 6.33
} | ||
5d543a | nt_count_with_divisor_count_v1_124444284_5106 | Let $t$ be an integer such that $36 \leq t \leq 699$. Let $N$ be the number of values of $t$ for which there exist positive integers $a \leq 27$ and $b \leq 14$ such that $t = 15a + 21b$. Let $M$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = N$. Determine the value of $441... | 88,242 | graphs = [
Graph(
let={
"_m": Const(44121),
"_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=27)), Geq(left=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 1.823 | 2026-02-08T06:23:44.350723Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T06:23:46.173353Z"
} | d77e11 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 5447
},
"timestamp": "2026-02-12T23:42:53.587Z",
"answer": 88242
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemm... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f52c79 | modular_inverse_v1_971394319_1159 | Let $a$ be the sum of all positive integers $n$ at most $270$ that are divisible by $135$. Let $m = 929$. Let $u$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 215296$. Let $r$ be the smallest positive integer $x$ such that $1 \leq x \leq u$ and $a \cdot x \equiv 1 \pmod{m... | 17,867 | graphs = [
Graph(
let={
"_m": Const(135),
"_n": Const(64149),
"a": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(270)), Eq(Mod(value=Var("n"), modulus=Ref("_m")), Const(0))))),
"m": Const(929),
... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE",
"B3"
] | 26d1a5 | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.04 | 2026-02-08T13:31:01.692966Z | {
"verified": true,
"answer": 17867,
"timestamp": "2026-02-08T13:31:01.732591Z"
} | 421417 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1443
},
"timestamp": "2026-02-15T16:37:44.150Z",
"answer": 17867
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9e99a7 | lin_form_endings_v1_677425708_2810 | Let $a = 9$ and $b = 21$. Let $k = 4$ and let $L$ be the least common multiple of $a$ and $b$. Define $s = kL + a + b$. Compute the remainder when $15209 \cdot s$ is divided by $62333$. | 50,294 | graphs = [
Graph(
let={
"a_coeff": Const(9),
"b_coeff": Const(21),
"k_val": Const(4),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scale... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:16:51.157987Z | {
"verified": true,
"answer": 50294,
"timestamp": "2026-02-08T05:16:51.158809Z"
} | 6b12b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 657
},
"timestamp": "2026-02-12T06:31:09.255Z",
"answer": 50294
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f032df | nt_sum_totient_over_divisors_v1_784195855_8103 | Let $m = 70$ and $n_0 = 2$. Define $S$ as the set of all positive integers $n$ such that
\begin{itemize}
\item $1 \leq n \leq \sum_{k=1}^{70} \phi(k) \left\lfloor \frac{70}{k} \right\rfloor$, and
\item the sum of the decimal digits of $n$ leaves a remainder of 1 when divided by 2.
\end{itemize}
Let $N$ be the number of... | 1,243 | graphs = [
Graph(
let={
"_m": Const(70),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(70), Var("k"))))... | NT | null | COMPUTE | sympy | K2 | [
"K2/L3B"
] | e3cab0 | nt_sum_totient_over_divisors_v1 | null | 7 | 0 | [
"K2",
"L3B"
] | 2 | 0.003 | 2026-02-08T10:49:29.952894Z | {
"verified": true,
"answer": 1243,
"timestamp": "2026-02-08T10:49:29.955866Z"
} | 150df6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 2992
},
"timestamp": "2026-02-16T16:07:44.205Z",
"answer": 1243
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a6f95e | alg_qf_psd_min_v1_601307018_7491 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 35$ and $1 \le b \le 35$ such that
$$25b^{2} + 34a^{2} + 22ab \le 18225.$$
Let $Q$ be the minimum value of
$$1100996\,a_1^{2} + 677536\,b_1^{2} - 1693840\,a_1b_1$$
over all ordered pairs $(a_1, b_1)$ of positive integers with $1 \le ... | 84,692 | graphs = [
Graph(
let={
"_c": Const(10),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Leq(Sum(Mul(Const(25), Pow(Var("b"), Const(2))), ... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF/QF_PSD_MIN/QF_PSD_DISTINCT",
"QF_PSD_COUNT_LEQ/QF_PSD_MIN"
] | b619ce | alg_qf_psd_min_v1 | null | 8 | 0 | [
"B3_DIFF",
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT",
"QF_PSD_MIN"
] | 4 | 1.219 | 2026-03-10T08:01:38.589265Z | {
"verified": true,
"answer": 84692,
"timestamp": "2026-03-10T08:01:39.808256Z"
} | 18a5cd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 473,
"completion_tokens": 11751
},
"timestamp": "2026-04-19T06:52:27.513Z",
"answer": 84692
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
547c82 | alg_qf_psd_count_v1_1218484723_6304 | Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 295$ and
$$1 \le b \le \left|\bigl\{(a1, b1) : 1 \le a1 \le 40,\, 1 \le b1 \le 40,\\ 10a1^{2} - 18a1b1 + \left|\bigl\{(a2, b2) : 1 \le a2 \le 25,\, 1 \le b2 \le 25,\, 16b2^{2} = 64\bigr\}\right| b1^{2} \\\le \left|\bigl\{t : \text{th... | 10 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(40),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(295)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSe... | ALG | null | COUNT | sympy | LIN_FORM | [
"QF_PSD_COUNT/QF_PSD_COUNT_LEQ",
"LIN_FORM/QF_PSD_COUNT_LEQ"
] | ba3525 | alg_qf_psd_count_v1 | null | 7 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 2.477 | 2026-02-25T07:52:16.258781Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-25T07:52:18.736086Z"
} | 1162c9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 387,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T01:09:49.794Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
a573fd | geo_visible_lattice_v1_458359167_4077 | Let $n = 55$. Define $S$ to be the set of all ordered pairs $(x, y)$ of positive integers such that $1 \le x, y \le n$ and $\gcd(x, y) = 1$. Let $r$ be the number of elements in $S$. Compute the Bell number $B_m$, where $m$ is the remainder when $|r|$ is divided by $11$. | 21,147 | graphs = [
Graph(
let={
"n": Const(55),
"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 | 0.245 | 2026-02-08T11:30:03.955909Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T11:30:04.200608Z"
} | 6393ae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 4331
},
"timestamp": "2026-02-24T14:11:01.814Z",
"answer": 21147
},
{
"... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||||
1fa4c2 | nt_count_divisors_in_range_v1_48377204_3176 | Let $ n = 83160 $. Let $ a = 36 $ and let $ b $ be the sum of Euler's totient function $ \phi(d) $ over all positive divisors $ d $ of 2972. Determine the number of positive divisors $ d_1 $ of $ n $ such that $ a \leq d_1 \leq b $. | 84 | graphs = [
Graph(
let={
"n": Const(83160),
"a": Const(36),
"b": SumOverDivisors(n=Const(value=2972), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": CountOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Divides(divisor=Var("d1"), dividend=Ref("n")), G... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.034 | 2026-02-08T17:13:26.357014Z | {
"verified": true,
"answer": 84,
"timestamp": "2026-02-08T17:13:26.390868Z"
} | 606171 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 2549
},
"timestamp": "2026-02-17T21:44:43.865Z",
"answer": 84
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
742d2d | modular_min_modexp_v1_1915831931_2021 | Let $m$ be the largest prime number less than or equal to the number of integers $t$ with $21 \le t \le 1179$ for which there exist positive integers $a \le 107$ and $b \le 18$ such that $t = 9a + 12b$. Let $u$ be the number of positive integers $k \le 23976$ that are divisible by $444$. Determine the smallest positive... | 26,220 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(11),
"b": Const(185),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condit... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"C2"
] | c04a9a | modular_min_modexp_v1 | null | 6 | 0 | [
"C2",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.079 | 2026-02-08T16:35:24.116019Z | {
"verified": true,
"answer": 26220,
"timestamp": "2026-02-08T16:35:24.194786Z"
} | ad12fd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 5329
},
"timestamp": "2026-02-17T07:00:04.667Z",
"answer": 26220
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cbcec6 | nt_count_digit_sum_v1_153355830_746 | Let $S$ be the sum of the integers from $1$ to $7$. Let $N$ be the number of positive integers $n \leq 161604$ such that the sum of the decimal digits of $n$ equals $S$. Let $Q$ be the remainder when $45272 \cdot N$ is divided by $94965$.
Compute $Q$. | 2,066 | graphs = [
Graph(
let={
"_n": Const(7),
"upper": Const(161604),
"target_sum": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("uppe... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_digit_sum_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 6.174 | 2026-02-08T04:09:26.000171Z | {
"verified": true,
"answer": 2066,
"timestamp": "2026-02-08T04:09:32.174163Z"
} | 7c3da5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 7539
},
"timestamp": "2026-02-10T15:31:59.656Z",
"answer": 2066
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
a08e95 | diophantine_fbi2_count_v1_124444284_5139 | Let $d_{\text{min}}$ be the smallest divisor of $1225$ that is at least $2$. Compute the number of positive divisors $d$ of $120$ such that $d_{\text{min}} \leq d \leq 68$, and $4 \leq \frac{120}{d} \leq 67$. | 9 | graphs = [
Graph(
let={
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1225)))))), Leq(Var("d"), Const(68)), D... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID",
"MIN_PRIME_FACTOR"
] | 2 | 0.404 | 2026-02-08T06:24:57.426096Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T06:24:57.830152Z"
} | f682bd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 803
},
"timestamp": "2026-02-12T23:40:56.009Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
f26939 | comb_count_derangements_v1_601307018_2017 | Let $D_n$ denote the number of derangements of $n$ elements. For each integer $a$ with $0 \le a \le 2808$, define $M = a^2 - 603 \bmod 2809$ and $R = M^2 - 603 \bmod 2809$. Let $S$ be the number of such $a$ for which $R = a$ and $M \ne a$. Let $n = \sum_{k=0}^{S} 2^k$. Compute $D_n$. | 1,854 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(2808)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))),
"n": Summation(var="k", start=Const(0), end=Ref("_n")... | COMB | null | COUNT | sympy | HALFPLANE_COUNT | [
"POLY_ORBIT_HENSEL/SUM_GEOM"
] | 8a1734 | comb_count_derangements_v1 | null | 8 | 0 | [
"HALFPLANE_COUNT",
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 3 | 0.236 | 2026-03-10T02:45:08.379759Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-03-10T02:45:08.615756Z"
} | fb18dd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 6884
},
"timestamp": "2026-04-18T16:01:21.932Z",
"answer": 1854
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
},
{
"lemma": "V7",
... | {
"lo": 1.36,
"mid": 4.42,
"hi": 6.81
} | ||
936af3 | nt_count_coprime_v1_717093673_1235 | Let $k$ be the largest prime number less than or equal to $26$. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \leq 50400$ and $\gcd(n_1, k) = 1$. | 48,209 | graphs = [
Graph(
let={
"_n": Const(26),
"upper": Const(50400),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditi... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 4.147 | 2026-02-08T15:58:19.135207Z | {
"verified": true,
"answer": 48209,
"timestamp": "2026-02-08T15:58:23.281977Z"
} | a8dda8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 571
},
"timestamp": "2026-02-16T17:16:32.108Z",
"answer": 48209
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c7f003 | comb_count_derangements_v1_153355830_1543 | Let $n = 7$. Let $r$ be the number of derangements of $n$ elements. Let $d$ be the smallest divisor of 17303 that is at least 2. Compute the Bell number $B_{|r| \bmod d}$. | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | comb_count_derangements_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T06:29:19.801198Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T06:29:19.802727Z"
} | 36f72c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1165
},
"timestamp": "2026-02-13T00:49:29.334Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
7d7c5a | nt_count_gcd_equals_v1_151522320_2391 | Let $k=13$ and $d=13$. Let $N$ be the number of integers $n$ such that $1\le n\le 6561$ and $\gcd(n,k)=d$.
Let
$$Q\equiv 83121\cdot N\pmod{61490},$$
with $0\le Q<61490$.
Compute $Q$. | 18,294 | graphs = [
Graph(
let={
"upper": Const(6561),
"k": Const(13),
"d": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
"Q... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/C3/MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 81a593 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"C3",
"LIN_FORM",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 4 | 2.646 | 2026-02-08T04:47:27.302422Z | {
"verified": true,
"answer": 18294,
"timestamp": "2026-02-08T04:47:29.948129Z"
} | 372dd9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 697
},
"timestamp": "2026-02-11T21:56:02.276Z",
"answer": 18294
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"statu... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
797c48 | comb_catalan_compute_v1_1915831931_2779 | Let $m = 10$. Let $k$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 9$, $1 \leq j \leq 10$, and $i + j = m$. Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = k$. Compute the $n$th Catalan number. | 16,796 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1"
] | 5b2e59 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.091 | 2026-02-08T17:08:21.826938Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T17:08:21.917657Z"
} | 8ffb68 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1854
},
"timestamp": "2026-02-17T20:19:34.576Z",
"answer": 16796
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
930a1a | nt_sum_divisors_compute_v1_153355830_574 | Compute the sum of all positive divisors of 47524. | 83,937 | graphs = [
Graph(
let={
"n": Const(47524),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"WILSON"
] | 9e4f5c | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"WILSON"
] | 2 | 0.002 | 2026-02-08T03:10:21.206864Z | {
"verified": true,
"answer": 83937,
"timestamp": "2026-02-08T03:10:21.208996Z"
} | 692d4c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 971
},
"timestamp": "2026-02-10T15:14:48.001Z",
"answer": 83937
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
63ac46_n | comb_factorial_compute_v1_1218484723_2342 | A lab is cataloging experimental setups, each described by two positive integers $(a,b)$ with $1 \le a \le 30$ and $1 \le b \le 30$. For each setup, a complexity score is computed as
$$108ab^{2} + M\,a^{2}b + C\,b^{3} + 64a^{E},$$
where
$$M = \min\{x + y : x, y > 0,\ xy = 5184\},$$
$$C = \left|\{(a_1,b_1) : 1 \le a_1 \... | 40,320 | COMB | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/POLY3_COUNT",
"K2/POLY3_COUNT",
"B3/POLY3_COUNT"
] | ddf00d | comb_factorial_compute_v1 | null | 7 | null | [
"B3",
"K2",
"POLY3_COUNT",
"QF_PSD_COUNT"
] | 4 | 0.032 | 2026-02-25T04:09:44.150614Z | null | a68e8b | 63ac46 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 374,
"completion_tokens": 2306
},
"timestamp": "2026-03-30T18:18:35.805Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_lat... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
6ee2cc | antilemma_k2_v1_349078426_1524 | Let $x = \sum_{k=1}^{58} \phi(k) \left\lfloor \frac{58}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the remainder when $\sum_{d \mid 256} \phi(d) - x$ is divided by $73507$. | 72,052 | graphs = [
Graph(
let={
"_n": Const(58),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(58), Var("k"))))),
"Q": Mod(value=Sub(SumOverDivisors(n=Const(value=256), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("x")), mo... | NT | COMB | COMPUTE | sympy | K13 | [
"K3",
"K2"
] | dd2711 | antilemma_k2_v1 | negation_mod | 5 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.004 | 2026-02-08T13:41:53.340136Z | {
"verified": true,
"answer": 72052,
"timestamp": "2026-02-08T13:41:53.344069Z"
} | 94a9f9 | 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": 1210
},
"timestamp": "2026-02-15T19:59:50.989Z",
"answer": 72052
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f7dd50 | alg_poly3_min_v1_1218484723_3028 | Let $C = \min\{ 18a_1b_1^2 + 36a_1^2b_1 + 9b_1^3 : a_1, b_1 \in \mathbb{Z}^+,\, 1 \leq a_1, b_1 \leq 26 \}$. Find the remainder when $$\min\{ -81a^2b - 27ab^2 - 9b^3 : a, b \in \mathbb{Z}^+,\, 1 \leq a \leq 63,\, 1 \leq b \leq C \}$$ is divided by $61683$. | 43,926 | graphs = [
Graph(
let={
"_n": Const(36),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(63)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=Solu... | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | alg_poly3_min_v1 | null | 6 | 0 | [
"POLY3_MIN"
] | 1 | 0.014 | 2026-02-25T04:47:08.727624Z | {
"verified": true,
"answer": 43926,
"timestamp": "2026-02-25T04:47:08.741230Z"
} | e894b1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 2950
},
"timestamp": "2026-03-29T07:57:13.543Z",
"answer": 43926
},
{
"... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
3d01ff | nt_count_digit_sum_v1_717093673_3387 | Let $n = 92146$. Let $s$ be the largest integer $k$ such that $3^k \leq 9234553868882$. Let $c$ be the number of positive integers $m$ with $1 \leq m \leq 357604$ such that the sum of the decimal digits of $m$ equals $s$. Compute the remainder when $44121 \times c$ is divided by $n$. | 70,635 | graphs = [
Graph(
let={
"_n": Const(92146),
"upper": Const(357604),
"target_sum": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(3), Var("k")), Const(9234553868882)))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(... | NT | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"MAX_VAL"
] | 1 | 16.887 | 2026-02-08T17:33:47.534466Z | {
"verified": true,
"answer": 70635,
"timestamp": "2026-02-08T17:34:04.421566Z"
} | c9fec9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 6326
},
"timestamp": "2026-02-18T04:01:00.953Z",
"answer": 70635
},
... | 1 | [
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4080fd | lte_diff_endings_v1_1742523217_1141 | Let $a = 35$, $b = 8$, $p = 3$, and $n = 1134$. Compute the largest integer $k$ such that $p^k$ divides $a^n - b^n$. Multiply this $k$ by $6370$, and compute the remainder when the result is divided by $68246$. | 44,590 | graphs = [
Graph(
let={
"a_val": Const(35),
"b_val": Const(8),
"p_val": Const(3),
"n_val": Const(1134),
"a_pow": Pow(Ref("a_val"), Ref("n_val")),
"b_pow": Pow(Ref("b_val"), Ref("n_val")),
"pow_diff": Sub(Ref("a_pow"), Ref("b... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 7 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:28:28.509837Z | {
"verified": true,
"answer": 44590,
"timestamp": "2026-02-08T03:28:28.510554Z"
} | 1dd7fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 636
},
"timestamp": "2026-02-10T04:01:15.268Z",
"answer": 44590
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
0520be | v7_endings_v1_548369836_191 | Compute the number of integers $k$ such that $0 \leq k \leq 3440$ and the largest integer $e$ for which $5^e$ divides $\binom{3440}{k}$ is exactly 3. | 1,004 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(3440)), Eq(MaxKDivides(target=Binom(n=Const(3440), k=Var("k")), base=Const(5)), Const(3))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.003 | 2026-02-08T02:48:20.029271Z | {
"verified": true,
"answer": 1004,
"timestamp": "2026-02-08T02:48:20.031781Z"
} | de8f93 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 7468
},
"timestamp": "2026-02-08T20:11:59.369Z",
"answer": 1004
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": 1.3,
"mid": 4.19,
"hi": 6.61
} | ||
fd1c29 | alg_poly_orbit_hensel_v1_601307018_3768 | For each non-negative integer $a$, define $N = (a^3 + a^2 - 4a + 4) \bmod 289$ and $M = (N^3 + N^2 - 4N + 4) \bmod 289$. Find the number of integers $a$ with $0 \le a \le 146811$ such that $M = a$ and $N \ne a$. | 1,016 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Pow(Var("a"), Const(2)), Mul(Const(-4), Var("a")), Const(4)), modulus=Const(289)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Pow(Ref("p1"), Const(2)), Mul(Const(-4), Ref("p1")), Const(4)), modulus=Const(289)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.014 | 2026-03-10T04:20:57.733318Z | {
"verified": true,
"answer": 1016,
"timestamp": "2026-03-10T04:20:57.747639Z"
} | d5490c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 9987
},
"timestamp": "2026-03-29T10:01:08.156Z",
"answer": 2
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
b1cbc8 | comb_count_derangements_v1_1520064083_845 | Let $d$ be the smallest integer greater than or equal to $2$ that divides $77$. Compute the number of derangements of $d$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(77))))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T03:37:47.218927Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T03:37:47.219687Z"
} | b67005 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 691
},
"timestamp": "2026-02-10T15:07:34.533Z",
"answer": 1854
},
{
"id... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
231ae6 | sequence_count_fib_divisible_v1_458359167_2622 | Let $m = \sum_{d \mid 198} \phi(d)$. Find the number of positive integers $n \leq m$ such that $11$ divides the $n$-th Fibonacci number. | 19 | graphs = [
Graph(
let={
"upper": SumOverDivisors(n=Const(value=198), var='d', expr=EulerPhi(n=Var(name='d'))),
"d": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"K3"
] | 54c41e | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"K3",
"MAX_DIVISOR"
] | 2 | 0.036 | 2026-02-08T06:23:01.247530Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T06:23:01.283609Z"
} | 1a2476 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 1564
},
"timestamp": "2026-02-13T03:13:29.025Z",
"answer": 19
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
1fa2dd | geo_count_lattice_triangle_v1_1526740231_397 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(111,13)$, and $(21,120)$, multiplied by 2. Let $B$ be the number of lattice points on the boundary of this triangle. Compute the remainder when $44121 \cdot \frac{A + 2 - B}{2}$ is divided by $61067$. | 9,458 | graphs = [
Graph(
let={
"_n": Const(21),
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=120)), Mul(Const(value=21), Sub(left=Const(value=0), right=Const(value=13))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const(value=13))), GCD(a=Abs(arg=Su... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T11:30:39.038884Z | {
"verified": true,
"answer": 9458,
"timestamp": "2026-02-08T11:30:39.043764Z"
} | 983ef9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 2392
},
"timestamp": "2026-02-14T15:10:43.984Z",
"answer": 9458
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
49137a | sequence_count_fib_divisible_v1_48377204_923 | Let $u = 945$ and $d = 8$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $F_n$ is divisible by $d$, where $F_n$ denotes the $n$th Fibonacci number. Let $r$ be this count. Find the smallest positive integer $k$ such that $F_k$ is divisible by $r + 2$. | 108 | graphs = [
Graph(
let={
"upper": Const(945),
"d": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
"Q": Fibo... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.034 | 2026-02-08T15:45:35.244567Z | {
"verified": true,
"answer": 108,
"timestamp": "2026-02-08T15:45:37.278830Z"
} | 0ef0e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 2157
},
"timestamp": "2026-02-16T13:24:16.568Z",
"answer": 108
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ca646f | comb_binomial_compute_v1_2051736721_1487 | Let $n = 15$ and let $k = \sum_{k1=1}^{3} k1$. Compute $\binom{n}{k}$. | 5,005 | graphs = [
Graph(
let={
"n": Const(15),
"k": Summation(var="k1", start=Const(1), end=Const(3), expr=Var("k1")),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_binomial_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T16:04:05.344885Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-02-08T16:04:05.346468Z"
} | 4909e3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 420
},
"timestamp": "2026-02-24T19:47:50.966Z",
"answer": 5005
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
76ab0b | nt_sum_divisors_mod_v1_1978505735_5137 | Let $x$ and $y$ be positive integers such that $xy = 396900$. Let $n$ be the minimum possible value of $x + y$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11491$. | 4,368 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11491... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T18:47:55.318738Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T18:47:55.320439Z"
} | c4326b | 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": 1404
},
"timestamp": "2026-02-18T19:48:15.109Z",
"answer": 4368
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c2b163 | nt_sum_divisors_mod_v1_1874849503_1015 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Define $\text{result}$ as the remainder when $\sigma$ is divided by $11161$. Let $Q$ be the remaind... | 5,343 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11161... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T13:30:28.641867Z | {
"verified": true,
"answer": 5343,
"timestamp": "2026-02-08T13:30:28.645881Z"
} | a7c5c8 | 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": 1791
},
"timestamp": "2026-02-09T23:57:48.371Z",
"answer": 5343
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
22949f | antilemma_sum_factor_cartesian_v1_1520064083_3001 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $c = |P|$. Let $\phi_c = \phi(c)$. Let $S$ be the set of all ordered pairs $(i, j)$ of integers with $1 \le i \le 12$ and $1 \le j \le 20$. Compute
$$
\sum_{(i,j) \in S} i \cd... | 16,380 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(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(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/ONE_PHI_2/SUM_FACTOR_CARTESIAN",
"SUM_FACTOR_CARTESIAN"
] | 0bec54 | antilemma_sum_factor_cartesian_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.001 | 2026-02-08T05:24:21.740668Z | {
"verified": true,
"answer": 16380,
"timestamp": "2026-02-08T05:24:21.741829Z"
} | 4f2d5c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 660
},
"timestamp": "2026-02-18T16:20:19.019Z",
"answer": 98280
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": ... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
f736b3 | nt_count_with_divisor_count_v1_349078426_1592 | Let $n = 6$. Consider all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $P$ be the set of all values of $xy$ for such pairs. Let $d_{\text{max}}$ be the maximum value in $P$. Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 75025$ and the number of positive divisors of $k... | 82 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(75025),
"div_count": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"B1"
] | 1 | 8.379 | 2026-02-08T13:44:02.655601Z | {
"verified": true,
"answer": 82,
"timestamp": "2026-02-08T13:44:11.034200Z"
} | c52d8b | 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": 2126
},
"timestamp": "2026-02-15T20:04:41.805Z",
"answer": 82
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
7a6700 | comb_sum_binomial_row_v1_458359167_2077 | Let $n$ be an integer. Consider the set of all prime numbers $n$ such that $2 \leq n \leq 13$. Let $p$ be the largest prime in this set.
Compute $2^p$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(13),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T05:07:09.710872Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T05:07:09.713190Z"
} | ccd25d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 302
},
"timestamp": "2026-02-11T22:54:49.344Z",
"answer": 8192
},
{
"id... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
b62f39 | nt_max_prime_below_v1_784195855_6725 | Let $N$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 29$, $1 \leq j \leq 166$, and $\gcd(i,j) = 1$. Let $p$ be the largest prime number $n$ such that $2 \leq n \leq 11821$. Let $q$ be the largest prime number at most $N$, and let $r$ be the largest prime number at most $400$. Com... | 14,696 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(29)), right=IntegerRange(start=Const(1), end=... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID/MAX_PRIME_BELOW"
] | d6c842 | nt_max_prime_below_v1 | two_moduli | 7 | 0 | [
"COUNT_COPRIME_GRID",
"MAX_PRIME_BELOW"
] | 2 | 0.279 | 2026-02-08T08:49:10.763883Z | {
"verified": true,
"answer": 14696,
"timestamp": "2026-02-08T08:49:11.043340Z"
} | 6e88a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 3548
},
"timestamp": "2026-02-13T21:58:56.198Z",
"answer": 14696
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ccf230 | geo_count_lattice_triangle_v1_1918700295_32 | Let $A$ be twice the area of a triangle with vertices at $(0,0)$, $(105,200)$, and $(16,0)$, given by
\[
A = \left| 105 \cdot 200 + 16 \cdot (0 - J) \right|,
\]
where $J$ is the number of positive integers $j$ such that $1 \le j \le 200$ and $j^2 \le 40000$.
Let $B$ be the sum of the greatest common divisors of the ab... | 8,850 | graphs = [
Graph(
let={
"_n": Const(200),
"area_2x": Abs(arg=Sum(Mul(Const(value=105), Const(value=200)), Mul(Const(value=16), Sub(left=Const(value=0), right=CountOverSet(set=SolutionsSet(var=Var(name='j'), condition=And(Geq(left=Var(name='j'), right=Const(value=1)), Leq(left=Var(nam... | ALG | NT | COUNT | sympy | C3 | [
"C3"
] | 8a214c | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"C3"
] | 1 | 0.007 | 2026-02-08T02:57:31.122871Z | {
"verified": true,
"answer": 8850,
"timestamp": "2026-02-08T02:57:31.130195Z"
} | d0149a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 308,
"completion_tokens": 2167
},
"timestamp": "2026-02-23T20:41:39.269Z",
"answer": 8850
},
{
"i... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.06,
"mid": 0.33,
"hi": 2.31
} | ||
67fb61 | comb_factorial_compute_v1_1978505735_6095 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 3104$ and $\binom{3104}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(3104),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(3104)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T19:24:49.774024Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T19:24:49.775483Z"
} | 80dfec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 2356
},
"timestamp": "2026-02-18T22:23:40.817Z",
"answer": 40320
},
{... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
3af47f | alg_qf_psd_orbit_v1_1218484723_628 | Let $T$ be the number of integer pairs $(a_3, b_3)$ with $1 \le a_3, b_3 \le 40$ such that $2b_3^4 + 8a_3^3b_3 + 12a_3^2b_3^2 + 2a_3^4 + 8a_3b_3^3 = 13530402$. Let $U$ be the number of integer pairs $(a_2, b_2)$ with $1 \le a_2 \le 30$, $1 \le b_2 \le T$, and $34a_2^2 - 2a_2b_2 + 5b_2^2 = 10985$. Let $S$ be the set of ... | 5 | graphs = [
Graph(
let={
"_c": Const(3),
"_m": Const(2),
"_n": Const(40),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(46)), Geq(Var("b"), Const(1)), Leq(V... | ALG | null | COUNT | sympy | SUM_GEOM | [
"POLY4_COUNT/QF_PSD_COUNT/SUM_SQUARES_IDENTITY"
] | d75633 | alg_qf_psd_orbit_v1 | null | 8 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT",
"SUM_GEOM",
"SUM_SQUARES_IDENTITY"
] | 4 | 1.771 | 2026-02-25T02:22:38.941942Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-25T02:22:40.712953Z"
} | 3d37b5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 482,
"completion_tokens": 9972
},
"timestamp": "2026-04-18T18:19:04.497Z",
"answer": 5
},
{
"id"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok_later"
}
] | {
"lo": 1.68,
"mid": 4.46,
"hi": 6.83
} | ||
9e0c9a | nt_count_intersection_v1_1915831931_773 | Let $N = 20000$ and $a = 7$. Let $b = \sum_{k=1}^{4} k$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. | 1,143 | graphs = [
Graph(
let={
"_n": Const(4),
"N": Const(20000),
"a": Const(7),
"b": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_intersection_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.997 | 2026-02-08T15:40:23.983186Z | {
"verified": true,
"answer": 1143,
"timestamp": "2026-02-08T15:40:24.980160Z"
} | 42e6b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 856
},
"timestamp": "2026-02-16T11:25:37.481Z",
"answer": 1143
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9ce41f | nt_count_coprime_v1_1978505735_3094 | Let $N$ be the number of positive integers $n$ with $1 \leq n \leq 1199$ such that $\gcd(n, 6) = 1$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = N$. Determine the number of positive integers $n_1$ with $1 \leq n_1 \leq 34596$ such that $\gcd(n_1, k) = 1$. | 13,838 | graphs = [
Graph(
let={
"_n": Const(1199),
"upper": Const(34596),
"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")), CountOverSet... | NT | null | COUNT | sympy | C4 | [
"C4/B3"
] | 046ad7 | nt_count_coprime_v1 | null | 6 | 0 | [
"B3",
"C4"
] | 2 | 4.251 | 2026-02-08T17:20:45.636117Z | {
"verified": true,
"answer": 13838,
"timestamp": "2026-02-08T17:20:49.887005Z"
} | 057b4f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1418
},
"timestamp": "2026-02-18T00:39:11.889Z",
"answer": 13838
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
76b592 | comb_sum_binomial_row_v1_1915831931_765 | Let $m = 5$. Define $S$ as the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 5$ and $1 \leq j \leq 2$. Let $T$ be the set obtained by applying the transformation $\phi(k) \left\lfloor \frac{m}{k} \right\rfloor$ to each pair $(k, j)$ in $S$, where $\phi$ denotes Euler's totient function... | 32,768 | graphs = [
Graph(
let={
"_m": Const(5),
"n": Div(Mul(Const(6), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Con... | NT | null | SUM | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"K2"
] | d64c9f | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.003 | 2026-02-08T15:39:50.889655Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T15:39:50.892591Z"
} | f813da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1170
},
"timestamp": "2026-02-16T11:27:40.622Z",
"answer": 32768
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6a4e64 | geo_count_lattice_rect_v1_601307018_1710 | Find the number of lattice points $(x, y)$ with $0 \le x \le 85$ and $0 \le y \le 22$. | 1,978 | graphs = [
Graph(
let={
"a": Const(85),
"b": Const(22),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | GEOM | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-03-10T02:27:49.911871Z | {
"verified": true,
"answer": 1978,
"timestamp": "2026-03-10T02:27:49.912542Z"
} | 0c5630 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 123
},
"timestamp": "2026-03-29T03:09:42.058Z",
"answer": 1978
},
{
"id... | 2 | [] | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||||
972a14 | diophantine_fbi2_count_v1_124444284_9309 | Let $k = 60$. Determine the number of positive integers $d$ such that $6 \leq d \leq 60$, $d$ divides $k$, and the quotient $\frac{k}{d}$ satisfies $5 \leq \frac{k}{d} \leq 59$. | 3 | graphs = [
Graph(
let={
"k": Const(60),
"a": Const(5),
"b": Const(4),
"upper": Const(55),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Const(60)), Divides(divisor=Var("d"), dividend=Ref(... | NT | null | COUNT | sympy | V8 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 2 | 0 | [
"B3",
"V8"
] | 2 | 0.056 | 2026-02-08T12:22:43.478370Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T12:22:43.534159Z"
} | 62f653 | 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": 667
},
"timestamp": "2026-02-15T00:43:30.635Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a07f55 | algebra_quadratic_discriminant_v1_1218484723_6461 | Let $R = -1^{\left|\{ (a_1, b_1) : 1 \le a_1 \le 15,\ 1 \le b_1 \le 15,\ a_1 \le b_1,\ 2b_1^{2} + 2a_1^{2} - 4a_1 b_1 = \left|\{ (a_2, b_2) : 1 \le a_2 \le 30,\ 1 \le b_2 \le \left|\{ (a_3, b_3) : 1 \le a_3 \le 40,\ 1 \le b_3 \le 40,\\ 17a_3^{4} + 102a_3^{2} b_3^{2} + 17b_3^{4} + 68a_3^{3} b_3 + 68a_3 b_3^{3} = 1569985... | 64,787 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"a": Const(3),
"b": Const(-1),
"c": Const(11),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Co... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_COUNT_LEQ/QF_PSD_ORBIT"
] | e02fc0 | algebra_quadratic_discriminant_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT_LEQ",
"QF_PSD_ORBIT"
] | 3 | 0.018 | 2026-02-25T08:01:26.053001Z | {
"verified": true,
"answer": 64787,
"timestamp": "2026-02-25T08:01:26.070685Z"
} | 30db7f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 402,
"completion_tokens": 8277
},
"timestamp": "2026-03-30T01:50:33.095Z",
"answer": 64787
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
edc58c | geo_count_lattice_triangle_v1_1218484723_5041 | Let $M = \left|256128 + 200 \cdot (0 - 256)\right|$, $R = \gcd(256, 256) + \gcd(|200 - 256|, |128 - 256|) + \gcd(|0 - 200|, |0 - 128|)$, and $S = \frac{M + 2 - R}{2}$. Compute $70000 - S$. | 60,919 | graphs = [
Graph(
let={
"_n": Const(128),
"area_2x": Abs(arg=Sum(Mul(Const(value=256), Ref(name='_n')), Mul(Const(value=200), Sub(left=Const(value=0), right=Const(value=256))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=256)), b=Abs(arg=Const(value=256))), GCD(a=Abs(arg=... | GEOM | NT | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.005 | 2026-02-25T06:39:57.281539Z | {
"verified": true,
"answer": 60919,
"timestamp": "2026-02-25T06:39:57.286734Z"
} | 77a518 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 751
},
"timestamp": "2026-03-29T19:10:21.874Z",
"answer": -32329
},
{
... | 1 | [
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
ceb419 | diophantine_fbi2_count_v1_397696148_965 | Let $n = 15$. For each integer $k$ from 1 to $n$, define
$$
a_k = \varphi(k) \left\lfloor \frac{1}{k} \sum_{k=1}^{5} \varphi(k) \left\lfloor \frac{5}{k} \right\rfloor \right\rfloor,
$$
where $\varphi$ denotes Euler's totient function. Let $k = \sum_{k=1}^{15} a_k$.
Now consider the set of all positive integers $d$ suc... | 11 | graphs = [
Graph(
let={
"_n": Const(15),
"k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))), Var("k"))))),
"result... | NT | null | COUNT | sympy | V1 | [
"K2/K2"
] | ddede2 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"K2",
"V1"
] | 2 | 0.131 | 2026-02-08T11:58:21.830939Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T11:58:21.961607Z"
} | a76503 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 2135
},
"timestamp": "2026-02-14T23:43:46.545Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5bb0de | nt_lcm_compute_v1_349078426_1832 | Let $S$ be the set of all integers $t$ such that $21 \leq t \leq 6681$ and $t = 9a + 12b$ for some positive integers $a \leq 221$ and $b \leq 391$. Let $N = |S|$. Let $a_{\text{max}}$ be the largest prime number at most $N$. Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1020100$, ... | 3,970 | 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=221)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"B3"
] | 2a7052 | nt_lcm_compute_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.004 | 2026-02-08T13:57:02.653001Z | {
"verified": true,
"answer": 3970,
"timestamp": "2026-02-08T13:57:02.656648Z"
} | 6a045c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 6423
},
"timestamp": "2026-02-15T22:41:39.261Z",
"answer": 3970
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"sta... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9876f6 | geo_count_lattice_rect_v1_1520064083_6735 | Compute the number of lattice points $(x,y)$ such that $0 \le x \le 300$ and $0 \le y \le 132$. | 40,033 | graphs = [
Graph(
let={
"a": Const(300),
"b": Const(132),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T08:17:31.439128Z | {
"verified": true,
"answer": 40033,
"timestamp": "2026-02-08T08:17:31.440797Z"
} | 47ad53 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 120
},
"timestamp": "2026-02-24T09:14:58.096Z",
"answer": 40033
},
{
"i... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
59e960 | comb_bell_compute_v1_809748730_176 | Let $m = 74529$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq T$ and $\binom{s}{j} \equiv 1 \pmod{2}$, where $T$ is the number of integers $t... | 11,485 | graphs = [
Graph(
let={
"_m": Const(74529),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V8",
"B3/V8"
] | 3f10a4 | comb_bell_compute_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"V8"
] | 3 | 0.004 | 2026-02-08T11:21:29.653889Z | {
"verified": true,
"answer": 11485,
"timestamp": "2026-02-08T11:21:29.657676Z"
} | 2ce720 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 309,
"completion_tokens": 6253
},
"timestamp": "2026-02-24T13:33:00.663Z",
"answer": 11485
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_F... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
8403f7 | comb_factorial_compute_v1_124444284_411 | Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 10241$ such that $\binom{10241}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(10241),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(10241)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T03:15:56.420222Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T03:15:56.423077Z"
} | 76da6c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1576
},
"timestamp": "2026-02-09T17:19:44.575Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
ac813d | antilemma_sum_equals_v1_1918700295_4060 | Let $n$ be the number of ordered pairs $(i, j)$ where $i$ and $j$ are integers with $1 \leq i \leq 3$ and $1 \leq j \leq 3$. Determine the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 7$, $1 \leq j \leq 7$, and $i + j = n$. Compute this value. | 6 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.047 | 2026-02-08T09:06:20.434483Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T09:06:20.481815Z"
} | ef5d72 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 709
},
"timestamp": "2026-02-24T10:34:30.185Z",
"answer": 6
},
{
"id": ... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
b53d90 | nt_count_divisible_and_v1_397696148_194 | Let $n = 198$ and $U = 194460$. Determine the number of positive integers $m$ such that $1 \leq m \leq U$, $m$ is divisible by $12$, and $m$ is divisible by $15$. Let this count be $C$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $M$ be the maximum value of $xy$ over... | 29,519 | graphs = [
Graph(
let={
"_n": Const(198),
"upper": Const(194460),
"d1": Const(12),
"d2": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), mod... | NT | null | COUNT | sympy | B1 | [
"B1"
] | bf138c | nt_count_divisible_and_v1 | quadratic_mod | 4 | 0 | [
"B1"
] | 1 | 7.807 | 2026-02-08T11:21:40.905103Z | {
"verified": true,
"answer": 29519,
"timestamp": "2026-02-08T11:21:48.712208Z"
} | 26669a | 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": 1291
},
"timestamp": "2026-02-14T12:22:37.317Z",
"answer": 29519
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f323df | nt_count_divisible_and_v1_1470522791_56 | Let $d_1$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 36$. Let $d_2 = 18$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 66060$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute $38416 - N$. | 36,581 | graphs = [
Graph(
let={
"upper": Const(66060),
"d1": 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(36)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 5.91 | 2026-02-08T12:48:30.772144Z | {
"verified": true,
"answer": 36581,
"timestamp": "2026-02-08T12:48:36.682110Z"
} | 881984 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 709
},
"timestamp": "2026-02-15T05:08:05.029Z",
"answer": 36581
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f48906 | modular_min_linear_v1_677425708_1696 | Let $a = 14198$. Let $S$ be the set of all positive integers $x_1$ and $x_2$ such that $x_1$ and $x_2$ are both odd and $x_1 + x_2 = 494$. Let $n_{\text{max}}$ be the number of elements in $S$. Define $b$ to be the largest prime number $n$ such that $2 \leq n \leq n_{\text{max}}$. Let $m = 26583$. Let $x$ be a positive... | 6,704 | graphs = [
Graph(
let={
"a": Const(14198),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(na... | NT | null | EXTREMUM | sympy | COMB1 | [
"COMB1/MAX_PRIME_BELOW"
] | 6a06f8 | modular_min_linear_v1 | null | 7 | 0 | [
"COMB1",
"MAX_PRIME_BELOW"
] | 2 | 5.022 | 2026-02-08T04:22:42.632659Z | {
"verified": true,
"answer": 6704,
"timestamp": "2026-02-08T04:22:47.655131Z"
} | 853db4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 3370
},
"timestamp": "2026-02-11T23:49:42.103Z",
"answer": 6704
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
201070 | modular_sum_quadratic_residues_v1_1742523217_4433 | Let $m = 2$. Define $n$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 60$, $\gcd(p, q) = 1$, and $p < q$. Let $p_{\text{min}}$ be the smallest divisor of $302764416173$ that is at least $m$. Compute the value of $\frac{p_{\text{min}}(p_{\text{min}} - 1)}{... | 9,653 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=60)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T07:17:30.770336Z | {
"verified": true,
"answer": 9653,
"timestamp": "2026-02-08T07:17:30.772887Z"
} | 5e6994 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 2854
},
"timestamp": "2026-02-13T09:19:53.475Z",
"answer": 9653
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"statu... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
293f9b | antilemma_k2_v1_124444284_4513 | Let $d = 2$. Let $S$ be the set of all real solutions $x$ to the equation $x^2 - 303x - 2488 = 0$, and let $n$ be the sum of all elements in $S$. For each positive integer $k$ from $1$ to $n$, define
$$
a_k = \varphi(k) \left\lfloor \frac{1}{k} \sum_{d \mid m} \varphi(d) \right\rfloor,
$$
where $m$ is the sum of all re... | 12,522 | graphs = [
Graph(
let={
"_d": Const(2),
"_c": Const(18396),
"_m": Const(44121),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_d")), Mul(Const(-303), Var("x")), Const(-2488)), Const(0)))),
"x": Summation(var="k... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K3/K2",
"VIETA_SUM/K2",
"K2"
] | 578119 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"K3",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T06:03:42.158622Z | {
"verified": true,
"answer": 12522,
"timestamp": "2026-02-08T06:03:42.160844Z"
} | ec5f87 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 2303
},
"timestamp": "2026-02-12T19:04:34.843Z",
"answer": 12522
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e8f356 | comb_sum_binomial_row_v1_458359167_2241 | Let $n = 13$. Define $p_0$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $p_0^{13}$. | 8,192 | graphs = [
Graph(
let={
"n": Const(13),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T05:13:36.011835Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T05:13:36.012866Z"
} | feadbe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 1141
},
"timestamp": "2026-02-12T05:54:28.330Z",
"answer": 8192
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8e41f2 | comb_count_surjections_v1_48377204_256 | Let $n$ be the number of ordered pairs $(i, j)$ where $i \in \{1, 2\}$ and $j \in \{1, 2, 3\}$. Let $k$ be the number of ordered pairs $(i, j)$ with $i \in \{1, 2, 3\}$, $j \in \{1, 2, 3, 4\}$, and $i + j = 4$. Define $S = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute the re... | 2,430 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(70030),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(3)))),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | e4fc6a | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.01 | 2026-02-08T15:19:15.147337Z | {
"verified": true,
"answer": 2430,
"timestamp": "2026-02-08T15:19:15.157749Z"
} | c64251 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 982
},
"timestamp": "2026-02-24T20:23:30.264Z",
"answer": 2430
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
85fab6 | antilemma_sum_equals_v1_1125832087_558 | Determine the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 64$, $1 \leq j \leq 65$, and $i + j = 65$. | 64 | graphs = [
Graph(
let={
"_n": Const(65),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(64)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.005 | 2026-02-08T03:09:07.458296Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T03:09:07.463519Z"
} | 8dd584 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 241
},
"timestamp": "2026-02-10T13:13:31.232Z",
"answer": 64
},
{
"id":... | 2 | [
{
"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",
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
69181f | comb_factorial_compute_v1_2051736721_4899 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 36928$ and $\binom{36928}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(36928),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(36928), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T18:15:14.761719Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T18:15:14.763255Z"
} | 4c9b59 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 1808
},
"timestamp": "2026-02-18T15:23:27.058Z",
"answer": 40320
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
0b24cf | nt_count_coprime_v1_655260480_441 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9$. Define $\sigma$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$.
Let $P$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = \sigma$. Define $k$ to be the maximum value of $x_1 ... | 31,974 | graphs = [
Graph(
let={
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(9)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(47961... | NT | null | COUNT | sympy | B3 | [
"B3/B1"
] | 7f76f7 | nt_count_coprime_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 4.653 | 2026-02-08T15:23:26.474350Z | {
"verified": true,
"answer": 31974,
"timestamp": "2026-02-08T15:23:31.126928Z"
} | b7cb8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 742
},
"timestamp": "2026-02-16T05:23:07.251Z",
"answer": 31974
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
195aa2 | nt_min_phi_inverse_v1_2051736721_1725 | Let $c = 4$. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = c$. Let $P$ be the set of all products $xy$ where $(x, y) \in S$. Let $n_{\text{max}}$ be the maximum value in $P$. Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 120$ and there exist integers $a$ ... | 31,602 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(50952),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_c")))), exp... | NT | null | EXTREMUM | sympy | B1 | [
"B1/SUM_ARITHMETIC",
"LIN_FORM"
] | d43315 | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"B1",
"LIN_FORM",
"SUM_ARITHMETIC"
] | 3 | 0.012 | 2026-02-08T16:10:50.613265Z | {
"verified": true,
"answer": 31602,
"timestamp": "2026-02-08T16:10:50.625705Z"
} | 75d173 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 1840
},
"timestamp": "2026-02-16T22:37:34.653Z",
"answer": 31602
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
650161 | geo_count_lattice_rect_v1_1978505735_7859 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 30$ and $0 \leq y \leq 48$. A lattice point is a point with integer coordinates. | 1,519 | graphs = [
Graph(
let={
"a": Const(30),
"b": Const(48),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T20:31:45.277650Z | {
"verified": true,
"answer": 1519,
"timestamp": "2026-02-08T20:31:45.279778Z"
} | e62e7f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 377
},
"timestamp": "2026-02-25T02:03:49.634Z",
"answer": 1519
},
{
... | 2 | [] | {
"lo": -10,
"mid": -7.4,
"hi": -4.8
} | ||||
2eabba | nt_min_phi_inverse_v1_865884756_2636 | Let $m = 2$ and let $n$ be the largest integer $k$ such that $2^k \leq 50313417$. Let $s$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = n$. Find the smallest positive integer $n'$ such that $1 \leq n' \leq s$ and $\phi(n') = 1$, where $\phi$ denotes Euler's totient... | 1 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("k1"), condition=Leq(Pow(Ref("_m"), Var("k1")), Const(50313417)))),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"MAX_VAL/B3"
] | b7a7b3 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B3",
"MAX_VAL",
"ONE_PHI_1"
] | 3 | 0.057 | 2026-02-08T16:51:45.095206Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:51:45.151811Z"
} | 570af2 | 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": 703
},
"timestamp": "2026-02-17T12:54:13.056Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
369058 | antilemma_count_primes_v1_798873815_220 | Let $n = 1373$. Define $x$ to be the number of prime numbers $p$ such that $2 \leq p \leq n$. Compute the value of
$$
x + 2^{x \bmod 15} \bmod 99477.$$
Give the result as an integer between $0$ and $99476$, inclusive. | 1,244 | graphs = [
Graph(
let={
"_n": Const(1373),
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(15))), modulus=C... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | antilemma_count_primes_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T02:31:30.413431Z | {
"verified": true,
"answer": 1244,
"timestamp": "2026-02-08T02:31:30.413935Z"
} | f8711a | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 335
},
"timestamp": "2026-02-08T21:10:39.665Z",
"answer": 1244
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -1.78,
"mid": 2.35,
"hi": 6.69
} | ||
6a2da9 | nt_count_divisible_and_v1_1520064083_4035 | Let $ S $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 22240656 $. Let $ u $ be the minimum value of $ x + y $ over all such pairs. Let $ d_1 = \sum_{k=1}^{3} k $ and $ d_2 = 9 $. Determine the number of positive integers $ n \leq u $ such that $ n $ is divisible by both $ d_1 $ and ... | 7,075 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(84991),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(22240656... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3"
] | dee757 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 2.548 | 2026-02-08T06:02:45.181662Z | {
"verified": true,
"answer": 7075,
"timestamp": "2026-02-08T06:02:47.729879Z"
} | 26cedd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1993
},
"timestamp": "2026-02-12T19:10:32.007Z",
"answer": 7075
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ca28a3 | nt_num_divisors_compute_v1_784195855_2610 | Let $n$ be the number of positive integers less than or equal to 52 whose digit sum is odd. Compute the number of positive divisors of $n$. | 4 | graphs = [
Graph(
let={
"_n": Const(52),
"n": 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))))),
"result": NumDivisors(n=Ref("n")),
},
... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"L3B"
] | 1 | 0.002 | 2026-02-08T05:54:21.798179Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T05:54:21.799988Z"
} | 1b73f5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 681
},
"timestamp": "2026-02-12T16:11:13.326Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status":... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
4a99b7 | nt_max_prime_below_v1_124444284_2609 | Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of prime numbers $n$ such that $N \leq n \leq 22801$. Compute the largest element of $S$. | 22,787 | graphs = [
Graph(
let={
"upper": Const(22801),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.524 | 2026-02-08T04:50:29.064731Z | {
"verified": true,
"answer": 22787,
"timestamp": "2026-02-08T04:50:29.589224Z"
} | e7a214 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 5961
},
"timestamp": "2026-02-11T22:17:22.091Z",
"answer": 22787
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
a5a037 | comb_count_surjections_v1_458359167_961 | Let $n$ be the number of integers $t$ with $10 \le t \le 24$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 3$, $1 \le b \le 2$, and $t = 4a + 6b$. Let $k = 2$. Let $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when $59035 \c... | 31,752 | graphs = [
Graph(
let={
"_n": Const(88498),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:12:15.416650Z | {
"verified": true,
"answer": 31752,
"timestamp": "2026-02-08T04:12:15.417909Z"
} | 3190cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1472
},
"timestamp": "2026-02-23T23:48:04.849Z",
"answer": 31752
},
{
"... | 1 | [
{
"lemma": "C2",
"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",
"status": "no"
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
1acef8 | nt_lcm_compute_v1_153355830_268 | Let $ T $ be the set of all integers $ t $ such that $ 7 \le t \le 100 $ and there exist positive integers $ a $ and $ b $ with $ 1 \le a \le 14 $, $ 1 \le b \le 15 $, and $ t = 5a + 2b $. Let $ s = |T| $. Define $ P $ to be the set of all ordered pairs $ (x, y) $ of positive integers such that $ x + y = s $. Let $ a $... | 53,077 | graphs = [
Graph(
let={
"_m": Const(64742),
"_n": Const(44121),
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(s... | NT | null | COMPUTE | sympy | L3B | [
"COUNT_COPRIME_GRID",
"LIN_FORM/B1"
] | 539abe | nt_lcm_compute_v1 | null | 6 | 0 | [
"B1",
"COUNT_COPRIME_GRID",
"L3B",
"LIN_FORM"
] | 4 | 0.009 | 2026-02-08T03:00:05.457907Z | {
"verified": true,
"answer": 53077,
"timestamp": "2026-02-08T03:00:05.467162Z"
} | 1c7dba | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 344,
"completion_tokens": 5717
},
"timestamp": "2026-02-10T12:31:13.053Z",
"answer": 53077
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
0ab724 | nt_count_divisible_and_v1_898971024_2486 | Let $n = 3$. Let $u$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 980100$. Let $d_1 = 4$ and let $d_2 = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the number of positive integers $m$ such t... | 165 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(980100)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3",
"K2"
] | f1ea07 | nt_count_divisible_and_v1 | null | 7 | 0 | [
"B3",
"K2"
] | 2 | 0.148 | 2026-02-08T16:47:03.923675Z | {
"verified": true,
"answer": 165,
"timestamp": "2026-02-08T16:47:04.071484Z"
} | 95bcd7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1019
},
"timestamp": "2026-02-17T12:54:04.805Z",
"answer": 165
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
989e2a | nt_num_divisors_compute_v1_1742523217_4971 | Let $n$ be the sum of the first $k$ positive integers, where $k$ is the number of positive integers $m$ at most 1848 for which 14 divides the $m$-th Fibonacci number. Let $d(n)$ denote the number of positive divisors of $n$. Compute the remainder when $91177 \cdot d(n)$ is divided by 51696. | 11,344 | graphs = [
Graph(
let={
"_n": Const(51696),
"n": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1848)), Divides(divisor=Const(14), dividend=Fibonacci(arg=Var(name='n')))))), expr=Var("k")),... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/SUM_ARITHMETIC"
] | a57ec2 | nt_num_divisors_compute_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T10:41:39.000355Z | {
"verified": true,
"answer": 11344,
"timestamp": "2026-02-08T10:41:39.002000Z"
} | 203254 | 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": 2496
},
"timestamp": "2026-02-14T08:23:16.820Z",
"answer": 11344
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0169c4 | nt_sum_over_divisible_v1_48377204_884 | Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 21316$ and $n$ is divisible by $62$. Let $r$ be the sum of all elements in $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $u$ be the minimum value of $x + y$ over all pairs $(x, y) \in T$. Let $P$... | 17,028 | graphs = [
Graph(
let={
"_m": Const(36),
"_n": Const(98947),
"upper": Const(21316),
"divisor": Const(62),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"),... | NT | COMB | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | 2f1f5e | nt_sum_over_divisible_v1 | bell_mod | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 2.66 | 2026-02-08T15:45:10.544755Z | {
"verified": true,
"answer": 17028,
"timestamp": "2026-02-08T15:45:13.205097Z"
} | 1f6c81 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1215
},
"timestamp": "2026-02-16T13:18:42.650Z",
"answer": 17028
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d14ed8 | sequence_fibonacci_compute_v1_397696148_2681 | Let $p$ and $q$ be positive integers such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Determine the number of such integers $p$. Let $n$ be the smallest divisor of 19343 that is greater than or equal to this count. Compute the $n$th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_m": Const(19343),
"_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=216)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T13:29:03.382794Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T13:29:03.384686Z"
} | db8219 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1461
},
"timestamp": "2026-02-15T16:41:55.698Z",
"answer": 28657
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"st... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
191767 | modular_mod_compute_v1_1978505735_4713 | Let $m = 2$ and $n = 57673$. Define $S$ as the set of all integers $n_1$ such that $1 \leq n_1 \leq 96$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{3}$. Let $a$ be the largest prime number less than or equal to the number of elements in $S$. Let $m' = 13924$ and define $r$ as the remainder when $a$ i... | 49,587 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(57673),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(96)),... | NT | null | COMPUTE | sympy | L3C | [
"L3C/MAX_PRIME_BELOW"
] | 8ff24e | modular_mod_compute_v1 | null | 6 | 0 | [
"L3C",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T18:27:11.822055Z | {
"verified": true,
"answer": 49587,
"timestamp": "2026-02-08T18:27:11.824422Z"
} | a1a962 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 3483
},
"timestamp": "2026-02-18T17:40:11.447Z",
"answer": 49587
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1d336a | modular_count_residue_v1_1874849503_1130 | Let $N = 68121$. Let $m$ be the smallest divisor of $2146981$ that is greater than or equal to $2$. Let $r = 9$. Consider the set of all positive integers $n$ such that $1 \leq n \leq N$ and $n \equiv r \pmod{m}$. Compute the number of elements in this set. | 4,007 | graphs = [
Graph(
let={
"upper": Const(68121),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2146981))))),
"r": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), con... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.504 | 2026-02-08T13:38:36.068253Z | {
"verified": true,
"answer": 4007,
"timestamp": "2026-02-08T13:38:38.571862Z"
} | 854004 | 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": 1236
},
"timestamp": "2026-02-10T01:29:28.089Z",
"answer": 4007
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.