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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
089712 | comb_count_permutations_fixed_v1_1742523217_2994 | Let $n$ be the number of integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 2$, $1 \leq b \leq 4$, $5 \leq t \leq 14$, and $t = 3a + 2b$. Let $k = 5$. Define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the remain... | 46,975 | graphs = [
Graph(
let={
"_n": Const(67049),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:29:43.336965Z | {
"verified": true,
"answer": 46975,
"timestamp": "2026-02-08T05:29:43.339418Z"
} | 577399 | 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": 1526
},
"timestamp": "2026-02-24T03:39:27.412Z",
"answer": 46975
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
0b27e2 | nt_sum_divisors_mod_v1_1125832087_579 | Let $s$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 705600$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $s$, where $\phi$ denotes Euler's totient function. Let $\sigma(n)$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)... | 5,952 | 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(705600)))), expr=Sum(Var("x"), Var("y")))),
"n": SumOverDiv... | NT | null | COMPUTE | sympy | B3 | [
"B3/K3"
] | 4a4ef2 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3",
"K3"
] | 2 | 0.003 | 2026-02-08T03:09:25.157398Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T03:09:25.160426Z"
} | 2da422 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1740
},
"timestamp": "2026-02-10T13:14:31.451Z",
"answer": 5952
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
8ba33b | algebra_vieta_sum_v1_458359167_4830 | Let $s$ be the minimum value of $x + y$ over all positive integers $x$ and $y$ such that $xy = 2916$. Let $R$ be the set of all positive integers $x$ such that
$$
x^3 - 19x^2 + s \cdot x - 180 = 0.
$$
Compute the product of all elements in $R$. | 180 | graphs = [
Graph(
let={
"_n": Const(3),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Ref(name='_n')), Mul(Const(value=-19), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(v... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_vieta_sum_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.013 | 2026-02-08T12:05:43.202089Z | {
"verified": true,
"answer": 180,
"timestamp": "2026-02-08T12:05:43.215030Z"
} | 8402a9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1183
},
"timestamp": "2026-02-14T22:17:37.292Z",
"answer": 180
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
adb5d7 | modular_mod_compute_v1_784195855_2571 | Let $a = 19881$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 19749136$. Let $m$ be the minimum value of $x + y$ over all such pairs. Compute the remainder when $a$ is divided by $m$. | 2,105 | graphs = [
Graph(
let={
"a": Const(19881),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(19749136)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T05:52:39.322485Z | {
"verified": true,
"answer": 2105,
"timestamp": "2026-02-08T05:52:39.328745Z"
} | e4da72 | 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": 720
},
"timestamp": "2026-02-12T16:06:53.871Z",
"answer": 2105
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
cddb3e | comb_sum_binomial_row_v1_153355830_392 | Let $A$ be the number of unordered pairs of coprime positive integers $p, q$ with $p < q$ and $pq = 216$. Let $B$ be the number of integers $t$ such that $7 \leq t \leq 27$ and $t = 4a + 3b$ for some integers $a, b$ with $1 \leq a \leq 3$ and $1 \leq b \leq 5$. Compute $A^B$. | 32,768 | 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 | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM"
] | a1eac8 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T03:03:49.802553Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T03:03:49.804744Z"
} | ced8bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1729
},
"timestamp": "2026-02-10T12:38:57.561Z",
"answer": 32768
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PAD... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
9319dd | nt_max_prime_below_v1_677425708_2022 | Let $ A $ be the set of all positive integers $ p $ for which there exists a positive integer $ q > p $ such that $ p \cdot q = 18 $ and $ \gcd(p, q) = 1 $. Let $ s $ be the number of elements in $ A $. Determine the largest prime number $ n $ such that $ s \leq n \leq 14161 $. | 14,159 | graphs = [
Graph(
let={
"upper": Const(14161),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.321 | 2026-02-08T04:43:08.318743Z | {
"verified": true,
"answer": 14159,
"timestamp": "2026-02-08T04:43:08.639778Z"
} | e691b7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1735
},
"timestamp": "2026-02-11T07:24:42.043Z",
"answer": 14159
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a30a45 | nt_sum_gcd_range_mod_v1_48377204_1620 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 34385$ and
$$
n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}.
$$
Let $k = \sum_{k_1=1}^{15} k_1$. Define
$$
S = \sum_{n_1=1}^{N} \gcd(n_1, k).
$$
Let $M = 11633$, and let $r$ be the remainder when $S$ is divided by $M$. Compute the r... | 42,583 | graphs = [
Graph(
let={
"_n": Const(15),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(34385)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"L3C"
] | 22c5b7 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"L3C",
"SUM_ARITHMETIC"
] | 2 | 0.612 | 2026-02-08T16:15:49.289968Z | {
"verified": true,
"answer": 42583,
"timestamp": "2026-02-08T16:15:49.901617Z"
} | f3854b | 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": 2768
},
"timestamp": "2026-02-17T00:50:59.565Z",
"answer": 42583
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f1859e | comb_sum_binomial_row_v1_784195855_2340 | Let $m = 245$. Let $d$ be the smallest divisor of $m$ that is at least $2$. Define
$$
n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{d}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute $2^n$. | 32,768 | graphs = [
Graph(
let={
"_m": Const(245),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Di... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2"
] | 352a97 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T05:41:50.570958Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T05:41:50.573065Z"
} | e7d44e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 561
},
"timestamp": "2026-02-11T23:01:02.273Z",
"answer": 32768
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"s... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
7bb4c8 | nt_count_digit_sum_v1_2051736721_2440 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 323400$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the number of elements in $S$. Now let $N$ be the number of positive integers $n \leq 9999$ such that the sum of the digits of $n$ equals $T$. Compute the Bell... | 203 | graphs = [
Graph(
let={
"upper": Const(9999),
"target_sum": 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=323400)), Eq(left=GCD(a=Var(name='... | NT | COMB | COUNT | sympy | LIN_FORM | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_digit_sum_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 12.55 | 2026-02-08T16:40:36.635520Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T16:40:49.185359Z"
} | ffb3d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 2319
},
"timestamp": "2026-02-17T10:32:10.671Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4dd571 | comb_sum_binomial_row_v1_717093673_2819 | Let $n$ be the number of integers $t$ with $7 \leq t \leq 25$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 5$, $1 \leq b \leq 3$, and $t = 2a + 5b$. Let $w = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $u = \sum_{k_1=0}^{0} (-1)^{k_1} \binom{0}{k_1}$. Define $N = n \cdot w \cdot u$. Compute $2^N$. | 32,768 | graphs = [
Graph(
let={
"_n": Const(2),
"n2": Const(0),
"w": Summation(var="k", start=Sub(Binom(n=Const(16), k=Const(16)), Const(1)), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"u": Summation... | COMB | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 3ea266 | comb_sum_binomial_row_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM",
"ZERO_BINOM_N"
] | 3 | 0.005 | 2026-02-08T17:13:01.922712Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T17:13:01.927217Z"
} | 76ee0f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 951
},
"timestamp": "2026-02-17T21:53:12.741Z",
"answer": 32768
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
8aaa87 | antilemma_k3_v1_677425708_2301 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $4375$, where $\phi$ denotes Euler's totient function. Compute the value of $x$. | 4,375 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=4375), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:58:48.101389Z | {
"verified": true,
"answer": 4375,
"timestamp": "2026-02-08T04:58:48.101759Z"
} | 0532d3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 452
},
"timestamp": "2026-02-11T22:36:18.607Z",
"answer": 4375
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ce50e4 | nt_sum_gcd_range_mod_v1_1520064083_822 | Let $N = 4356$ and $M = 11497$. Define $k$ to be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 20736$. Let $s = \sum_{n=1}^{N} \gcd(n, k)$. Define $c$ to be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 7817616$. Fin... | 57,208 | graphs = [
Graph(
let={
"_n": Const(87617),
"N": Const(4356),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(20736)))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | e0298c | nt_sum_gcd_range_mod_v1 | affine_mod | 5 | 0 | [
"B3"
] | 1 | 0.202 | 2026-02-08T03:37:28.860306Z | {
"verified": true,
"answer": 57208,
"timestamp": "2026-02-08T03:37:29.062049Z"
} | c47849 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 5011
},
"timestamp": "2026-02-10T15:07:09.433Z",
"answer": 57208
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
4b4282 | nt_num_divisors_compute_v1_784195855_2458 | Let $n$ be the sum of all real solutions $x$ to the equation
$$
x^2 - 2020x - 32576 = 0.
$$
Compute the number of positive divisors of $n$. | 12 | graphs = [
Graph(
let={
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-2020), Var("x")), Const(-32576)), Const(0)))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T05:45:12.491572Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T05:45:12.493483Z"
} | be9d6c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 747
},
"timestamp": "2026-02-11T23:09:11.978Z",
"answer": 12
},
{
"id": 11,
... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
3b1ba8 | antilemma_sum_equals_v1_1520064083_4456 | Let $\mathcal{S}$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 97$, $1 \leq j \leq 98$, and $i + j = 98$. Let $x$ be the number of elements in $\mathcal{S}$. Compute the remainder when $44121 \cdot x$ is divided by $76826$. | 54,307 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(98)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(97)), right=IntegerRange(start=Const(1), end=Const(98))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T06:17:26.805426Z | {
"verified": true,
"answer": 54307,
"timestamp": "2026-02-08T06:17:26.809798Z"
} | ba6208 | 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": 1563
},
"timestamp": "2026-02-24T05:46:49.253Z",
"answer": 54307
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
ad3110_n | alg_qf_psd_orbit_v1_1218484723_3420 | An architect designs square rooms with side lengths $a$ and $b$ (in meters), where $a \le b$ and both are positive integers up to 195. The combined area of two such squares, scaled by a factor of 25, must equal 616250 square meters. How many distinct room-pair designs satisfy this condition? | 6 | ALG | null | COUNT | sympy | POLY4_COUNT | [
"LIN_FORM/POLY_ORBIT_HENSEL",
"B1/POLY_ORBIT_HENSEL"
] | 5d1f37 | alg_qf_psd_orbit_v1 | null | 2 | null | [
"B1",
"LIN_FORM",
"POLY4_COUNT",
"POLY_ORBIT_HENSEL"
] | 4 | 1.198 | 2026-02-25T05:07:49.932115Z | null | 4e80b1 | ad3110 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 6460
},
"timestamp": "2026-03-30T20:03:31.641Z",
"answer": 6
},
{
"id":... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
8a52d9 | nt_max_prime_below_v1_1978505735_2090 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $P$. Let $S$ be the set of all prime numbers $n$ such that $m \leq n \leq 10883$. Determine the value of the largest element in $S$. | 10,883 | graphs = [
Graph(
let={
"upper": Const(10883),
"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 | 0.28 | 2026-02-08T16:39:12.714333Z | {
"verified": true,
"answer": 10883,
"timestamp": "2026-02-08T16:39:12.994115Z"
} | 8c0cf2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 1577
},
"timestamp": "2026-02-17T08:54:10.272Z",
"answer": 10883
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
664f46 | nt_min_coprime_above_v1_1978505735_2296 | Let $n$ be the number of integers $n'$ such that $1 \leq n' \leq 184$ and the sum of the decimal digits of $n'$ is even. Let $s = 12321$ and $u = 12367$. Let $r$ be the smallest integer $n_1$ such that $s < n_1 \leq u$ and $\gcd(n_1, 36) = 1$. Let $p$ be the largest prime number at most $n$. Compute the remainder when ... | 41,866 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(184)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_m")), Const(0))))),
"start": Const(12321),
"upper": Const... | NT | null | EXTREMUM | sympy | L3B | [
"L3B/MAX_PRIME_BELOW"
] | ec756f | nt_min_coprime_above_v1 | negation_mod | 5 | 0 | [
"L3B",
"MAX_PRIME_BELOW"
] | 2 | 0.012 | 2026-02-08T16:49:01.783373Z | {
"verified": true,
"answer": 41866,
"timestamp": "2026-02-08T16:49:01.795458Z"
} | 1d4d3d | 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": 1907
},
"timestamp": "2026-02-17T12:36:45.253Z",
"answer": 41866
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e6a00f | antilemma_sum_equals_v1_458359167_3183 | Let $n = 6$. Determine the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 5$, $1 \leq j \leq 6$, and $i + j = n$. | 5 | graphs = [
Graph(
let={
"_n": Const(6),
"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(5)), right=IntegerRange(start=Const(1), end=Const... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T07:00:55.764474Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T07:00:55.776200Z"
} | 6e6e23 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 174
},
"timestamp": "2026-02-24T07:27:40.906Z",
"answer": 5
},
{
"id": ... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
02b42d | antilemma_sum_equals_v1_1915831931_2861 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 8$ and $1 \leq j \leq 12$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 94$, $1 \leq j \leq 95$, and $i + j = n$. | 94 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(12)))),
"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 | 0.125 | 2026-02-08T17:11:46.658921Z | {
"verified": true,
"answer": 94,
"timestamp": "2026-02-08T17:11:46.784184Z"
} | c09e33 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 727
},
"timestamp": "2026-02-17T22:28:39.314Z",
"answer": 94
},
{
... | 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": -8,
"mid": -4.75,
"hi": -2.28
} | ||
4a6ec4 | nt_lcm_compute_v1_151522320_745 | Let $A$ be the set of all integers $t$ such that $7 \leq t \leq 894$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 97$, $1 \leq b \leq 140$, and $t = 2a + 5b$. Let $a = |A|$. Compute the remainder when $24025 - \text{lcm}(a, 2522)$ is divided by $65505$. | 3,782 | graphs = [
Graph(
let={
"a": 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=97)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_lcm_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:29:36.186212Z | {
"verified": true,
"answer": 3782,
"timestamp": "2026-02-08T03:29:36.187768Z"
} | 5e10da | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 3881
},
"timestamp": "2026-02-10T13:36:32.376Z",
"answer": 20364
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
3b09ce | antilemma_k2_v1_784195855_5397 | Let $m = 2$ and $n = 372$. Let $S$ be the set of all integers $x$ such that $x^2 - 372x + 17696 = 0$. Let $k_{\text{sum}}$ be the sum of all positive integers $k$ from 1 to the sum of the elements in $S$, inclusive. Define
$$
x = \sum_{k=1}^{k_{\text{sum}}} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 372} \phi(d) \ri... | 37,520 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(372),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-372), Var("x")), Const(17696)), Const(0)))), expr=Mul(EulerPhi(n=Var("k"))... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"K3/K2",
"K2"
] | 4108ea | antilemma_k2_v1 | null | 7 | 0 | [
"K13",
"K2",
"K3",
"VIETA_SUM"
] | 4 | 0.006 | 2026-02-08T07:52:34.063820Z | {
"verified": true,
"answer": 37520,
"timestamp": "2026-02-08T07:52:34.069691Z"
} | 403dc4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1549
},
"timestamp": "2026-02-13T13:17:15.008Z",
"answer": 37520
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0a7aea | comb_count_derangements_v1_458359167_3158 | Let $n$ be the largest prime number not exceeding $7$. Let $r = !n$, the number of derangements of $n$ elements. Let $c$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 14$. Compute the value of $$\sum_{i=0}^{d-1} \left( \text{digit}_i(r) \cdot (i+1)^2 \right) + c,$$ where $... | 161 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": MaxOverSe... | NT | COMB | COUNT | sympy | B1 | [
"B1",
"MAX_PRIME_BELOW"
] | 913a2e | comb_count_derangements_v1 | digits_weighted_mod | 5 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T07:00:06.470226Z | {
"verified": true,
"answer": 161,
"timestamp": "2026-02-08T07:00:06.473341Z"
} | bf6a78 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 816
},
"timestamp": "2026-02-13T07:05:38.506Z",
"answer": 161
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e8d8e9 | modular_mod_compute_v1_865884756_6767 | Let $m$ be the largest prime number less than or equal to $1213$. Compute the remainder when $512$ is divided by $m$. | 512 | graphs = [
Graph(
let={
"_n": Const(1213),
"a": Const(512),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_mod_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T19:22:55.674087Z | {
"verified": true,
"answer": 512,
"timestamp": "2026-02-08T19:22:55.675998Z"
} | 5da66d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 383
},
"timestamp": "2026-02-16T18:38:10.550Z",
"answer": 512
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
764f0f | comb_factorial_compute_v1_153355830_2005 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $m$ be the minimum element of $T$. Let $n$ be the largest prime number satisfying $2 \leq n \leq m$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(ar... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | comb_factorial_compute_v1 | null | 3 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T06:50:55.488388Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T06:50:55.489941Z"
} | 2d626b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 469
},
"timestamp": "2026-02-15T17:47:25.076Z",
"answer": 5040
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
307802 | modular_count_residue_v1_153355830_550 | Let $n$ be a positive integer such that $1 \leq n \leq 50625$ and $n \equiv 1 \pmod{3}$. Compute the number of such integers $n$.
Let $c$ be the largest prime number less than or equal to 5004.
Find the remainder when $\left( (\text{number of such } n) \bmod{199} \right) + c \cdot \left( (\text{number of such } n) \... | 41,958 | graphs = [
Graph(
let={
"upper": Const(50625),
"m": Const(3),
"r": Const(1),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"))))),
... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | modular_count_residue_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.828 | 2026-02-08T03:09:33.536452Z | {
"verified": true,
"answer": 41958,
"timestamp": "2026-02-08T03:09:36.363975Z"
} | 5d2192 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 2144
},
"timestamp": "2026-02-10T15:14:06.895Z",
"answer": 41958
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
1d74e4 | diophantine_fbi2_count_v1_124444284_3042 | Let $k = 840$. Determine the number of positive integers $d$ such that $4 \leq d \leq 114$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 113$. Call this number $r$.
Let $m = 1225$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $c$ be the minimum value of $x + y$ over all ... | 1,276 | graphs = [
Graph(
let={
"_m": Const(1225),
"_n": Const(113),
"k": Const(840),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(114)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k")... | NT | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL",
"B3"
] | 82a41b | diophantine_fbi2_count_v1 | quadratic_mod | 5 | 0 | [
"B3",
"MAX_VAL"
] | 2 | 0.039 | 2026-02-08T05:09:57.556258Z | {
"verified": true,
"answer": 1276,
"timestamp": "2026-02-08T05:09:57.594831Z"
} | 2a7997 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 2865
},
"timestamp": "2026-02-11T23:06:53.208Z",
"answer": 1276
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K5",
"status": "no"
},
... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
fb9824 | antilemma_v1_legendre_168721529_655 | Let $m=4$ and $N=29764$. Let $p$ be the greatest prime number between $2$ and $12$, inclusive. Let $x$ be the largest integer $k$ such that $p^k$ divides $74756!$.
Let $T$ be the set of all integers $t$ such that there exist integers $a$ and $b$ with $1\le a\le 5$, $1\le b\le 3$, $7\le t\le 25$, and
$$t = 2a + 5b.$$
L... | 54,624 | graphs = [
Graph(
let={
"_c": Const(58129),
"_m": Const(4),
"_n": Const(29764),
"x": MaxKDivides(target=Factorial(Const(74756)), base=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C5",
"MAX_PRIME_BELOW/V1",
"V1"
] | 07e81d | antilemma_v1_legendre | negation_mod | 7 | 0 | [
"C5",
"LIN_FORM",
"MAX_PRIME_BELOW",
"V1"
] | 4 | 0.005 | 2026-02-08T13:10:46.110185Z | {
"verified": true,
"answer": 54624,
"timestamp": "2026-02-08T13:10:46.115148Z"
} | e58624 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 341,
"completion_tokens": 2206
},
"timestamp": "2026-02-09T07:31:06.994Z",
"answer": 54624
},
{
"... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FAC... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
561334 | comb_sum_binomial_row_v1_349078426_1216 | Let $n_0 = 21$. Let $S$ be the set of all positive integers $d$ such that $1 \leq d \leq 23$ and $d$ divides $667$. Let $M$ be the maximum element of $S$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq M$ and $\gcd(n, n_0) = 1$. Let $n$ be the number of elements in $T$. Compute $2^n$. | 16,384 | graphs = [
Graph(
let={
"_n": Const(21),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(23)), Divides(divisor=Var("d"), dividend... | NT | null | SUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/C4"
] | ac1e32 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"C4",
"MAX_DIVISOR"
] | 2 | 0.002 | 2026-02-08T13:31:14.629931Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-08T13:31:14.631892Z"
} | 703374 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 771
},
"timestamp": "2026-02-15T16:48:56.693Z",
"answer": 16384
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma":... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
9809f6 | comb_factorial_compute_v1_397696148_2105 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 24$. Let $m$ be the number of elements in $S$. Let $n$ be the largest prime number satisfying $m \le n \le 8$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(8),
"n": 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'), Var(name='q')... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_factorial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T12:57:24.162188Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T12:57:24.164274Z"
} | fa03ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 653
},
"timestamp": "2026-02-15T07:43:31.353Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"sta... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
fa801e | algebra_quadratic_discriminant_v1_48377204_270 | Let $ a = -9 $, $ b = 6 $, and $ m = 21 $. Define $ c = \frac{3}{m} \sum_{k=1}^{3} \sum_{j=1}^{7} k $. Compute the value of $ b^2 - 4ac $. | 252 | graphs = [
Graph(
let={
"_m": Const(21),
"_n": Const(4),
"a": Const(-9),
"b": Const(6),
"c": Div(Mul(Const(3), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=In... | NT | null | COMPUTE | sympy | V1 | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT",
"V1"
] | 3 | 0.009 | 2026-02-08T15:19:51.457408Z | {
"verified": true,
"answer": 252,
"timestamp": "2026-02-08T15:19:51.466888Z"
} | 4ebb54 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 265
},
"timestamp": "2026-02-16T05:22:44.601Z",
"answer": 252
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "SUM_INDEPENDENT",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
a057df | antilemma_sum_equals_v1_677425708_1147 | Let $n$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 7$ and $1 \leq b \leq 11$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$, $1 \leq i \leq 75$, and $1 \leq j \leq 76$. Determine the value of $x$. | 75 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(11)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.061 | 2026-02-08T04:01:12.396540Z | {
"verified": true,
"answer": 75,
"timestamp": "2026-02-08T04:01:12.457251Z"
} | b42d9d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 3924
},
"timestamp": "2026-02-09T16:15:10.857Z",
"answer": 75
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
cde006 | comb_count_derangements_v1_717093673_2418 | Let $n_1$ range over the positive integers from 1 to 8. Define $n$ to be the sum of all such $n_1$ for which $n_1$ is divisible by 8. Compute the number of derangements of $n$ elements, denoted $!n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(8),
"n": SumOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Eq(Mod(value=Var("n1"), modulus=Const(8)), Const(0))))),
"result": Subfactorial(arg=Ref(name='n')),
},
... | COMB | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | comb_count_derangements_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.003 | 2026-02-08T16:50:04.928221Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T16:50:04.931329Z"
} | fb9a21 | 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": 1147
},
"timestamp": "2026-02-17T12:29:15.554Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lem... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
db51f2 | geo_count_lattice_rect_v1_677425708_4111 | Let $a = 81$ and $b = 29$. Define $R$ to be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $r$ be the remainder when $|R|$ is divided by 11. Compute the $r$-th Bell number. | 877 | graphs = [
Graph(
let={
"a": Const(81),
"b": Const(29),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T06:25:58.842542Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T06:25:58.843049Z"
} | eba370 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 699
},
"timestamp": "2026-02-24T06:08:34.408Z",
"answer": 877
},
{
"id"... | 1 | [] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||||
1b8e9a | nt_sum_divisors_mod_v1_1918700295_1374 | Let $n$ be the number of positive integers $k$ such that the smallest sum $x + y$ over all ordered pairs $(x, y)$ of positive integers with $xy = 225$ divides the $k$-th Fibonacci number, and $k \leq 302400$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divid... | 8,975 | graphs = [
Graph(
let={
"_n": Const(225),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(302400)), Divides(divisor=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositiv... | NT | null | COMPUTE | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | nt_sum_divisors_mod_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.003 | 2026-02-08T05:48:31.131218Z | {
"verified": true,
"answer": 8975,
"timestamp": "2026-02-08T05:48:31.134637Z"
} | fc0775 | 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": 1411
},
"timestamp": "2026-02-12T14:14:52.697Z",
"answer": 8975
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status":... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
233d13 | antilemma_k3_v1_458359167_3835 | Let $m = 55191$ and $n = 39192$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Let $A$ be the sum of $\phi(d)$ over all positive divisors $d$ of $7229$. Let $B$ be the sum of $\phi(d)$ over all positive divisors $d$ of $A$. Compute the remainder when $B \cdot x$ is divided by $m$. | 23,565 | graphs = [
Graph(
let={
"_m": Const(55191),
"_n": Const(39192),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(SumOverDivisors(n=SumOverDivisors(n=Const(value=7229), var='d', expr=EulerPhi(n=Var(name='d'))),... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3",
"K3"
] | 574452 | antilemma_k3_v1 | affine_mod | 4 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T11:23:18.934186Z | {
"verified": true,
"answer": 23565,
"timestamp": "2026-02-08T11:23:18.936259Z"
} | a2ac8a | 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": 6781
},
"timestamp": "2026-02-14T13:48:56.017Z",
"answer": 23565
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4de797 | modular_sum_quadratic_residues_v1_677425708_3407 | Let $p$ be the largest prime number $n$ such that $2 \leq n \leq 354$. Compute $\frac{p(p-1)}{4}$. | 31,064 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(354)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T05:41:24.748097Z | {
"verified": true,
"answer": 31064,
"timestamp": "2026-02-08T05:41:24.750661Z"
} | dcd39b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 679
},
"timestamp": "2026-02-12T13:54:35.446Z",
"answer": 31064
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
ca151c | modular_mod_compute_v1_1439011603_1857 | Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1000000$. Find the remainder when $-39204$ is divided by $m$. | 796 | graphs = [
Graph(
let={
"a": Const(-39204),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1000000)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:19:44.445541Z | {
"verified": true,
"answer": 796,
"timestamp": "2026-02-08T16:19:44.447982Z"
} | c268b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 734
},
"timestamp": "2026-02-17T01:38:14.211Z",
"answer": 796
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ee111b | sequence_fibonacci_compute_v1_1520064083_10018 | Let $n$ be the smallest positive integer divisor of $640987$ that is at least as large as the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Compute the $n$-th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T11:09:11.060435Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T11:09:11.061941Z"
} | e964fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 2395
},
"timestamp": "2026-02-14T10:35:20.958Z",
"answer": 28657
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
efa4bb | sequence_count_fib_divisible_v1_1439011603_1937 | Let $\text{upper}$ be the number of integers $t$ with $19 \leq t \leq 951$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 98$, $1 \leq b \leq 150$, and $t = 5a + 3b + 11$. Let $d = 4$. Compute the number of positive integers $n$ with $1 \leq n \leq \text{upper}$ such that the $n$-th Fibonacci number is ... | 154 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=98)), Geq(left=Var(name='b'), right=Const(va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.122 | 2026-02-08T16:23:23.157790Z | {
"verified": true,
"answer": 154,
"timestamp": "2026-02-08T16:23:23.279397Z"
} | fca259 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 3646
},
"timestamp": "2026-02-17T03:53:55.003Z",
"answer": 154
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1c6b3d | comb_count_surjections_v1_1520064083_3605 | Let $k$ be the number of integers $t$ in the range $5 \leq t \leq 12$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Let $n = 6$. Determine the value of $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $... | 720 | graphs = [
Graph(
let={
"n": Const(6),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(nam... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T05:46:49.327783Z | {
"verified": true,
"answer": 720,
"timestamp": "2026-02-08T05:46:49.330362Z"
} | dc0806 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 1073
},
"timestamp": "2026-02-24T04:27:55.424Z",
"answer": 720
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
310cbe | modular_modexp_compute_v1_784195855_8490 | Let $a = 43$ and let $e$ be the number of ordered pairs $(x, y)$ of integers such that $1 \le x \le 88$ and $1 \le y \le 88$. Let $m = 25200$. Compute the remainder when $a^e$ is divided by $m$. | 16,801 | graphs = [
Graph(
let={
"a": Const(43),
"e": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(88)), right=IntegerRange(start=Const(1), end=Const(88)))),
"m": Const(25200),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m"))... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | modular_modexp_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T16:07:14.666818Z | {
"verified": true,
"answer": 16801,
"timestamp": "2026-02-08T16:07:14.668880Z"
} | 878418 | 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": 1739
},
"timestamp": "2026-02-16T21:06:59.122Z",
"answer": 16801
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ce29d | lin_form_endings_v1_1874849503_974 | Let $t$ be an integer satisfying $70 \leq t \leq 1070$. Determine the number of such $t$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 23$, and $t = 30a + 40b$. Multiply this number by 8191, and let the result be $S$. Find the remainder when $S$ is divided by 79502. | 62,627 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=C... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:29:41.079466Z | {
"verified": true,
"answer": 62627,
"timestamp": "2026-02-08T13:29:41.081245Z"
} | b61203 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 5760
},
"timestamp": "2026-02-24T18:34:32.115Z",
"answer": 62627
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
19a7e7_n | alg_sym_quad_system_v1_1218484723_3621 | An engineer is designing a triangular truss with side labels $a$, $b$, and $c$, all positive integers. The geometry of the truss requires
$$a^{2} + b^{2} + c^{2} = ab + bc + ca.$$
The total load on the three joints must equal a specific count: let this count be the number of integers $n$ with $1 \le n \le 53982$ such ... | 27,310 | ALG | null | COMPUTE | sympy | C5 | [
"C5",
"B3"
] | 2a47df | alg_sym_quad_system_v1 | null | 7 | null | [
"B3",
"C5"
] | 2 | 0.018 | 2026-02-25T05:14:24.249795Z | null | 83cbbe | 19a7e7 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 381,
"completion_tokens": 6477
},
"timestamp": "2026-03-30T20:20:54.229Z",
"answer": 10
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
39476a | diophantine_product_count_v1_458359167_176 | Let $n$ range over the positive integers from 1 to 5544. Define $\text{upper}$ to be the number of such $n$ for which the $n$th Fibonacci number is divisible by 24. Let $k = 720$. Now consider the set of positive integers $x$ such that $1 \leq x \leq \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \leq \text{upper}$. ... | 28 | graphs = [
Graph(
let={
"_n": Const(24),
"k": Const(720),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(5544)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Co... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | diophantine_product_count_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MOBIUS_COPRIME"
] | 2 | 0.149 | 2026-02-08T03:03:09.481740Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T03:03:09.631162Z"
} | c4f15f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 6520
},
"timestamp": "2026-02-10T12:32:11.042Z",
"answer": 28
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
... | {
"lo": -0.39,
"mid": 1.8,
"hi": 3.62
} | ||
9c441f | diophantine_fbi2_count_v1_168721529_1749 | Let $T$ be the set of all integers $t$ such that there exist positive integers $a$, $b$ with $1 \leq a \leq 15$, $1 \leq b \leq 8$, and $t = 6a + 15b$, and $21 \leq t \leq 210$. Let $N$ be the number of elements in $T$. Find the number of positive integers $d$ such that $6 \leq d \leq N$, $d$ divides $420$, and $2 \leq... | 11 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(420),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(nam... | NT | null | COUNT | sympy | C3 | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 5.67 | 2026-02-08T13:54:15.067082Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T13:54:20.736975Z"
} | 9abc1e | 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": 7925
},
"timestamp": "2026-02-09T21:11:07.317Z",
"answer": 11
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
e1a6e0 | antilemma_cartesian_v1_1915831931_254 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 11$ and $1 \leq j \leq 13$. Let $c = 625$. Compute $c - x$. | 482 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=Const(13)))),
"_c": Const(625),
"Q": Sub(Ref("_c"), Ref("x")),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T15:17:13.143497Z | {
"verified": true,
"answer": 482,
"timestamp": "2026-02-08T15:17:13.144317Z"
} | b901ee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 272
},
"timestamp": "2026-02-24T20:32:07.972Z",
"answer": 482
},
{
"id"... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
65d106 | nt_min_coprime_above_v1_717093673_2191 | Let $a$ be the smallest integer $n$ such that $86436 < n \leq 86768$ and $\gcd(n, 322) = 1$. Let $b$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 25\,000\,000$. Compute the remainder when $b - a$ is divided by $86654$. | 10,217 | graphs = [
Graph(
let={
"start": Const(86436),
"upper": Const(86768),
"modulus": Const(322),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | fc629c | nt_min_coprime_above_v1 | negation_mod | 3 | 0 | [
"B3"
] | 1 | 0.054 | 2026-02-08T16:36:36.178707Z | {
"verified": true,
"answer": 10217,
"timestamp": "2026-02-08T16:36:36.232437Z"
} | 0ea88c | 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": 2106
},
"timestamp": "2026-02-17T08:19:41.970Z",
"answer": 10217
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
219618 | comb_factorial_compute_v1_151522320_1413 | Let $m = 23$. Define $k$ to be the number of integers $n$ with $1 \leq n \leq m$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 12$ and $\gcd(p, q) = 1$. Define $n$ to be the largest ... | 5,040 | graphs = [
Graph(
let={
"_m": Const(23),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
"... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"L3C/MAX_PRIME_BELOW"
] | 05d7f9 | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"L3C",
"MAX_PRIME_BELOW"
] | 3 | 0.003 | 2026-02-08T03:59:38.913299Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T03:59:38.915930Z"
} | 0bbfa3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 1552
},
"timestamp": "2026-02-11T16:12:07.788Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
d98caa | modular_min_linear_v1_1918700295_2506 | Let $a = \sum_{d \mid 2649} \phi(d)$, where $\phi$ is Euler's totient function. Let $x$ be the smallest positive integer such that $x \leq 3394$ and $a \cdot x \equiv 92 \pmod{3394}$. Compute the remainder when $44121 \cdot x$ is divided by $70505$. | 38,558 | graphs = [
Graph(
let={
"_n": Const(2649),
"a": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"b": Const(92),
"m": Const(3394),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)),... | NT | null | EXTREMUM | sympy | K3 | [
"K3"
] | 54c41e | modular_min_linear_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.252 | 2026-02-08T07:56:11.331864Z | {
"verified": true,
"answer": 38558,
"timestamp": "2026-02-08T07:56:11.583896Z"
} | 9b60f0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 3102
},
"timestamp": "2026-02-13T13:49:19.615Z",
"answer": 38558
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e96ce5 | nt_count_primes_v1_784195855_2339 | Compute the number of ordered pairs $(p, q)$ of positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let this count be $L$. Compute the number of prime numbers $n$ such that $L \leq n \leq 45369$. | 4,707 | graphs = [
Graph(
let={
"upper": Const(45369),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 9.058 | 2026-02-08T05:41:41.505658Z | {
"verified": true,
"answer": 4707,
"timestamp": "2026-02-08T05:41:50.564019Z"
} | 9c8471 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 2024
},
"timestamp": "2026-02-12T13:08:07.603Z",
"answer": 4707
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6d9e20 | diophantine_product_count_v1_50713871_85 | Let $k$ be the number of integers $t$ such that $7 \leq t \leq 430$ and there exist positive integers $a \leq 58$ and $b \leq 70$ satisfying $t = 5a + 2b$. Let $u = 332$. Define $r$ to be the number of positive integers $x \leq u$ such that $x$ divides $k$ and $\frac{k}{x} \leq u$. Find the value of $65361 \cdot r \bmo... | 33,406 | graphs = [
Graph(
let={
"_n": Const(50162),
"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=58)), Geq(left=V... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.019 | 2026-02-08T02:44:50.688752Z | {
"verified": true,
"answer": 33406,
"timestamp": "2026-02-08T02:44:50.708220Z"
} | 060c75 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 6140
},
"timestamp": "2026-02-08T19:48:27.980Z",
"answer": 32606
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 3.89,
"hi": 5.66
} | ||
a4c9a2 | comb_factorial_compute_v1_601307018_8827 | Let $n = \sum_{k=0}^{2} 2^k$ and let $M = n!$. Find the remainder when $44121M$ is divided by $99538$. | 1,948 | graphs = [
Graph(
let={
"_n": Const(99538),
"n": Summation(var="k", start=Const(0), end=Const(2), expr=Pow(Const(2), Var("k"))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Ref("_n")),
},
goal=Ref("Q"... | COMB | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_factorial_compute_v1 | null | 2 | 0 | [
"SUM_GEOM"
] | 1 | 0.002 | 2026-03-10T09:16:56.643258Z | {
"verified": true,
"answer": 1948,
"timestamp": "2026-03-10T09:16:56.645430Z"
} | 44a29b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 1059
},
"timestamp": "2026-04-19T09:54:23.469Z",
"answer": 1948
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
342d9a | nt_sum_divisors_mod_v1_124444284_9837 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6350400$. For each pair $(x, y)$, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $\sigma$ denote the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $10247$. | 9,097 | 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(6350400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1024... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T12:42:02.516444Z | {
"verified": true,
"answer": 9097,
"timestamp": "2026-02-08T12:42:02.518603Z"
} | ef395a | 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": 5070
},
"timestamp": "2026-02-15T04:09:17.661Z",
"answer": 9097
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
692ef9 | antilemma_k3_v1_784195855_7265 | Let $n = 25615$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi(d)$ denotes Euler's totient function. Compute $x$. | 25,615 | graphs = [
Graph(
let={
"_n": Const(25615),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T09:10:17.188299Z | {
"verified": true,
"answer": 25615,
"timestamp": "2026-02-08T09:10:17.188655Z"
} | 8b1c23 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 617
},
"timestamp": "2026-02-15T20:35:19.631Z",
"answer": 10240
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
40ad33 | nt_sum_totient_over_divisors_v1_865884756_1614 | Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $2520$, where $\phi$ denotes Euler's totient function. Let $S$ be the sum of $\phi(d_1)$ over all positive divisors $d_1$ of $n$. Compute $S$. | 2,520 | graphs = [
Graph(
let={
"_n": Const(2520),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": SumOverDivisors(n=Ref(name='n'), var='d1', expr=EulerPhi(n=Var(name='d1'))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.012 | 2026-02-08T16:11:26.136039Z | {
"verified": true,
"answer": 2520,
"timestamp": "2026-02-08T16:11:26.148500Z"
} | 1ee60a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 323
},
"timestamp": "2026-02-16T23:02:22.397Z",
"answer": 2520
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
49ce84 | diophantine_fbi2_count_v1_1978505735_524 | Let $n = 54$. Let $k$ be the number of integers $t$ such that $9 \leq t \leq 74$ and there exist integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 16$, and $t = 7a + 2b$. Let $r$ be the number of divisors $d$ of $k$ such that $5 \leq d \leq 54$ and $5 \leq \frac{k}{d} \leq 54$. Let $c$ be the largest prime nu... | 13,388 | graphs = [
Graph(
let={
"_n": Const(54),
"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=6)), Geq(left=Var(n... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | 4a5bfb | diophantine_fbi2_count_v1 | affine_mod | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.015 | 2026-02-08T15:26:05.836879Z | {
"verified": true,
"answer": 13388,
"timestamp": "2026-02-08T15:26:05.851488Z"
} | cfd14a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2926
},
"timestamp": "2026-02-16T05:46:04.198Z",
"answer": 13388
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
176866 | comb_count_derangements_v1_677425708_1480 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 45056$ and $\binom{45056}{j}$ is odd. Compute the subfactorial of $n$, denoted $!n$, which is the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_n": Const(45056),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(45056)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T04:13:36.412853Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T04:13:36.413944Z"
} | 0255ac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1226
},
"timestamp": "2026-02-09T20:32:59.144Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
bdb38f_n | sequence_fibonacci_compute_v1_601307018_862 | A composer assigns musical motifs based on Fibonacci and Bell numbers. The 24th Fibonacci number determines a seed value $M$. The number of ways to write 22 as a sum of two positive odd integers gives a modulus $k$. The final motif index is the Bell number $B_{M \bmod k}$. Compute this index. | 5 | ALG | COMB | COMPUTE | sympy | STARS_BARS | [
"COMB1"
] | d93ba8 | sequence_fibonacci_compute_v1 | bell_mod | 5 | null | [
"COMB1",
"STARS_BARS"
] | 2 | 0.508 | 2026-03-10T01:28:33.954188Z | null | b18287 | bdb38f | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1804
},
"timestamp": "2026-03-29T14:40:11.366Z",
"answer": 1
},
{
"id... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
9d7b9d | modular_min_linear_v1_1874849503_137 | Let $S$ be the set of all integers $n$ such that $1 \le n \le p$, where $p$ is the largest prime number less than or equal to $5853$. Define $a$ to be the number of integers in $S$ that are relatively prime to $30$. Let $m = 18643$ and $b = 1261$. Determine the value of the smallest positive integer $x$ such that $1 \l... | 15,252 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5853)), IsPrime(Var("n")))))), Eq(GCD(a=Var("n"), b=Const(30)), Const... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/C4"
] | a99ef8 | modular_min_linear_v1 | null | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 1.891 | 2026-02-08T12:49:45.525631Z | {
"verified": true,
"answer": 15252,
"timestamp": "2026-02-08T12:49:47.416859Z"
} | ac58de | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 5821
},
"timestamp": "2026-02-10T03:33:20.774Z",
"answer": 15252
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIM... | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
e14879 | geo_count_lattice_rect_v1_1978505735_2103 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 180$ and $0 \leq y \leq 221$. | 40,182 | graphs = [
Graph(
let={
"a": Const(180),
"b": Const(221),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T16:39:41.590196Z | {
"verified": true,
"answer": 40182,
"timestamp": "2026-02-08T16:39:41.590826Z"
} | a8f350 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 1084
},
"timestamp": "2026-02-24T21:46:10.428Z",
"answer": 40182
},
{... | 1 | [] | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||||
4d1109 | nt_gcd_compute_v1_1978505735_300 | Let $a = 118641$ and $b = 276829$. Let $d$ be the greatest common divisor of $a$ and $b$.
Compute $d$. | 39,547 | graphs = [
Graph(
let={
"a": Const(118641),
"b": Const(276829),
"result": GCD(a=Ref("a"), b=Ref("b")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C4/MOBIUS_SQUAREFREE",
"DIVISOR_PARITY"
] | 46bdbd | nt_gcd_compute_v1 | null | 2 | 0 | [
"C4",
"DIVISOR_PARITY",
"LIN_FORM",
"MOBIUS_SQUAREFREE"
] | 4 | 0.007 | 2026-02-08T15:17:41.120420Z | {
"verified": true,
"answer": 39547,
"timestamp": "2026-02-08T15:17:41.127097Z"
} | 13743c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 419
},
"timestamp": "2026-02-16T05:21:38.901Z",
"answer": 39547
},
{
"id": 11,
... | 2 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
9edca0 | nt_lcm_compute_v1_124444284_6784 | Let $a = 1095$ and let $b$ be the number of positive integers $n \leq 8284$ such that $4$ divides $n$ and $\gcd(n, 15) = 1$. Let $\text{result} = \text{lcm}(a, b)$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 64$, and let $m = \min\{x + y \mid (x, y) \in S\}$. Compute the remai... | 73,127 | graphs = [
Graph(
let={
"_n": Const(8284),
"a": Const(1095),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(4), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(15)), Const(1))))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3",
"C5"
] | cc81ff | nt_lcm_compute_v1 | mod_exp | 6 | 0 | [
"B3",
"C5"
] | 2 | 0.002 | 2026-02-08T08:38:17.434754Z | {
"verified": true,
"answer": 73127,
"timestamp": "2026-02-08T08:38:17.437189Z"
} | c384c7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1423
},
"timestamp": "2026-02-13T20:12:24.153Z",
"answer": 73127
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
601e8d_n | geo_visible_lattice_v1_1419126231_943 | A city planner designs a $196 \times 196$ grid of city blocks, each at integer coordinates $(x,y)$ with $1 \leq x, y \leq 196$. A diagonal walkway connects the southwest corner of block $(1,1)$ to the northeast corner of block $(x,y)$. The walkway is considered *unobstructed* if no other grid point lies on the segment ... | 54,527 | GEOM | GEOM | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | null | null | null | 0.769 | 2026-02-25T10:27:09.365336Z | null | 5c5b28 | 601e8d | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 13923
},
"timestamp": "2026-03-31T04:09:25.980Z",
"answer": 54103
},
{
... | 1 | [] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |||
5bfee7 | comb_bell_compute_v1_865884756_1262 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 220500$, $\gcd(p, q) = 1$, and $p < q$. Let $B_n$ denote the $n$th Bell number, which is the number of partitions of a set of $n$ elements. Compute the remainder when $69163 \cdot B_n$ is divided by $78387$. | 65,496 | 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=220500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T15:51:36.148417Z | {
"verified": true,
"answer": 65496,
"timestamp": "2026-02-08T15:51:36.150167Z"
} | 91f8b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1814
},
"timestamp": "2026-02-16T14:23:16.705Z",
"answer": 65496
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab52e1 | modular_count_residue_v1_784195855_5026 | Let $m$ be the number of positive integers $n$ such that $1 \le n \le 54$ and the sum of the digits of $n$ is even. Let $r$ be the smallest divisor of $41327$ that is at least $2$. Compute the number of positive integers $n$ such that $1 \le n \le 51076$ and $n \equiv r \pmod{m}$. | 1,892 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(51076),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(54)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"r": MinOverSet(s... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"L3B"
] | 50af68 | modular_count_residue_v1 | null | 5 | 0 | [
"L3B",
"MIN_PRIME_FACTOR"
] | 2 | 1.679 | 2026-02-08T07:35:48.485830Z | {
"verified": true,
"answer": 1892,
"timestamp": "2026-02-08T07:35:50.165284Z"
} | c4615a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 1775
},
"timestamp": "2026-02-13T11:19:04.962Z",
"answer": 1965
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"statu... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a0123b | nt_count_intersection_v1_458359167_4635 | Let $N = 10000$. Let $b$ be the number of integers $t$ such that $7 \leq t \leq 30$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 5$, and $t = 5a + 2b$. Compute the number of positive integers $n \leq N$ such that $3$ divides $n$ and $\gcd(n, b) = 1$. | 1,334 | graphs = [
Graph(
let={
"N": Const(10000),
"a": Const(3),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Co... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.472 | 2026-02-08T11:57:10.163809Z | {
"verified": true,
"answer": 1334,
"timestamp": "2026-02-08T11:57:10.635404Z"
} | 4b91f8 | 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": 2509
},
"timestamp": "2026-02-14T21:18:29.879Z",
"answer": 1334
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
5a6e16 | diophantine_product_count_v1_1742523217_3317 | Let $k$ be the sum of $\phi(d)$ over all positive divisors $d$ of $180$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $x$ such that $1 \leq x \leq 120$, $x$ divides $k$, and $\frac{k}{x} \leq 120$. | 16 | graphs = [
Graph(
let={
"k": SumOverDivisors(n=Const(value=180), var='d', expr=EulerPhi(n=Var(name='d'))),
"upper": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | diophantine_product_count_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.012 | 2026-02-08T05:46:40.579970Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T05:46:40.592141Z"
} | 187e68 | 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": 871
},
"timestamp": "2026-02-12T14:50:04.680Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
49141b | antilemma_count_primes_v1_1918700295_52 | Compute the number of prime numbers $n$ such that $2 \leq n \leq 2887$. | 418 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(2887)), IsPrime(Var("n"))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | antilemma_count_primes_v1 | null | 6 | 0 | [
"COUNT_PRIMES"
] | 1 | 0 | 2026-02-08T02:57:54.738793Z | {
"verified": true,
"answer": 418,
"timestamp": "2026-02-08T02:57:54.739250Z"
} | f8790b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 7714
},
"timestamp": "2026-02-08T22:20:03.013Z",
"answer": 418
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
e8cc85 | antilemma_v7_kummer_798873815_167 | Compute the largest integer $k$ such that $5^k$ divides $\binom{185}{74}$. | 3 | graphs = [
Graph(
let={
"x": MaxKDivides(target=Binom(n=Const(185), k=Const(74)), base=Const(5)),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | antilemma_v7_kummer | null | 6 | null | [
"V7"
] | 1 | 0.038 | 2026-02-08T02:29:55.429804Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T02:29:55.467997Z"
} | 202bfb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 835
},
"timestamp": "2026-02-08T19:06:43.285Z",
"answer": 3
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.46,
"mid": -4.17,
"hi": -1.14
} | ||
99e7e0 | nt_count_divisible_and_v1_397696148_1924 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 15681600$. Let $T$ be the set of all values $x + y$ for $(x, y) \in S$. Let $m$ be the minimum value in $T$. Compute the number of positive integers $n$ such that $1 \leq n \leq m$, $n$ is divisible by $6$, and $n$ is divisible by $10... | 1,520 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(15681600)))), expr=Sum(Var("x"), Var("y")))),
"d1": Cons... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.545 | 2026-02-08T12:50:55.153089Z | {
"verified": true,
"answer": 1520,
"timestamp": "2026-02-08T12:50:55.697897Z"
} | 984b6d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 3332
},
"timestamp": "2026-02-15T06:40:08.971Z",
"answer": 1520
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
69167f | comb_factorial_compute_v1_601307018_361 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ satisfying $$
64a^3 + 144a^2b + 27b^3 + C \cdot a b^2 = 658503,
$$ where $C = \left|\left\{ t : t = 2a_1 + 7b_1\ \text{for some integers}\ a_1,b_1\ \text{with}\ 1 \le a_1 \le 412,\ 1 \le b_1 \le 85,\ \text{and}\ 9 \le t \le 14... | 64,260 | graphs = [
Graph(
let={
"_m": Const(15),
"_n": Const(67585),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/QF_PSD_COUNT_LEQ/POLY3_COUNT"
] | fb45da | comb_factorial_compute_v1 | null | 7 | 0 | [
"LIN_FORM",
"POLY3_COUNT",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.043 | 2026-03-10T00:54:19.674740Z | {
"verified": true,
"answer": 64260,
"timestamp": "2026-03-10T00:54:19.718121Z"
} | 2c9b8e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T22:54:04.753Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma"... | {
"lo": 5.22,
"mid": 7.83,
"hi": 10
} | ||
ce96a0 | sequence_lucas_compute_v1_458359167_3288 | Let $n$ be the smallest divisor of $437$ that is greater than or equal to $2$. Compute the $n$-th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_n": Const(437),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_lucas_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T08:15:33.796169Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T08:15:33.797135Z"
} | b98b43 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 726
},
"timestamp": "2026-02-13T16:25:13.074Z",
"answer": 9349
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
8bfc74 | antilemma_cartesian_v1_151522320_876 | Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 16$ and $1 \leq b \leq 23$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $x + 2$. | 285 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(23)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T03:37:34.137479Z | {
"verified": true,
"answer": 285,
"timestamp": "2026-02-08T03:37:34.138395Z"
} | 689dc3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 2032
},
"timestamp": "2026-02-10T15:12:27.064Z",
"answer": 285
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
6648ac | geo_visible_lattice_v1_1125832087_120 | A lattice point $(x, y)$ is called visible from the origin if $\gcd(x, y) = 1$. Let $n = 77$. Compute the number of visible lattice points $(x, y)$ such that $1 \leq x \leq n$ and $1 \leq y \leq n$.
Find the value of this number. | 3,663 | graphs = [
Graph(
let={
"n": Const(77),
"result": VisibleLatticePoints(n=Ref(name='n')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 0.127 | 2026-02-08T02:52:25.243270Z | {
"verified": true,
"answer": 3663,
"timestamp": "2026-02-08T02:52:25.369812Z"
} | 07c104 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 2461
},
"timestamp": "2026-02-10T11:46:53.025Z",
"answer": 3663
},
{
"i... | 1 | [] | {
"lo": 2.57,
"mid": 4,
"hi": 5.3
} | ||||
a3b7bb | antilemma_k3_v1_1978505735_1084 | Compute the sum of $\varphi(d)$ over all positive divisors $d$ of $13108$, where $\varphi$ denotes Euler's totient function. | 13,108 | graphs = [
Graph(
let={
"_n": Const(13108),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:49:10.687347Z | {
"verified": true,
"answer": 13108,
"timestamp": "2026-02-08T15:49:10.688017Z"
} | 9fb6d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 828
},
"timestamp": "2026-02-16T14:42:33.674Z",
"answer": 13108
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e45b57 | diophantine_fbi2_count_v1_865884756_541 | Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 960$. Let $m = 170$ and $n = 3$. Determine the number of integers $d$ such that $2 \leq d \leq 170$, $d$ divides $k$, $\frac{k}{d} \geq 3$, and $\frac{k}{d} \leq \sum_{k1=1}^{18} k1$. Compute this number. | 20 | graphs = [
Graph(
let={
"_m": Const(170),
"_n": Const(3),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(... | NT | null | COUNT | sympy | K14 | [
"SUM_ARITHMETIC",
"COMB1"
] | 095a4b | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"COMB1",
"K14",
"SUM_ARITHMETIC"
] | 3 | 0.325 | 2026-02-08T15:29:37.388699Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T15:29:37.713991Z"
} | b17804 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1594
},
"timestamp": "2026-02-16T07:38:12.423Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2f70d9 | nt_count_phi_equals_v1_865884756_2840 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1562500$. For each such pair, compute $x + y$, and let $u$ be the minimum of these sums. Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 1092$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 315$, $1 \le... | 2 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1562500)))), expr=Sum(Var("x"), Var("y")))),
"k": CountO... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.429 | 2026-02-08T16:58:14.162928Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:58:14.592020Z"
} | 698428 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 5673
},
"timestamp": "2026-02-17T16:23:42.591Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ec1e33 | nt_count_divisible_and_v1_168721529_1964 | Let $n = 2054$ and let $d_1$ be the number of nonnegative integers $j$ such that $0 \le j \le 2054$ and $\binom{2054}{j}$ is odd. Let $d_2$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Compute the number of positive integers $n$ such that $1 \le n \le 25872$,... | 1,078 | graphs = [
Graph(
let={
"_n": Const(2054),
"upper": Const(25872),
"d1": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(2054), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonne... | ALG | COMB | COUNT | sympy | B3 | [
"B3",
"V8"
] | 5b3848 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B3",
"V8"
] | 2 | 0.863 | 2026-02-08T14:02:09.418202Z | {
"verified": true,
"answer": 1078,
"timestamp": "2026-02-08T14:02:10.281320Z"
} | b7d641 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 617
},
"timestamp": "2026-02-10T00:08:48.433Z",
"answer": 1078
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
9dee4d | antilemma_sum_equals_v1_1918700295_3814 | Let $T$ be the set of ordered pairs $(i,j)$ such that $1 \leq i \leq 52$, $1 \leq j \leq 53$, and $i + j = 53$. Let $x$ be the number of elements in $T$.
Let $S$ be the set of positive integers $t$ such that $16 \leq t \leq 224$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 19$, an... | 29,306 | graphs = [
Graph(
let={
"_n": Const(53),
"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(52)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 4ac49b | antilemma_sum_equals_v1 | crt_mix_3 | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM",
"ONE_BINOM_0"
] | 3 | 0.008 | 2026-02-08T08:57:46.064842Z | {
"verified": true,
"answer": 29306,
"timestamp": "2026-02-08T08:57:46.072620Z"
} | f145cf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 374,
"completion_tokens": 30628
},
"timestamp": "2026-02-24T10:15:11.515Z",
"answer": 55400
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
8d62e6 | diophantine_sum_product_min_v1_458359167_2229 | Let $n = 7$, $S = 8$, and $P = 16$. Define $\text{result}$ to be the smallest positive integer $x$ such that $1 \leq x \leq n$ and $x(S - x) = P$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1119364$. Define $c$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Co... | 2,112 | graphs = [
Graph(
let={
"_n": Const(7),
"S": Const(8),
"P": Const(16),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("_n")), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
"_c... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | fc629c | diophantine_sum_product_min_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T05:13:30.470230Z | {
"verified": true,
"answer": 2112,
"timestamp": "2026-02-08T05:13:30.474680Z"
} | 5ef26a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 1020
},
"timestamp": "2026-02-11T23:01:51.214Z",
"answer": 2112
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
8e263b | nt_count_digit_sum_v1_124444284_6857 | Let $s$ be the number of integers $t$ such that $7 \leq t \leq 36$ and $t = 3a + 4b$ for some integers $a, b$ with $1 \leq a \leq 4$ and $1 \leq b \leq 6$. Let $r$ be the number of positive integers $n \leq 99999$ such that the sum of the decimal digits of $n$ is equal to $s$. Compute $78961 - r$. | 73,086 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 3.66 | 2026-02-08T08:40:39.210699Z | {
"verified": true,
"answer": 73086,
"timestamp": "2026-02-08T08:40:42.871128Z"
} | 9fd698 | 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": 2499
},
"timestamp": "2026-02-13T20:39:51.841Z",
"answer": 73086
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c58fc5 | nt_count_divisible_v1_1742523217_1128 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. Let $d$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Determine the number of positive integers $n$ such that $n \leq 66430$ and $n$ is divisible by $d$. | 4,745 | graphs = [
Graph(
let={
"upper": Const(66430),
"divisor": 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(49)))), expr=Sum(Var("x"), Var(... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_v1 | null | 3 | 0 | [
"B3"
] | 1 | 2.09 | 2026-02-08T03:26:52.457347Z | {
"verified": true,
"answer": 4745,
"timestamp": "2026-02-08T03:26:54.547675Z"
} | e62a58 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1949
},
"timestamp": "2026-02-10T03:51:01.697Z",
"answer": 4745
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
7dbf6b | modular_modexp_compute_v1_1520064083_3884 | Let $e$ be the number of positive integers $n$ such that $1 \leq n \leq 19208$ and the $n$th Fibonacci number is divisible by $7$. Compute the remainder when $47^e$ is divided by $18225$. | 4,547 | graphs = [
Graph(
let={
"_n": Const(7),
"a": Const(47),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19208)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"m": Const(18225)... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | modular_modexp_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T05:56:53.737349Z | {
"verified": true,
"answer": 4547,
"timestamp": "2026-02-08T05:56:53.738519Z"
} | f9e81c | 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": 3257
},
"timestamp": "2026-02-12T17:29:21.366Z",
"answer": 4547
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
54a198 | comb_count_permutations_fixed_v1_1520064083_7795 | Let $m = 2$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 10$. Define $n_0$ to be the maximum value of $xy$ over all pairs $(x,y) \in P$. Now, let $Q$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n_0$. Define $n$ to be the minimum value of $x + ... | 240 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(10)))), expr=Mul(Var("x"), Var("y")))),
... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B1/B3"
] | 57e303 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"B1",
"B3",
"MIN_PRIME_FACTOR"
] | 3 | 0.003 | 2026-02-08T09:18:31.264391Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T09:18:31.267856Z"
} | 9c42ee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1005
},
"timestamp": "2026-02-14T03:01:09.321Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2b03a4 | modular_sum_quadratic_residues_v1_1874849503_631 | Let $p$ be the largest prime number less than or equal to $521$. Compute $\frac{p(p-1)}{4}$. Multiply this value by $26006$, and let $R$ be the remainder when the product is divided by $85185$. Compute $R$. | 16,135 | graphs = [
Graph(
let={
"_n": Const(85185),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(521)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=M... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T13:13:32.552242Z | {
"verified": true,
"answer": 16135,
"timestamp": "2026-02-08T13:13:32.556100Z"
} | e4a99a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 2295
},
"timestamp": "2026-02-09T19:14:20.674Z",
"answer": 16135
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
3de90e | comb_count_surjections_v1_1978505735_1682 | Let $t$ be an integer. Let $s$ be the number of values of $t$ in the range $5 \leq t \leq 22$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 4$, and $t = 2a + 3b$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s$. Let $k = 4$. Let ... | 41,709 | graphs = [
Graph(
let={
"_n": Const(65505),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COUNT | sympy | COMB1 | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.031 | 2026-02-08T16:21:17.173861Z | {
"verified": true,
"answer": 41709,
"timestamp": "2026-02-08T16:21:17.204570Z"
} | eaea07 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 3458
},
"timestamp": "2026-02-24T20:37:06.687Z",
"answer": 41709
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM"... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
31e0b8 | comb_bell_compute_v1_1520064083_5574 | Let $T$ be the set of all positive integers $t$ at most 350 for which there exist positive integers $a \leq 21$ and $b \leq 19$ such that $t = 4a + 14b$. Let $n$ be the number of positive integers at most $|T|$ that are divisible by 7 and relatively prime to 6. Let $B_n$ denote the $n$-th Bell number, the number of par... | 22,405 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(93527),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name=... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C5"
] | 683493 | comb_bell_compute_v1 | null | 6 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T07:26:30.826478Z | {
"verified": true,
"answer": 22405,
"timestamp": "2026-02-08T07:26:30.828372Z"
} | 3d0642 | 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": 4223
},
"timestamp": "2026-02-13T10:19:37.172Z",
"answer": 22405
},
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
06f392 | comb_sum_binomial_row_v1_601307018_2466 | Let $N$ be the largest positive integer $d$ such that $d^2 \leq 1055744$ and $d \mid 1055744$. Let $M = 2^{15}$. Find the remainder when $N - M$ is divided by $85622$. | 53,878 | graphs = [
Graph(
let={
"n": Const(15),
"result": Pow(Const(2), Ref("n")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(1055744)), Leq(Mul(Var("d"), Var("d")), Const(1055744))))),
... | COMB | NT | SUM | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | ff7764 | comb_sum_binomial_row_v1 | negation_mod | 3 | 0 | [
"B3_CLOSEST"
] | 1 | 0.004 | 2026-03-10T03:12:09.014949Z | {
"verified": true,
"answer": 53878,
"timestamp": "2026-03-10T03:12:09.018482Z"
} | 5dcd3c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:27:06.036Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"sta... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
493d35 | algebra_poly_eval_v1_1918700295_3387 | Let $z$ be the largest prime number $n$ such that $2 \leq n \leq 21$. Compute the value of $$
\frac{12z^3 + 43z^2 + 28z - 18}{85}.
$$ | 1,157 | graphs = [
Graph(
let={
"_n": Const(3),
"z": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(21)), IsPrime(Var("n"))))),
"result": Div(Sum(Mul(Const(12), Pow(Ref("z"), Ref("_n"))), Mul(Const(43), Pow(Ref("z"), Const(2))... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T08:35:50.887391Z | {
"verified": true,
"answer": 1157,
"timestamp": "2026-02-08T08:35:50.891335Z"
} | 30cfbf | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 430
},
"timestamp": "2026-02-15T20:16:55.237Z",
"answer": 1149
},
{
"id": 11,... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
f61eaa | modular_inverse_v1_397696148_1995 | Let $a = 178$. Let $m$ be the number of positive integers $n$ such that $1 \leq n \leq 1891$ and $\gcd(n, 10) = 1$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 142884$. Define $s_{\text{min}}$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Determine the smalles... | 370 | graphs = [
Graph(
let={
"a": Const(178),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1891)), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elemen... | NT | null | EXTREMUM | sympy | B3 | [
"B3",
"C4"
] | 8d18b3 | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"C4"
] | 2 | 0.035 | 2026-02-08T12:53:48.707482Z | {
"verified": true,
"answer": 370,
"timestamp": "2026-02-08T12:53:48.742677Z"
} | d11278 | 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": 1599
},
"timestamp": "2026-02-15T06:46:00.923Z",
"answer": 370
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
94c45c | geo_count_lattice_triangle_v1_1218484723_46 | Let $M = \left|\min\{ 9b^3 + 51a^2b + 35a^3 + 33ab^2 \mid 1 \le a, b \le 14\} \cdot 127 + 41 \cdot (-128)\right|$, and let $R = \gcd(128, 128) + \gcd(|41 - 128|, |127 - 128|) + \gcd(|0 - 41|, |0 - 127|)$. Compute $\frac{M + 2 - R}{2}$. | 5,440 | graphs = [
Graph(
let={
"_n": Const(127),
"area_2x": Abs(arg=Sum(Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=14)), Geq(left=Va... | GEOM | NT | COUNT | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"POLY3_MIN"
] | 1 | 0.005 | 2026-02-25T01:44:37.298039Z | {
"verified": true,
"answer": 5440,
"timestamp": "2026-02-25T01:44:37.302975Z"
} | 186795 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 905
},
"timestamp": "2026-03-28T21:37:18.660Z",
"answer": 5440
},
{
"id... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
}
] | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
fa9f92 | modular_count_residue_v1_717093673_3762 | Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6718464$. Let $s$ be the minimum value of $x + y$ as $(x, y)$ ranges over $A$. Let $B$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = s$. Let $r$ be the minimum value of $x_1 + y_1$ as $(x_1, y_... | 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(6718464)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | modular_count_residue_v1 | null | 6 | 0 | [
"B3"
] | 1 | 2.116 | 2026-02-08T17:49:49.754774Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T17:49:51.870815Z"
} | 3e845b | 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": 1890
},
"timestamp": "2026-02-18T08:57:03.690Z",
"answer": 1170
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
76102b | antilemma_sum_equals_v1_1978505735_4 | Let $n$ be the number of integers $t$ such that $8 \leq t \leq 60$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 9$, and $t = 3a + 5b$. Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 43$, $1 \leq j \leq 43$, and $i + j = n$. Compute $77777 - x$. | 77,735 | graphs = [
Graph(
let={
"_m": Const(77777),
"_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=5)), Geq(left=V... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.072 | 2026-02-08T15:08:19.361617Z | {
"verified": true,
"answer": 77735,
"timestamp": "2026-02-08T15:08:19.433130Z"
} | 3b8cf0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 3897
},
"timestamp": "2026-02-10T06:39:11.868Z",
"answer": 77735
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
a098d2 | comb_bell_compute_v1_1116507919_238 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 2$ and $1 \leq j \leq 4$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the remainder when $11201 \cdot B_n$ is divided by 84192. | 66,540 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(4)))),
"result": Bell(Ref("n")),
"_c": Const(11201),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modu... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_bell_compute_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T02:29:32.923834Z | {
"verified": true,
"answer": 66540,
"timestamp": "2026-02-08T02:29:32.925016Z"
} | 7c4dd7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1069
},
"timestamp": "2026-02-08T19:16:27.827Z",
"answer": 66540
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -0.94,
"mid": 0.81,
"hi": 2.32
} | ||
f915b7 | nt_count_gcd_equals_v1_151522320_2292 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 158$. Let $u$ be the maximum value of $xy$ over all such pairs. Let $r$ be the number of positive integers $n$ with $1 \leq n \leq u$ such that $\gcd(n, 351) = 1$. Let $p_{\text{max}}$ be the largest prime number $n$ such that $2 \... | 31,570 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(313),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(158)))), e... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B1"
] | 490d53 | nt_count_gcd_equals_v1 | two_moduli | 5 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 3.836 | 2026-02-08T04:43:42.237189Z | {
"verified": true,
"answer": 31570,
"timestamp": "2026-02-08T04:43:46.073558Z"
} | e99a0b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 1595
},
"timestamp": "2026-02-11T21:48:58.224Z",
"answer": 31670
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
0282e9 | modular_min_modexp_v1_1439011603_3090 | Let $a = 7$. Let $b$ be the number of integers $t$ such that $12 \leq t \leq 462$ and there exist integers $a'$ and $b'$ satisfying $1 \leq a' \leq 61$, $1 \leq b' \leq 7$, and $t = 7a' + 5b'$. Let $m = 563$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq 281$ and $7^x \equiv b \pmod{... | 143 | graphs = [
Graph(
let={
"a": Const(7),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=61)), Geq(left=Var(na... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_modexp_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.03 | 2026-02-08T17:13:58.307814Z | {
"verified": true,
"answer": 143,
"timestamp": "2026-02-08T17:13:58.338311Z"
} | a6de89 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 8013
},
"timestamp": "2026-02-17T22:12:09.450Z",
"answer": 143
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
533f7d | antilemma_k2_v1_168721529_981 | Let $x = \sum_{k=1}^{271} \phi(k) \left\lfloor \frac{271}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $c = 46165$. Compute the remainder when $c \cdot x$ is divided by $92489$. | 29,596 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(271), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(271), Var("k"))))),
"_c": Const(46165),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(92489)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T13:22:23.959024Z | {
"verified": true,
"answer": 29596,
"timestamp": "2026-02-08T13:22:23.960300Z"
} | 21ca99 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 3427
},
"timestamp": "2026-02-09T11:32:38.468Z",
"answer": 29596
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
b5d2fb | diophantine_fbi2_min_v1_1742523217_4622 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. Let $k$ be the minimum value of $x + y$ over all such pairs. Let $d$ be a positive integer such that $2 \leq d \leq 24$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Let $r$ be the smallest such $d$. Compute the remainder when $987... | 29,030 | graphs = [
Graph(
let={
"_n": Const(84204),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(49)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T08:59:54.123790Z | {
"verified": true,
"answer": 29030,
"timestamp": "2026-02-08T08:59:54.128506Z"
} | d6fa04 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 628
},
"timestamp": "2026-02-13T23:09:33.155Z",
"answer": 29030
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
3a8e24 | algebra_quadratic_discriminant_v1_458359167_5801 | Let $m = 2$. Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 900$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the number of elements in $A$. Let $E$ be the set of all positive integers $n$ such that $1 \leq n \leq m$ and $n$ is even. Let $s$ be the sum of all... | 31,280 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(61790),
"a": Const(-2),
"b": Const(-10),
"c": Const(-5),
"result": Sub(Pow(Ref("b"), SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"SUM_DIVISIBLE"
] | e5b6b4 | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"SUM_DIVISIBLE"
] | 2 | 0.004 | 2026-02-08T12:42:04.835293Z | {
"verified": true,
"answer": 31280,
"timestamp": "2026-02-08T12:42:04.839278Z"
} | 42d6e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 1379
},
"timestamp": "2026-02-15T03:57:19.289Z",
"answer": 31280
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
fe0b45 | sequence_fibonacci_compute_v1_2051736721_5981 | Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 16451$ such that $\binom{16451}{j}$ is odd, increased by $4$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 6,765 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16451)), Eq(Mod(value=Binom(n=Const(16451), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')), Const(4)),... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | sequence_fibonacci_compute_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T18:53:41.327182Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T18:53:41.328891Z"
} | 53089a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1748
},
"timestamp": "2026-02-18T20:15:53.368Z",
"answer": 6765
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} |
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