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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
7eff5b | sequence_count_fib_divisible_v1_50713871_25 | Let $u$ be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 10$, $1 \leq j \leq 19$, and $\gcd(i,j) = 1$. Let $d = 12$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $d$ divides the $n$-th Fibonacci number. Let this count be $c$. Find the remainder when $44121 \cdot c$ is divided by... | 61,344 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.007 | 2026-02-08T02:43:36.511536Z | {
"verified": true,
"answer": 61344,
"timestamp": "2026-02-08T02:43:36.518888Z"
} | c39476 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2318
},
"timestamp": "2026-02-08T19:45:09.031Z",
"answer": 61344
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -0.08,
"mid": 2.16,
"hi": 4.1
} | ||
ffb5f3 | nt_num_divisors_compute_v1_1918700295_686 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 34$. Let $r$ be the number of positive divisors of $n$. Find the remainder when $44121 \cdot r$ is divided by $59575$. | 13,213 | graphs = [
Graph(
let={
"_n": Const(34),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T03:23:08.990036Z | {
"verified": true,
"answer": 13213,
"timestamp": "2026-02-08T03:23:08.993055Z"
} | 5e3667 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 378
},
"timestamp": "2026-02-10T14:11:55.018Z",
"answer": 13213
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a368bc | antilemma_sum_equals_v1_1520064083_4189 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 57$, $1 \leq i \leq 55$, and $1 \leq j \leq 56$. Compute the value of
$$
x + \phi(x + 1) + \tau(x + 1),
$$
where $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$, and $\t... | 87 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(57)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(55)), right=IntegerRange(start=Const(1), end=Const(56))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.006 | 2026-02-08T06:08:19.933264Z | {
"verified": true,
"answer": 87,
"timestamp": "2026-02-08T06:08:19.938969Z"
} | 8a9388 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 732
},
"timestamp": "2026-02-24T05:28:09.054Z",
"answer": 87
},
{
"id":... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
264109 | geo_count_lattice_rect_v1_865884756_405 | Compute the number of lattice points in the rectangle defined by $0 \leq x \leq 144$ and $0 \leq y \leq 416$, including the boundary. | 60,465 | graphs = [
Graph(
let={
"a": Const(144),
"b": Const(416),
"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 | 2026-02-08T15:21:05.365297Z | {
"verified": true,
"answer": 60465,
"timestamp": "2026-02-08T15:21:05.366059Z"
} | 46c6f5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 181
},
"timestamp": "2026-02-24T20:31:37.533Z",
"answer": 60465
},
{
"i... | 1 | [] | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||||
a3ea53 | nt_count_coprime_v1_48377204_2051 | Let $k$ be the largest integer such that $3^k \leq 486592498$. Let $S$ be the set of all integers $n$ with $1 \leq n \leq 66564$ such that $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 22,188 | graphs = [
Graph(
let={
"upper": Const(66564),
"k": MaxOverSet(set=SolutionsSet(var=Var("k1"), condition=Leq(Pow(Const(3), Var("k1")), Const(486592498)))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("uppe... | NT | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_VAL"
] | 1 | 5.831 | 2026-02-08T16:34:32.049366Z | {
"verified": true,
"answer": 22188,
"timestamp": "2026-02-08T16:34:37.880468Z"
} | 481e80 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 878
},
"timestamp": "2026-02-17T07:17:28.725Z",
"answer": 22188
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b029cf | comb_count_partitions_v1_151522320_2575 | Let $n$ be a positive integer such that $1 \leq n \leq 216$, $4$ divides $n$, and $\gcd(n, 35) = 1$. Let $k$ be the number of such integers $n$. Compute the number of unordered ways to write $k$ as a sum of one or more positive integers, disregarding order. | 26,015 | graphs = [
Graph(
let={
"_n": Const(216),
"n": 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(35)), Const(1))))),
"result": Partition(arg... | NT | COMB | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | comb_count_partitions_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T04:52:56.103802Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T04:52:56.106287Z"
} | 2588da | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1390
},
"timestamp": "2026-02-11T22:23:34.855Z",
"answer": 26015
},
{
"... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
052de3 | geo_count_lattice_rect_v1_168721529_946 | Let $ a = 90 $ and $ b = 124 $. Compute the number of lattice points in the rectangle $ [0, a] \times [0, b] $. | 11,375 | graphs = [
Graph(
let={
"a": Const(90),
"b": Const(124),
"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 | 2026-02-08T13:21:11.900805Z | {
"verified": true,
"answer": 11375,
"timestamp": "2026-02-08T13:21:11.901364Z"
} | 8375ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 293
},
"timestamp": "2026-02-09T11:06:25.787Z",
"answer": 11375
},
{
"i... | 1 | [] | {
"lo": -5.98,
"mid": -3.99,
"hi": -2
} | ||||
6b9504 | comb_binomial_compute_v1_124444284_5848 | Let $n = 12$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 611$ and $\gcd(n, 20) = 1$. Let $k$ be the smallest integer $d$ such that $d \geq 2$ and $d$ divides the number of elements in $S$. Compute the remainder when $\binom{n}{k} \times 14323$ is divided by $68292$. | 7,344 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(12),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"... | NT | null | COMPUTE | sympy | C4 | [
"C4/MIN_PRIME_FACTOR"
] | 411729 | comb_binomial_compute_v1 | null | 5 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T06:54:31.626661Z | {
"verified": true,
"answer": 7344,
"timestamp": "2026-02-08T06:54:31.628553Z"
} | 78e10a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 2898
},
"timestamp": "2026-02-13T06:05:50.346Z",
"answer": 7344
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d84f7c | nt_count_divisors_in_range_v1_898971024_1351 | Let $n = 1680$, $a = 12$, and $b = 124$. Define $d$ to be a positive divisor of $n$ such that $a \leq d \leq b$. Let $r$ be the number of such divisors $d$.
Now consider the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 19518724$. Let $s$ be the minimum value of $x + y$ over all such pa... | 8,815 | graphs = [
Graph(
let={
"n": Const(1680),
"a": Const(12),
"b": Const(124),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
"Q": S... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | nt_count_divisors_in_range_v1 | negation_mod | 3 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T16:05:21.177859Z | {
"verified": true,
"answer": 8815,
"timestamp": "2026-02-08T16:05:21.185770Z"
} | 8e3c82 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 5534
},
"timestamp": "2026-02-16T20:17:30.419Z",
"answer": 8815
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1b0d40 | comb_factorial_compute_v1_1125832087_2327 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 771750$, and $\gcd(p, q) = 1$. Let $n$ be the number of elements in $S$. Compute the remainder when $82331 \cdot n!$ is divided by $58471$. | 11,837 | graphs = [
Graph(
let={
"_n": Const(58471),
"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=771750)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T04:32:59.107433Z | {
"verified": true,
"answer": 11837,
"timestamp": "2026-02-08T04:32:59.109418Z"
} | abb0d7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2224
},
"timestamp": "2026-02-10T17:05:29.945Z",
"answer": 11837
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
27aa13 | antilemma_sum_equals_v1_1470522791_140 | Let $m = 63$. Define $n$ to be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 63$ and $1 \le j \le 63$ such that $i + j = m$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 60$ and $1 \le j \le 61$ such that $i + j = n$. Compute the value of $$
+ \phi(|x| + 1) + \tau(... | 122 | graphs = [
Graph(
let={
"_m": Const(63),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(63)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | 638fa3 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM",
"ONE_FACTORIAL_0"
] | 3 | 0.11 | 2026-02-08T12:50:50.215528Z | {
"verified": true,
"answer": 122,
"timestamp": "2026-02-08T12:50:50.325574Z"
} | 964dfd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 1958
},
"timestamp": "2026-02-24T16:35:58.651Z",
"answer": 122
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
d129ca | diophantine_sum_product_min_v1_1520064083_7455 | Let $S = 40$. Let $P$ be the sum of all positive integers $n$ such that $1 \leq n \leq 114$ and $n$ is divisible by $19$. Determine the value of $x$, where $x$ is the smallest positive integer satisfying $1 \leq x \leq 39$ and $x(S - x) = P$. | 19 | graphs = [
Graph(
let={
"_n": Const(19),
"S": Const(40),
"P": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(114)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0))))),
"result": MinOverSet(set=Solution... | NT | null | EXTREMUM | sympy | B3 | [
"SUM_DIVISIBLE"
] | 02dbe3 | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 4.559 | 2026-02-08T09:03:20.177599Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T09:03:24.736252Z"
} | 0647dc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 541
},
"timestamp": "2026-02-15T20:29:49.653Z",
"answer": 19
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
295eee | comb_count_derangements_v1_798873815_405 | Let $c = 2$. Let $m$ be the number of positive integers $p$ such that $p < q$, $pq = 36$, and $\gcd(p, q) = 1$ for some positive integer $q$. Let $n$ be the largest prime number satisfying $c \leq n \leq 20$. Compute the number of prime numbers $p$ such that $m \leq p \leq n$, and denote this count by $k$. Let $D_k$ be... | 1,320 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW/COUNT_PRIMES"
] | d6f56d | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"COUNT_PRIMES",
"MAX_PRIME_BELOW"
] | 3 | 0.002 | 2026-02-08T02:38:05.005431Z | {
"verified": true,
"answer": 1320,
"timestamp": "2026-02-08T02:38:05.007641Z"
} | 145570 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 3902
},
"timestamp": "2026-02-08T19:28:45.853Z",
"answer": 1320
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"st... | {
"lo": 0.29,
"mid": 2.1,
"hi": 3.76
} | ||
1309ee | alg_poly4_count_v1_601307018_2774 | Let $B = \left|\{ (a_1, b_1) \mid 1 \le a_1, b_1 \le 20,\ -2a_1b_1 + 2b_1^2 + 13a_1^2 \le 3125 \}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 300$ and $1 \le b \le B$ such that $a^4 - 8a^3b + 24a^2b^2 - 32ab^3 + 16b^4 = 3111696$. | 279 | graphs = [
Graph(
let={
"_n": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(300)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a... | ALG | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_count_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT_LEQ"
] | 2 | 5.054 | 2026-03-10T03:25:47.711737Z | {
"verified": true,
"answer": 279,
"timestamp": "2026-03-10T03:25:52.765798Z"
} | 6ba868 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 3742
},
"timestamp": "2026-03-29T06:29:58.578Z",
"answer": 279
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
a87c53 | modular_count_residue_v1_865884756_3581 | Let $m$ be the largest positive divisor of 999 that is less than or equal to 27.
Determine the number of positive integers $n$ such that $1 \leq n \leq 69696$ and $n \equiv 1 \pmod{m}$. | 2,582 | graphs = [
Graph(
let={
"upper": Const(69696),
"m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(27)), Divides(divisor=Var("d"), dividend=Const(999))))),
"r": Const(1),
"result": CountOverSet(set=Solution... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | modular_count_residue_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 2.235 | 2026-02-08T17:30:33.053491Z | {
"verified": true,
"answer": 2582,
"timestamp": "2026-02-08T17:30:35.288795Z"
} | 5208dc | 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": 1423
},
"timestamp": "2026-02-18T02:47:51.694Z",
"answer": 2582
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c3b124 | modular_count_residue_v1_655260480_850 | Let $r = \sum_{k=0}^{4} (-1)^k \binom{4}{k}$. Compute the number of positive integers $n \leq 46656$ such that $n \equiv r \pmod{4}$. Subtract this count from $58653$ and report the result. | 46,989 | graphs = [
Graph(
let={
"upper": Const(46656),
"m": Const(4),
"r": Summation(var="k", start=Const(0), end=Const(4), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(4), k=Var("k")))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | modular_count_residue_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 2.052 | 2026-02-08T15:39:28.566962Z | {
"verified": true,
"answer": 46989,
"timestamp": "2026-02-08T15:39:30.618955Z"
} | 074e22 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 434
},
"timestamp": "2026-02-24T18:14:50.786Z",
"answer": 46989
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
f44b98 | modular_inverse_v1_1439011603_717 | Let $a = 56$. Let $m$ be the number of integers $t$ such that $21 \leq t \leq 933$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 268$, $1 \leq b \leq 127$, and $t = 2a + 3b + 16$. Let $u$ be the number of integers $t_1$ such that $5 \leq t_1 \leq 916$ and there exist positive integers $a$ and $b$ wi... | 667 | graphs = [
Graph(
let={
"a": Const(56),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=268)), Geq(left=Var(... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_inverse_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.044 | 2026-02-08T15:41:02.370973Z | {
"verified": true,
"answer": 667,
"timestamp": "2026-02-08T15:41:02.414688Z"
} | f152a8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 3703
},
"timestamp": "2026-02-16T11:07:37.492Z",
"answer": 667
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
33b494 | nt_count_with_divisor_count_v1_1918700295_336 | Let $m = 6$ and $u = 36100$. Let $S$ be the set of all ordered pairs $(k, j)$ such that $1 \leq k \leq 3$ and $1 \leq j \leq 5$. Let $d = \frac{m}{30} \sum_{(k,j) \in S} k$. Compute the number of positive integers $n \leq u$ such that the number of positive divisors of $n$ is exactly $d$. | 2,309 | graphs = [
Graph(
let={
"_m": Const(6),
"upper": Const(36100),
"div_count": Div(Mul(Ref("_m"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3))... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_INDEPENDENT",
"SUM_ARITHMETIC"
] | 9f7183 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 3.185 | 2026-02-08T03:09:44.711267Z | {
"verified": true,
"answer": 2309,
"timestamp": "2026-02-08T03:09:47.896260Z"
} | 3e246b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 16728
},
"timestamp": "2026-02-23T17:15:27.172Z",
"answer": 2313
},
{
... | 0 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "SUM_INDEPENDENT",
"status": ... | {
"lo": 4.28,
"mid": 7.01,
"hi": 10
} | ||
c60afa | nt_num_divisors_compute_v1_1742523217_2155 | Let $n = 13225$. Let $d$ be the number of positive divisors of $n$. Let $m = |d| + 2$. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $m$. Compute $k$. | 10 | graphs = [
Graph(
let={
"n": Const(13225),
"result": NumDivisors(n=Ref("n")),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 2 | 0.04 | 2026-02-08T04:30:23.919234Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T04:30:23.959628Z"
} | 9af4b8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 852
},
"timestamp": "2026-02-10T17:12:17.297Z",
"answer": 10
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
4ffd48 | nt_count_with_divisor_count_v1_1915831931_1686 | Let $S$ be the set of all integers $t$ such that $55 \leq t \leq 26632$ and there exist positive integers $a \leq 1126$ and $b \leq 463$ satisfying $t = 15a + 21b + 19$. Let $U$ be the number of elements in $S$. Determine the number of positive integers $n \leq U$ such that $n$ has exactly $6$ positive divisors. | 684 | 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=1126)), Geq(left=Var(name='b'), right=Const(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.438 | 2026-02-08T16:22:13.935265Z | {
"verified": true,
"answer": 684,
"timestamp": "2026-02-08T16:22:14.373392Z"
} | dae944 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 7439
},
"timestamp": "2026-02-17T02:12:54.833Z",
"answer": 684
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b4b996 | comb_sum_binomial_row_v1_1978505735_294 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $Q$ be the remainder when $44121 \cdot 2^n$ is divided by $61979$. Compute $Q$. | 50,831 | graphs = [
Graph(
let={
"_n": Const(61979),
"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(36)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T15:17:41.046862Z | {
"verified": true,
"answer": 50831,
"timestamp": "2026-02-08T15:17:41.049491Z"
} | bc7700 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 1391
},
"timestamp": "2026-02-16T02:13:03.572Z",
"answer": 50831
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a797b1 | nt_min_with_divisor_count_v1_124444284_9236 | Let $p$ and $q$ be positive integers such that $pq = 60$, $\gcd(p, q) = 1$, and $p < q$. Let $d$ be the number of such values of $p$. Find the smallest positive integer $n$ with $1 \leq n \leq 2500$ such that the number of positive divisors of $n$ is equal to $d$. Compute this value of $n$. | 6 | graphs = [
Graph(
let={
"upper": Const(2500),
"div_count": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=60)), Eq(left=GCD(a=Var(name='p'), ... | NT | null | EXTREMUM | sympy | B3 | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 1.754 | 2026-02-08T12:19:40.011100Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T12:19:41.765517Z"
} | ba5616 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1306
},
"timestamp": "2026-02-15T00:07:09.027Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7c54fb | nt_count_gcd_equals_v1_1439011603_1866 | Let $c = 169$, $m = 174$, and $N = 20449$. Consider all ordered pairs $(x,y)$ of positive integers such that
$$x + y = m.$$Let $U$ be the set of all values of $xy$ over these pairs, and let $u$ be the maximum element of $U$.
Let $M$ be the number of integers $t$ such that $12 \le t \le 204$ and there exist integers $a$... | 1 | graphs = [
Graph(
let={
"_c": Const(169),
"_m": Const(174),
"_n": Const(20449),
"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... | NT | COMB | COUNT | sympy | LIN_FORM | [
"MIN_PRIME_FACTOR",
"LIN_FORM/SUM_DIVISIBLE",
"B1"
] | be6bc6 | nt_count_gcd_equals_v1 | bell_mod | 8 | 0 | [
"B1",
"LIN_FORM",
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 4 | 17.8 | 2026-02-08T16:20:07.682536Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:20:25.482485Z"
} | 150cb5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 365,
"completion_tokens": 6118
},
"timestamp": "2026-02-17T01:43:52.763Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
34f4b9 | nt_max_prime_below_v1_151522320_213 | Let $s$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9653449$. Define $m$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $s$. Let $r$ be the largest prime number $n$ such that $2 \leq n \leq 50176$. Let $d_{\text{max}}$ be the largest positive divisor of $38632438$ that is a... | 48,537 | graphs = [
Graph(
let={
"_m": Const(2),
"_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(9653449)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | EXTREMUM | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 84eb3e | nt_max_prime_below_v1 | affine_mod | 6 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 1.305 | 2026-02-08T03:03:53.672071Z | {
"verified": true,
"answer": 48537,
"timestamp": "2026-02-08T03:03:54.976934Z"
} | 56ebab | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 8996
},
"timestamp": "2026-02-23T16:47:18.973Z",
"answer": 48537
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
de04ba | comb_count_derangements_v1_784195855_1088 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 50176$. For each pair $(x, y) \in S$, compute $x + y$, and let $m$ be the minimum value among these sums. Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 448$ such that $\binom{m}{j} \equiv 1 \pmod{2}$. Le... | 33,128 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(448)), Eq(Mod(value=Binom(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositiv... | COMB | null | COUNT | sympy | B3 | [
"B3/V8"
] | 4fad5b | comb_count_derangements_v1 | null | 6 | 0 | [
"B3",
"V8"
] | 2 | 0.004 | 2026-02-08T04:50:58.002152Z | {
"verified": true,
"answer": 33128,
"timestamp": "2026-02-08T04:50:58.006314Z"
} | 45f434 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1179
},
"timestamp": "2026-02-24T02:01:12.342Z",
"answer": 33128
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
35895a | nt_count_with_divisor_count_v1_784195855_3331 | Let $\text{div\_count}$ be the smallest integer $d \geq 2$ that divides $13013$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq 15129$ and the number of positive divisors of $n$ is equal to $\text{div\_count}$. Compute the value of $$3^{|\text{result}|} \bmod 99991 + 70756.$$ Determ... | 70,765 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(15129),
"div_count": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(13013))))),
"result": CountOverSet(set=SolutionsSet(var=Var("... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.345 | 2026-02-08T06:20:44.378129Z | {
"verified": true,
"answer": 70765,
"timestamp": "2026-02-08T06:20:45.722976Z"
} | 713dff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 915
},
"timestamp": "2026-02-12T23:21:06.632Z",
"answer": 70765
},
{... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
33ccee | antilemma_k2_v1_1440796553_1249 | Let $m = 2$. Let $S$ be the set of all real solutions $x$ to the equation $x^2 - 368x - 29145 = 0$. Let $n$ be the sum of all elements of $S$. Let $T$ be the set of all real solutions $x$ to the equation $x^2 - 368x - 42873 = 0$, and let $s$ be the sum of all elements of $T$. Define
$$
x = \sum_{k=1}^{s} \varphi(k) \le... | 8,817 | graphs = [
Graph(
let={
"_c": Const(75413),
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-368), Var("x")), Const(-29145)), Mul(Const(17), Const(0))))),
"x": Summation(var="k", start=Const(... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"IDENTITY_MUL_ZERO",
"K2"
] | f516ae | antilemma_k2_v1 | null | 6 | 0 | [
"IDENTITY_MUL_ZERO",
"K2",
"VIETA_SUM"
] | 3 | 0.004 | 2026-02-08T12:15:20.083797Z | {
"verified": true,
"answer": 8817,
"timestamp": "2026-02-08T12:15:20.087880Z"
} | 97f24b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 2049
},
"timestamp": "2026-02-15T18:30:48.687Z",
"answer": 8817
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "IDENTITY_MUL_ZERO",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8ad6d3 | comb_count_derangements_v1_124444284_1641 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 37800$. Compute the remainder when $44121 \cdot !n$ is divided by $98023$, where $!n$ denotes the number of derangements of $n$ objects. | 45,245 | graphs = [
Graph(
let={
"_n": Const(44121),
"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=37800)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T04:03:58.671977Z | {
"verified": true,
"answer": 45245,
"timestamp": "2026-02-08T04:03:58.676417Z"
} | 1a805b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 3109
},
"timestamp": "2026-02-10T15:21:21.997Z",
"answer": 45245
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e24bf7 | modular_sum_quadratic_residues_v1_2051736721_571 | Let $p$ be the sum of all real solutions $x$ to the equation $x^2 - 541x + 37260 = 0$. Define $T = \frac{p(p-1)}{4}$. Compute the value of $82369 - T$. | 9,334 | graphs = [
Graph(
let={
"_n": Const(2),
"p": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-541), Var("x")), Const(37260)), Const(0)))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Sub(... | NT | null | SUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T15:31:48.954198Z | {
"verified": true,
"answer": 9334,
"timestamp": "2026-02-08T15:31:48.955617Z"
} | 53f3cf | 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": 487
},
"timestamp": "2026-02-16T09:03:54.845Z",
"answer": 9334
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ea55dc | diophantine_product_count_v1_655260480_1347 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 176400$. Let $m = 51076$, and let $u$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = m$. Let $r$ be the number of positive integers $x_2 \leq u$ such that $x_2$... | 57,413 | graphs = [
Graph(
let={
"_m": Const(51076),
"_n": Const(33743),
"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(176400))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.027 | 2026-02-08T16:04:14.980317Z | {
"verified": true,
"answer": 57413,
"timestamp": "2026-02-08T16:04:15.007778Z"
} | 3e390d | 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": 2399
},
"timestamp": "2026-02-16T20:31:46.512Z",
"answer": 57413
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1e67e9 | nt_sum_totient_over_divisors_v1_1918700295_4280 | Let $n$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 4347225$. Let $Q$ be the remainder when $28768$ multiplied by the sum of $\phi(d)$ over all positive divisors $d$ of $n$ is divided by $87137$. Compute $Q$. | 62,048 | graphs = [
Graph(
let={
"_n": Const(28768),
"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(4347225)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T09:16:34.704773Z | {
"verified": true,
"answer": 62048,
"timestamp": "2026-02-08T09:16:34.713321Z"
} | 829b4a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 7628
},
"timestamp": "2026-02-14T02:21:30.709Z",
"answer": 62048
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e86700 | nt_num_divisors_compute_v1_1918700295_798 | Compute the number of positive divisors of $94249$. | 3 | graphs = [
Graph(
let={
"n": Const(94249),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.004 | 2026-02-08T03:30:26.319134Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T03:30:26.322831Z"
} | 723cee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 2080
},
"timestamp": "2026-02-10T14:45:05.810Z",
"answer": 3
},
{
"id":... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
e307b5 | diophantine_fbi2_count_v1_784195855_9882 | Let $n = 184$ and $k = 360$. Define $S$ as the set of all integers $t$ such that there exist positive integers $a$ and $b$ satisfying $1 \le a \le 16$, $1 \le b \le 71$, $5 \le t \le 190$, and $t = 3a + 2b$. Let $m$ be the number of elements in $S$. Now consider the set of all positive integers $d$ such that $5 \le d \... | 16 | graphs = [
Graph(
let={
"_n": Const(184),
"k": Const(360),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(n... | NT | null | COUNT | sympy | K2 | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.052 | 2026-02-08T17:15:06.404299Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T17:15:06.456266Z"
} | 4c4a23 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 4927
},
"timestamp": "2026-02-18T00:06:08.275Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a9c070_l | modular_sum_quadratic_residues_v1_548369836_30 | Let $p$ be the number of integers $t$ such that $31 \leq t \leq 979$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 49$, $1 \leq b \leq 45$, and
$$
t = 6a + 15b + 10.
$$
Compute $\frac{p(p-1)}{4}$. | 25,043 | NT | ALG | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T02:43:13.896406Z | {
"verified": false,
"answer": 24414,
"timestamp": "2026-02-08T02:43:13.898162Z"
} | 42b538 | a9c070 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:59:32.571Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": 1.68,
"mid": 3.8,
"hi": 5.62
} | |
467140 | comb_count_surjections_v1_153355830_2471 | Let $n = 7$ and $k = 3$. Let $r = k! \cdot S(n,k)$, where $S(n,k)$ denotes the Stirling number of the second kind. Let $m = |r| + 2$. Find the smallest positive integer $k$ such that the $k$th Fibonacci number is divisible by $m$. (The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$... | 228 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | COMB | NT | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.013 | 2026-02-08T07:08:46.206878Z | {
"verified": true,
"answer": 228,
"timestamp": "2026-02-08T07:08:46.220146Z"
} | 7868ad | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 3881
},
"timestamp": "2026-02-24T07:40:12.330Z",
"answer": 456
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
8d04ce | alg_poly3_min_v1_601307018_8514 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers such that $1 \le a_1 \le 40$, $1 \le b_1 \le 40$, and $13a_1^2 + 2b_1^2 - 2a_1b_1 \le 2192$. Let $A = |S|$. Find the remainder when the minimum value of $7a^3 - 42ab^2 - 63b^3$ over all positive integers $a, b$ with $1 \le a \le A$ and $1 \le b \le 3... | 21,256 | graphs = [
Graph(
let={
"_n": Const(367),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=... | ALG | null | COMPUTE | sympy | HALFPLANE_COUNT | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_min_v1 | null | 4 | 0 | [
"HALFPLANE_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.62 | 2026-03-10T08:59:23.233417Z | {
"verified": true,
"answer": 21256,
"timestamp": "2026-03-10T08:59:23.853731Z"
} | cae12d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 7444
},
"timestamp": "2026-04-19T09:12:54.149Z",
"answer": 21256
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
5eb30c | nt_count_gcd_equals_v1_677425708_40 | Let $a = 3127$ and $b = 79$. Let $h$ be the sum of $\mu(d)$ over all positive divisors $d$ of $\gcd(a, b)$.\\
Let $w$ be the sum of $\mu(d)$ over all positive divisors $d$ of $1$.\\
Let $U = 7056 \cdot h \cdot w$.\\
Let $k = 116$ and $d = 1$.\\
Determine the number of positive integers $n$ such that $n \leq U$ and $\gc... | 3,406 | graphs = [
Graph(
let={
"a": Const(3127),
"b": Const(79),
"h": SumOverDivisors(n=GCD(a=Ref(name='a'), b=Ref(name='b')), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n": Const(1),
"w": SumOverDivisors(n=Ref(name='n'), var='d', expr=MoebiusMu(n=Var(na... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"MOBIUS_SUM"
] | b623bd | nt_count_gcd_equals_v1 | null | 4 | 2 | [
"MOBIUS_COPRIME",
"MOBIUS_SUM"
] | 2 | 0.542 | 2026-02-08T03:01:06.107459Z | {
"verified": true,
"answer": 3406,
"timestamp": "2026-02-08T03:01:06.649297Z"
} | 76ddd7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1359
},
"timestamp": "2026-02-08T20:16:42.393Z",
"answer": 3406
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -6.51,
"mid": -0.53,
"hi": 4.75
} | ||
5717d0 | sequence_fibonacci_compute_v1_124444284_9506 | Let $r$ be the sum of all real solutions $x$ to the equation $x^2 - 46x + 480 = 0$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = r$. Compute the remainder when $44121 \cdot F_n$ is divided by $52418$, where $F_n$ denotes the $n$th Fibonacci number. Find the value o... | 919 | graphs = [
Graph(
let={
"_m": Const(52418),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-46), Var("x")), Const(480)), Const(0)))),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condit... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/COMB1"
] | 1756b4 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"COMB1",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T12:32:28.458520Z | {
"verified": true,
"answer": 919,
"timestamp": "2026-02-08T12:32:28.460204Z"
} | 81909b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1311
},
"timestamp": "2026-02-15T02:17:57.766Z",
"answer": 919
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lem... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
060d55 | nt_sum_divisors_mod_v1_1742523217_5072 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = 1587600$.
Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $10333$.
Find the value of this remainder. | 9,360 | 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(1587600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1033... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T10:46:57.895874Z | {
"verified": true,
"answer": 9360,
"timestamp": "2026-02-08T10:46:57.900468Z"
} | b811cf | 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": 1443
},
"timestamp": "2026-02-14T08:41:52.401Z",
"answer": 9360
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c8b28b | antilemma_sum_primes_v1_1742523217_5610 | Let $n_0 = 2$. Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q > p$ with $p \cdot q = 5400$ and $\gcd(p, q) = 1$. Let $N = |P|$. Define $x$ to be the number of prime numbers $n$ such that $n_0 \leq n \leq N$. Compute $24964 - x$. | 24,959 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(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(Va... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_PRIMES",
"SUM_PRIMES"
] | 020700 | antilemma_sum_primes_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"SUM_PRIMES"
] | 2 | 0.001 | 2026-02-08T11:05:58.258015Z | {
"verified": true,
"answer": 24959,
"timestamp": "2026-02-08T11:05:58.259251Z"
} | ddee52 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 441
},
"timestamp": "2026-02-21T13:03:50.372Z",
"answer": 24959
}
] | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
},
{
"lemma": "V5",
"sta... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
8d974d | comb_sum_binomial_row_v1_865884756_4336 | Let $x$ and $y$ be positive integers such that $x + y$ is minimized, subject to the condition that $xy$ equals the maximum value of $x_1 y_1$ over all pairs of positive integers $(x_1, y_1)$ satisfying $x_1 + y_1 = 10$. Denote this minimal sum by $n$.
Let $S$ be the set of all positive integers $p$ for which there exi... | 53,980 | graphs = [
Graph(
let={
"_m": Const(64774),
"_n": Const(42649),
"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")), MaxOverSet(set... | NT | null | SUM | sympy | L3C | [
"L3C",
"COPRIME_PAIRS",
"B1/B3"
] | cc2dbf | comb_sum_binomial_row_v1 | affine_mod | 7 | 0 | [
"B1",
"B3",
"COPRIME_PAIRS",
"L3C"
] | 4 | 0.005 | 2026-02-08T17:53:30.756521Z | {
"verified": true,
"answer": 53980,
"timestamp": "2026-02-08T17:53:30.761573Z"
} | d040a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 1875
},
"timestamp": "2026-02-18T09:11:57.312Z",
"answer": 53980
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
19551a | modular_sum_quadratic_residues_v1_1520064083_5307 | Let $p$ be the largest prime number such that $2 \leq p \leq 405$. Compute $\frac{p(p-1)}{4}$. | 40,100 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(405)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T06:44:08.407754Z | {
"verified": true,
"answer": 40100,
"timestamp": "2026-02-08T06:44:08.408834Z"
} | d5efcf | 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": 413
},
"timestamp": "2026-02-13T04:09:52.728Z",
"answer": 40100
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
226857 | alg_qf_psd_min_v1_1218484723_3257 | Find the minimum value of
$$
4140b^2 - 552cd + 4232a^2 - 1840ac + 2576c^2 + \left(\min\{ x + y : x > 0, y > 0, xy = 2592100 \}\right) d^2 - 920ad + 1656bc + 5888ab + 2024bd
$$
over all ordered quadruples $(a, b, c, d)$ of positive integers with $1 \le a, b, c, d \le 15$. | 20,424 | graphs = [
Graph(
let={
"_n": Const(15),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Geq(Var("c")... | ALG | null | COMPUTE | sympy | STARS_BARS | [
"B3"
] | 0cd20d | alg_qf_psd_min_v1 | null | 4 | 0 | [
"B3",
"STARS_BARS"
] | 2 | 1.884 | 2026-02-25T04:57:24.897946Z | {
"verified": true,
"answer": 20424,
"timestamp": "2026-02-25T04:57:26.782099Z"
} | 5a8b1f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 8598
},
"timestamp": "2026-03-29T09:15:31.646Z",
"answer": 20424
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
ff9ac7 | antilemma_sum_equals_v1_1915831931_3897 | Let $t$ be an integer such that $8 \leq t \leq 44$. Define $n$ to be the number of such $t$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 4$, and $t = 3a + 5b$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 29$, $1 \leq j \leq ... | 28 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(name='b'), right=Const(value=... | 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 | 0.036 | 2026-02-08T18:00:55.181615Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T18:00:55.217391Z"
} | 60da6a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2716
},
"timestamp": "2026-02-18T11:56:18.629Z",
"answer": 28
},
{
... | 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": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
977a7b_n | alg_poly4_min_v1_1218484723_6062 | An engineer models energy consumption of a system as $E(a, b) = 8282b^4 + 6464a^3b + 21008ab^3 + 3232a^4 + 24240a^2b^2$, where $a$ and $b$ are positive integer parameters each between $1$ and $410$. To optimize efficiency, she seeks the lowest possible energy value. What is this minimum energy output? | 63,226 | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/QF_PSD_COUNT_LEQ",
"VIETA_SUM"
] | a2550c | alg_poly4_min_v1 | null | 4 | null | [
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT_LEQ",
"VIETA_SUM"
] | 3 | 1.518 | 2026-02-25T07:41:48.251087Z | null | 3beec3 | 977a7b | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1120
},
"timestamp": "2026-03-31T00:38:04.566Z",
"answer": 63226
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
af1f3e | nt_count_divisible_v1_677425708_493 | Let $N = 75076$ and define $d$ to be the number of ordered pairs $(a,b)$ where $a$ is an integer satisfying $1 \le a \le 3$ and $b$ is an integer satisfying $1 \le b \le 7$. Determine the number of positive integers $n$ such that $1 \le n \le N$ and $n$ is divisible by $d$. | 3,575 | graphs = [
Graph(
let={
"upper": Const(75076),
"divisor": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(7)))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_count_divisible_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 2.452 | 2026-02-08T03:34:23.195719Z | {
"verified": true,
"answer": 3575,
"timestamp": "2026-02-08T03:34:25.647752Z"
} | 956c64 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 744
},
"timestamp": "2026-02-08T20:39:23.268Z",
"answer": 3575
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
b6be90 | algebra_vieta_sum_v1_655260480_5149 | Let $Q$ be the absolute value of the product of all real solutions $x$ to the equation $x^4 - 12x^3 - 29x^2 + 588x - 980 = 0$. Find the value of $Q$. | 980 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=4)), Mul(Const(value=-12), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=-29), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Cons... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | algebra_vieta_sum_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 0.032 | 2026-02-08T18:18:09.426572Z | {
"verified": true,
"answer": 980,
"timestamp": "2026-02-08T18:18:09.458962Z"
} | bd8512 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 568
},
"timestamp": "2026-02-16T12:17:55.199Z",
"answer": 980
},
{
"id": 11,
... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
2ee137 | sequence_count_fib_divisible_v1_784195855_1935 | Compute the number of positive integers $n$ such that $n \leq 968$ and the $n$-th Fibonacci number is divisible by $13$. | 138 | graphs = [
Graph(
let={
"upper": Const(968),
"d": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.08 | 2026-02-08T05:24:41.340248Z | {
"verified": true,
"answer": 138,
"timestamp": "2026-02-08T05:24:41.419848Z"
} | 2c1f6e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 761
},
"timestamp": "2026-02-11T22:35:38.049Z",
"answer": 80
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
3de5db | alg_poly_preperiod_count_v1_601307018_9204 | For an integer $a$, define $f(a) = (a^4 - a^3 + 5a^2 - 5) \bmod 41$. Let $N = f(a)$, $M = f(N)$, $R = f(M)$, and $S = f(R)$. Find the number of non-negative integers $a$ with $0 \le a \le 17752$ such that $S = N$, $M \ne N$, and $R \ne N$. | 2,165 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(4)), Mul(Const(-1), Pow(Var("a"), Const(3))), Mul(Const(5), Pow(Var("a"), Const(2))), Const(-5)), modulus=Const(41)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(4)), Mul(Const(-1), Pow(Ref("p1"), Const(3))), Mul(Const(5), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.064 | 2026-03-10T09:35:59.903582Z | {
"verified": true,
"answer": 2165,
"timestamp": "2026-03-10T09:35:59.967280Z"
} | 8983b2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 9155
},
"timestamp": "2026-04-19T10:50:39.493Z",
"answer": 2165
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
46254f | sequence_fibonacci_compute_v1_151522320_1656 | Let $m = 241$. Let $S$ be the set of all integers $n$ with $1 \leq n \leq m$ such that the sum of the decimal digits of $n$ is odd. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = |S|$. Let $n$ be the minimum value of $x + y$ over all such pairs. Define $\text{result} = F_n$, the $... | 41,825 | graphs = [
Graph(
let={
"_m": Const(241),
"_n": Const(59536),
"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")), CountOverSet(set... | NT | null | COMPUTE | sympy | L3B | [
"L3B/B3"
] | f2ec8b | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B3",
"L3B"
] | 2 | 0.002 | 2026-02-08T04:10:17.148948Z | {
"verified": true,
"answer": 41825,
"timestamp": "2026-02-08T04:10:17.150699Z"
} | 1230e0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 2137
},
"timestamp": "2026-02-10T15:38:17.356Z",
"answer": 41825
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
cfd1c8 | modular_sum_quadratic_residues_v1_1520064083_2291 | Let $m = 132$. Define $n$ to be the number of nonnegative integers $j$ with $0 \leq j \leq 132$ such that $\binom{132}{j}$ is odd. Let $p$ be the number of integers $t$ with $11 \leq t \leq 309$ for which there exist positive integers $a \leq 30$ and $b \leq 27$ such that $t = 4a + 7b$. Compute the value of $\frac{p(p-... | 19,670 | graphs = [
Graph(
let={
"_m": Const(132),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Const(132), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"p": ... | ALG | COMB | SUM | sympy | V8 | [
"V8/LIN_FORM"
] | e9c298 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.004 | 2026-02-08T04:38:23.413796Z | {
"verified": true,
"answer": 19670,
"timestamp": "2026-02-08T04:38:23.417757Z"
} | d3c61b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T01:24:10.228Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
57e02a | antilemma_sum_primes_v1_1742523217_1321 | Let $m$ be the number of positive integers $n$ such that $1 \leq n \leq 29$ and $\gcd(n, 12) = 1$. Let $x$ be the sum of all prime numbers $n$ such that $2 \leq n \leq 3$. Let $c$ be the number of positive integers $n$ such that $1 \leq n \leq 22089$ and $\gcd(n, m) = 1$. Compute $x^2 + 23x + c$. | 8,976 | graphs = [
Graph(
let={
"_d": Const(3),
"_m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(29)), Eq(GCD(a=Var("n"), b=Const(12)), Const(1))))),
"_n": Const(2),
"x": SumOverSet(set=SolutionsSet(var=Var("... | NT | null | COMPUTE | sympy | C4 | [
"C4/C4",
"SUM_PRIMES"
] | 26c772 | antilemma_sum_primes_v1 | quadratic_mod | 4 | 0 | [
"C4",
"SUM_PRIMES"
] | 2 | 0.003 | 2026-02-08T03:40:43.621534Z | {
"verified": true,
"answer": 8976,
"timestamp": "2026-02-08T03:40:43.624083Z"
} | bc13af | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1287
},
"timestamp": "2026-02-10T06:39:20.768Z",
"answer": 8976
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
},
{
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
d37a4d | diophantine_sum_product_min_v1_971394319_267 | Let $S = 69$ and $P = 488$. Let $y$ be the smallest positive integer such that $1 \leq y^3 \leq 68$ and $y^3(S - y^3) = P$. Let $r = y^3$. Let $M$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 126$. Compute $M - r$. | 3,961 | graphs = [
Graph(
let={
"_n": Const(3),
"S": Const(69),
"P": Const(488),
"_result_y": MinOverSet(set=SolutionsSet(var=Var("y"), condition=And(Geq(Pow(Var("y"), Const(3)), Const(1)), Leq(Pow(Var("y"), Const(3)), Const(68)), Eq(Mul(Pow(Var("y"), Ref("_n")), Sub(... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | d2b6e1 | diophantine_sum_product_min_v1 | negation_mod | 6 | 0 | [
"B1"
] | 1 | 0.009 | 2026-02-08T12:55:54.671076Z | {
"verified": true,
"answer": 3961,
"timestamp": "2026-02-08T12:55:54.680307Z"
} | 742e9f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 953
},
"timestamp": "2026-02-15T08:03:49.536Z",
"answer": 3961
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d10d07 | modular_min_linear_v1_153355830_1697 | Let $a = 48349$, $b = 15523$, and $m = 57170$. Let $x_0$ be the smallest positive integer $x$ such that $1 \leq x \leq m$ and $$48349x \equiv 15523 \pmod{57170}.$$ Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. Define $k$ to be the minimum value of $x + y$ as $(x, y)$ ranges ... | 52,915 | graphs = [
Graph(
let={
"_n": Const(73331),
"a": Const(48349),
"b": Const(15523),
"m": Const(57170),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var(... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 385411 | modular_min_linear_v1 | mod_exp | 5 | 0 | [
"B3"
] | 1 | 2.294 | 2026-02-08T06:33:47.974752Z | {
"verified": true,
"answer": 52915,
"timestamp": "2026-02-08T06:33:50.268877Z"
} | 3cc20d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 2074
},
"timestamp": "2026-02-13T01:48:54.983Z",
"answer": 52915
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9bfd2d | comb_sum_binomial_row_v1_717093673_2531 | Let $n$ be the number of positive integers $n_1$ such that $1 \le n_1 \le 97$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{7}$. Compute $2^n$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(97)), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | SUM | sympy | L3C | [
"L3C"
] | 73f8b0 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T16:55:17.545943Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T16:55:17.547057Z"
} | 4d96d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 994
},
"timestamp": "2026-02-17T15:01:56.848Z",
"answer": 8192
},
{
... | 1 | [
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
623de9 | comb_binomial_compute_v1_2051736721_236 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 11280$ and $\binom{11280}{j}$ is odd. Compute $\binom{n}{7}$. | 11,440 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(11280)), Eq(Mod(value=Binom(n=Const(11280), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"k... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_binomial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T15:18:33.496872Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T15:18:33.499369Z"
} | fbcfe9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1066
},
"timestamp": "2026-02-24T20:32:37.466Z",
"answer": 11440
},
{
"... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
981a56 | nt_sum_divisors_mod_v1_458359167_5740 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Define $n$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $10301$. | 4,368 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10301... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T12:40:18.613122Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T12:40:18.615891Z"
} | 7de887 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1089
},
"timestamp": "2026-02-15T03:53:27.292Z",
"answer": 4368
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9d1411 | comb_count_partitions_v1_809748730_1844 | Let $ T $ be the set of all integers $ t $ such that $ 20 \leq t \leq 128 $ and there exist positive integers $ a \leq 12 $ and $ b \leq 4 $ satisfying $ t = 6a + 14b $. Let $ n $ be the number of elements in $ T $. Compute the number of integer partitions of $ n $. | 63,261 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=12)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:43:32.440876Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T12:43:32.441938Z"
} | f67373 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 4403
},
"timestamp": "2026-02-24T16:13:33.202Z",
"answer": 61071
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
d5f79c | sequence_lucas_compute_v1_784195855_4160 | Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying the following conditions:
- $1 \leq a \leq 6$,
- $1 \leq b \leq 4$,
- $7 \leq t \leq 32$,
- $t = 2a + 5b$.
Let $n$ be the number of elements in $S$. Let $L_n$ denote the $n$th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, an... | 79,591 | graphs = [
Graph(
let={
"_n": Const(70989),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T06:52:35.229493Z | {
"verified": true,
"answer": 79591,
"timestamp": "2026-02-08T06:52:35.232364Z"
} | 90f59d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 2154
},
"timestamp": "2026-02-13T05:44:59.096Z",
"answer": 79591
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b1d1bb | sequence_lucas_compute_v1_677425708_2102 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 10230$ and $465$ divides $k$. Compute the $n$-th Lucas number. | 39,603 | graphs = [
Graph(
let={
"_n": Const(10230),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Const(465), dividend=Var("k"))), domain='positive_integers')),
"result": Lucas(arg=Ref(name='n')),... | ALG | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | sequence_lucas_compute_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T04:47:30.894069Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T04:47:30.894908Z"
} | 8efc67 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 774
},
"timestamp": "2026-02-10T05:55:08.630Z",
"answer": 39603
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.32
} | ||
8da361 | modular_mod_compute_v1_1431428450_267 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 262144$. Let $m$ be the minimum value of $x + y$ over all pairs in $S$. Let $a = -13203$, and let $r$ be the remainder when $a$ is divided by $m$. Define $T$ as the set of all positive integers $t$ such that $18 \leq t \leq 60$ and th... | 8,301 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-13203),
"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(262144)))), ... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 4d14cd | modular_mod_compute_v1 | mod_exp | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T13:22:13.999044Z | {
"verified": true,
"answer": 8301,
"timestamp": "2026-02-08T13:22:14.003470Z"
} | c55e78 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 1577
},
"timestamp": "2026-02-15T13:56:30.352Z",
"answer": 8301
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8a6247 | diophantine_product_count_v1_2051736721_3976 | Let $m = 14$. Let $n$ be a positive integer such that $1 \le n \le 3861$, $9$ divides $n$, and $\gcd(n, 14) = 1$. Let $N$ be the number of such integers $n$. Define $u = \sum_{d \mid N} \phi(d)$, where $\phi$ is Euler's totient function. Let $k = 480$. Determine the number of positive integers $x$ such that $1 \le x \l... | 20 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(3861)), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_m")), Const(1))))),
"k": Const(480),
... | NT | null | COUNT | sympy | C5 | [
"C5/K3"
] | fe33d2 | diophantine_product_count_v1 | null | 7 | 0 | [
"C5",
"K3"
] | 2 | 0.025 | 2026-02-08T17:38:51.131721Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T17:38:51.156714Z"
} | d1092a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1512
},
"timestamp": "2026-02-18T05:52:27.143Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5b4066 | algebra_quadratic_discriminant_v1_1125832087_185 | Let $a = 3$, $b = -5$, and $c = 6$. Define the discriminant $D = b^2 - 4ac$. Let $r$ be the value of $2$ if $D > 0$, and $0$ otherwise. Additionally, let $s = 1$ if $D$ equals the sum of $\mu(d)$ over all positive divisors $d$ of $\gcd(54, 36)$, and $0$ otherwise. Compute $16086 \cdot (r + s)$. | 0 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(-5),
"c": Const(6),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), SumOv... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 0.003 | 2026-02-08T02:55:26.512734Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T02:55:26.516019Z"
} | 51006c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 340
},
"timestamp": "2026-02-17T15:49:49.721Z",
"answer": 0
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"statu... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
162961 | diophantine_fbi2_count_v1_124444284_1208 | Let $k = 180$. Consider the set of all positive integers $d$ such that $4 \leq d \leq 63$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 61$. Let $r$ be the number of elements in this set. Compute the smallest positive integer $Q$ such that the $Q$-th Fibonacci number is divisible by $r + 2$. (Recall that the Fibonacci... | 20 | graphs = [
Graph(
let={
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(63)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(Ref("k"), Var("d")), Const(61)... | NT | null | COUNT | sympy | V1 | [
"COUNT_FIB_DIVISIBLE/LIOUVILLE_ONE",
"MOBIUS_COPRIME"
] | cc5937 | diophantine_fbi2_count_v1 | null | 4 | 2 | [
"COUNT_FIB_DIVISIBLE",
"LIOUVILLE_ONE",
"MOBIUS_COPRIME",
"V1"
] | 4 | 2.809 | 2026-02-08T03:44:27.028649Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T03:44:29.837569Z"
} | 7f9c95 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 1603
},
"timestamp": "2026-02-10T04:26:41.051Z",
"answer": 20
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": ... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
7d5e41 | nt_min_phi_inverse_v1_1915831931_3224 | Let $m = 14$. Define $N$ as the number of integers $t$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 63$, $1 \leq b \leq 20$, $7 \leq t \leq 355$, and $t = 5a + 2b$. Define $U$ as the number of positive integers $n$ such that $1 \leq n \leq N$, $3$ divides $n$, and $\gcd(n, 14) = 1$. Defi... | 13 | graphs = [
Graph(
let={
"_m": Const(14),
"_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=63)), Geq(left=Var... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/C5"
] | 683493 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 0.089 | 2026-02-08T17:25:55.712033Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T17:25:55.801408Z"
} | ed831c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 3885
},
"timestamp": "2026-02-18T02:55:03.139Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a96c72 | nt_max_prime_below_v1_1742523217_1253 | Let $S$ be the set of all positive integers $n$ such that $n$ is divisible by 2, $\gcd(n, 15) = 1$, and $1 \leq n \leq 4$. Let $T$ be the set of all prime numbers $n$ such that the number of elements in $S$ is less than or equal to $n$ and $n \leq 19321$. Define $r$ to be the maximum element of $T$. Let $Q$ be the rema... | 2,786 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(19321),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Cons... | NT | null | EXTREMUM | sympy | C5 | [
"C5"
] | 1d9668 | nt_max_prime_below_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.733 | 2026-02-08T03:35:05.831719Z | {
"verified": true,
"answer": 2786,
"timestamp": "2026-02-08T03:35:06.564480Z"
} | 1350ee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 2548
},
"timestamp": "2026-02-10T05:43:58.446Z",
"answer": 2786
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
354c10 | nt_euler_phi_compute_v1_677425708_1390 | Let $p$ be the largest integer such that $31^p$ divides $31^{73}$. Let $q = 17$ and $r = 2$. Define $n_2 = p \cdot q \cdot r$. Let $m$ be the remainder when the number of positive divisors of $n_2$ is divided by 2. Let $n_1 = \varphi(2)$, and let $w = \sum_{d \mid n_1} \mu(d)$, where $\mu$ is the M\"obius function. Def... | 34,320 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxKDivides(target=Pow(Const(31), Const(73)), base=Const(31)),
"q": Const(17),
"r": Const(2),
"n2": Mul(Ref("p"), Ref("q"), Ref("r")),
"m": Mod(value=NumDivisors(n=Ref("n2")), modulus=Ref("_n... | NT | null | COMPUTE | sympy | K14 | [
"K14/DIVISOR_PARITY",
"MOBIUS_SUM",
"ONE_PHI_2"
] | e20a33 | nt_euler_phi_compute_v1 | null | 5 | 2 | [
"DIVISOR_PARITY",
"K14",
"MOBIUS_SUM",
"ONE_PHI_2"
] | 4 | 0.002 | 2026-02-08T04:10:06.826635Z | {
"verified": true,
"answer": 34320,
"timestamp": "2026-02-08T04:10:06.828692Z"
} | d3ab15 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 1760
},
"timestamp": "2026-02-09T19:22:19.064Z",
"answer": 34320
},
{
"... | 1 | [
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"stat... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
f2ad01 | comb_factorial_compute_v1_1742523217_1897 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p \cdot q = 2940$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$.
Define $r = n!$.
Compute the remainder when $46705 \cdot r$ is divided by $72497$. | 36,025 | graphs = [
Graph(
let={
"_n": Const(72497),
"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=2940)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T04:19:24.199548Z | {
"verified": true,
"answer": 36025,
"timestamp": "2026-02-08T04:19:24.201132Z"
} | a6cd70 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1968
},
"timestamp": "2026-02-10T16:10:52.315Z",
"answer": 36025
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
18a41f | modular_mod_compute_v1_784195855_7317 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 25$. Let $m$ be the number of integers $t$ with $19 \leq t \leq 3868$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 109$, $1 \leq b \leq 520$, and $t = 2a + 7b + 10$. Let $r$ be the remainder when $a$ is divided by $m$. Compute t... | 17,163 | graphs = [
Graph(
let={
"_n": Const(58712),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(25)), IsPrime(Var("n"))))),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | modular_mod_compute_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T09:12:27.141725Z | {
"verified": true,
"answer": 17163,
"timestamp": "2026-02-08T09:12:27.143816Z"
} | f1fd9a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 4076
},
"timestamp": "2026-02-14T01:29:17.527Z",
"answer": 17163
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3e0d85 | alg_poly4_count_v1_1218484723_6423 | Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 78$ and $1 \le b \le 78$ such that
$$-2048 a^{3} b + \sum_{(a1, b1, c),\, a1^{2} + b1^{2} + c^{2} = a1 b1 + b1 c + c a1,\, 1a1 + 5b1 + \left|\{ t : \text{there exist integers } a1, b1 \text{ with } 1 \le a1 \le 2, 1 \le b1 \le 4 \tex... | 98 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(512),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(78)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(78)), Eq(Sum(Mul(Const... | ALG | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/SUM_SQUARES_IDENTITY"
] | 4e9382 | alg_poly4_count_v1 | null | 8 | 0 | [
"LIN_FORM",
"SUM_SQUARES_IDENTITY"
] | 2 | 0.114 | 2026-02-25T07:59:37.897487Z | {
"verified": true,
"answer": 98,
"timestamp": "2026-02-25T07:59:38.011201Z"
} | 5698f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 381,
"completion_tokens": 6419
},
"timestamp": "2026-03-30T01:38:23.265Z",
"answer": 98
},
{
"id"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok_later"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
0783a2 | lin_form_endings_v1_1520064083_8201 | Let $a = 12$, $b = 42$, $A = 14$, and $B = 45$. Let $g = \gcd(a, b)$. Define
$$
n = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1.
$$
Let $k = 18165$ and $M = 87077$. Compute the remainder when $k \cdot n$ is divided by $M$. | 76,962 | graphs = [
Graph(
let={
"a_coeff": Const(12),
"b_coeff": Const(42),
"A_val": Const(14),
"B_val": Const(45),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T10:04:51.545337Z | {
"verified": true,
"answer": 76962,
"timestamp": "2026-02-08T10:04:51.546335Z"
} | 0554c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 837
},
"timestamp": "2026-02-14T06:16:04.122Z",
"answer": 76962
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e62899 | nt_count_coprime_and_v1_124444284_5326 | Let $U$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 183$, $1 \le b \le 1069$, $33 \le t \le 24645$, and $t = 12a + 21b$. Let $k_1$ be the number of integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 3$, $1 \le b \le 3$, $5 \le t \l... | 4,962 | 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=183)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_and_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 1.147 | 2026-02-08T06:32:45.298347Z | {
"verified": true,
"answer": 4962,
"timestamp": "2026-02-08T06:32:46.445814Z"
} | f34ce1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 4400
},
"timestamp": "2026-02-13T01:21:00.763Z",
"answer": 4962
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9e44b5 | antilemma_k2_v1_1440796553_461 | Let
$$
x = \sum_{k=1}^{420} \phi(k) \left\lfloor \frac{420}{k} \right\rfloor.
$$
Compute the remainder when
$$
x + \phi(|x| + 1) + \tau(|x| + 1)
$$
is divided by $95735$, where $\phi$ denotes Euler's totient function and $\tau(m)$ denotes the number of positive divisors of $m$. | 81,087 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(420), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(420), Var("k"))))),
"Q": Mod(value=Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Const(1)))), mo... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T11:48:26.234524Z | {
"verified": true,
"answer": 81087,
"timestamp": "2026-02-08T11:48:26.235713Z"
} | 1d301f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 4358
},
"timestamp": "2026-02-14T19:20:16.904Z",
"answer": 81087
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
933e6a | nt_count_intersection_v1_2051736721_705 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25000000$. Let $N$ be the minimum value of $x + y$ over all such pairs. Let $a = 7$ and $b = 18$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $7$ divides $n$, and $\gcd(n, 18) = 1$. Let this number be $k... | 72,002 | graphs = [
Graph(
let={
"_n": Const(92466),
"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(25000000)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.356 | 2026-02-08T15:38:41.551805Z | {
"verified": true,
"answer": 72002,
"timestamp": "2026-02-08T15:38:41.907777Z"
} | 79872c | 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": 1574
},
"timestamp": "2026-02-16T10:05:18.340Z",
"answer": 72002
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9a6df3 | diophantine_fbi2_min_v1_124444284_10382 | Let $m = 60$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 4$. Define $n$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $k = 48$. Let $T$ be the set of all ordered pairs $(i,j)$ where $i$ is an integer from 1 to 58 inclusive and $j$ is an integer from 1 to 59... | 4 | graphs = [
Graph(
let={
"_m": Const(60),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(4)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3/COUNT_SUM_EQUALS"
] | 63dc97 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3",
"COUNT_SUM_EQUALS"
] | 2 | 0.021 | 2026-02-08T13:02:25.973548Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T13:02:25.994110Z"
} | 286404 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 821
},
"timestamp": "2026-02-15T09:03:13.684Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
7c837f | modular_mod_compute_v1_1520064083_7019 | Compute the remainder when $20160$ is divided by $1283$. | 915 | graphs = [
Graph(
let={
"a": Const(20160),
"m": Const(1283),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_mod_compute_v1 | null | 2 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.015 | 2026-02-08T08:43:04.892417Z | {
"verified": true,
"answer": 915,
"timestamp": "2026-02-08T08:43:04.907820Z"
} | a4313e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 62,
"completion_tokens": 322
},
"timestamp": "2026-02-13T20:51:36.469Z",
"answer": 915
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
687496 | geo_count_lattice_rect_v1_655260480_4374 | Compute the number of lattice points $(x, y)$ such that $0 \le x \le 77$ and $0 \le y \le 114$. | 8,970 | graphs = [
Graph(
let={
"a": Const(77),
"b": Const(114),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T17:54:18.077876Z | {
"verified": true,
"answer": 8970,
"timestamp": "2026-02-08T17:54:18.078430Z"
} | af0804 | 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": 361
},
"timestamp": "2026-02-18T09:39:25.902Z",
"answer": 8970
},
{
... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||||
920132_n | alg_sum_powers_v1_1419126231_1708 | A factory assigns production codes using the formula $t = 12a + 15b + 10$, where $a$ is a line number from $1$ to $289$ and $b$ is a shift number from $1$ to $457$. Only codes $t$ between $37$ and $10333$ inclusive are valid. Let $S$ be the set of all valid codes. Each day, the factory computes a value $M$ as the sum o... | 1,795 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sum_powers_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-25T11:14:28.400569Z | null | ca0e97 | 920132 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T05:03:35.302Z",
"answer": 49157
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
95d8ef | modular_count_residue_v1_865884756_1966 | Let $m$ be the smallest integer $d$ such that $d \geq 2$ and $d$ divides $15$. Let $r = 1$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 65025$ and $n \equiv r \pmod{m}$. | 21,675 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(65025),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(15))))),
"r": Const(1),
"result": CountOverSet(set=Soluti... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.192 | 2026-02-08T16:24:48.119054Z | {
"verified": true,
"answer": 21675,
"timestamp": "2026-02-08T16:24:50.311019Z"
} | 0ccf50 | 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": 547
},
"timestamp": "2026-02-17T03:22:35.204Z",
"answer": 21675
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
984e26 | comb_count_derangements_v1_1520064083_10030 | Let $m = 6$. Consider all ordered pairs of positive integers $(x, y)$ such that $x + y = m$. Let $P$ be the set of all values of $xy$ for such pairs. Define $N$ to be the maximum element of $P$.
Let $n$ be the largest prime number such that $2 \leq n \leq N$. Define $\text{result} = !n$, the number of derangements of ... | 51,138 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=V... | NT | COMB | COUNT | sympy | LTE_DIFF | [
"B1/MAX_PRIME_BELOW"
] | 2fc9f0 | comb_count_derangements_v1 | null | 6 | 0 | [
"B1",
"LTE_DIFF",
"MAX_PRIME_BELOW"
] | 3 | 0.009 | 2026-02-08T11:09:16.046321Z | {
"verified": true,
"answer": 51138,
"timestamp": "2026-02-08T11:09:16.055723Z"
} | b2a1fe | 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": 1220
},
"timestamp": "2026-02-14T10:46:01.862Z",
"answer": 51138
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c8e6aa | nt_count_divisible_and_v1_798873815_295 | Let $N$ be the number of positive integers $n$ such that $n \leq 174060$ and $n$ is divisible by both $9$ and $12$. Let $S$ be the set of all real solutions $x$ to the equation $x^2 - 293x - 14448 = 0$, and let $T$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 674$. Comput... | 14,264 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(174060),
"d1": Const(9),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulu... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM",
"COMB1"
] | 646807 | nt_count_divisible_and_v1 | two_moduli | 7 | 0 | [
"COMB1",
"VIETA_SUM"
] | 2 | 5.509 | 2026-02-08T02:32:35.893013Z | {
"verified": true,
"answer": 14264,
"timestamp": "2026-02-08T02:32:41.401770Z"
} | 44439c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 930
},
"timestamp": "2026-02-08T19:19:54.002Z",
"answer": 14264
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"... | {
"lo": -0.84,
"mid": 0.99,
"hi": 2.62
} | ||
f5f0e4 | nt_count_coprime_v1_1440796553_1292 | Let $n_0 = 52$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n_0$. Let $N$ be the number of elements in $S$. Let $k$ be the largest prime number $n$ such that $2 \leq n \leq N$.
Let $U = 16384$. Find the number of integers $n$ such that $1 \leq n \leq U$ and $\gc... | 15,672 | graphs = [
Graph(
let={
"_n": Const(52),
"upper": Const(16384),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(n... | NT | null | COUNT | sympy | COMB1 | [
"COMB1/MAX_PRIME_BELOW"
] | 6a06f8 | nt_count_coprime_v1 | null | 5 | 0 | [
"COMB1",
"MAX_PRIME_BELOW"
] | 2 | 1.581 | 2026-02-08T13:38:17.115434Z | {
"verified": true,
"answer": 15672,
"timestamp": "2026-02-08T13:38:18.696338Z"
} | bf3c79 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 872
},
"timestamp": "2026-02-15T19:26:02.228Z",
"answer": 15672
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "n... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8c26d9 | sequence_fibonacci_compute_v1_865884756_199 | Let $n$ be the number of integers $t$ in the range $8 \leq t \leq 35$ such that $t = 5a + 3b$ for some positive integers $a$ and $b$ with $1 \leq a \leq 4$ and $1 \leq b \leq 5$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 6,765 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T15:15:51.229246Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T15:15:51.231173Z"
} | c7e421 | 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": 929
},
"timestamp": "2026-02-10T05:27:15.276Z",
"answer": 6765
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
ff7763 | comb_binomial_compute_v1_601307018_9591 | Let $k$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 220$. Let $M = \binom{16}{k}$. Find the remainder when $39353M$ is divided by $93942$. | 28,256 | graphs = [
Graph(
let={
"_n": Const(93942),
"n": Const(16),
"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(220)))), exp... | COMB | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3_DIFF"
] | 1 | 0.004 | 2026-03-10T10:01:31.422971Z | {
"verified": true,
"answer": 28256,
"timestamp": "2026-03-10T10:01:31.427381Z"
} | 7d5daf | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1813
},
"timestamp": "2026-04-19T11:36:19.704Z",
"answer": 28256
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
e117a6 | nt_min_crt_v1_784195855_8679 | Let $S$ be the set of all ordered pairs $(a,b)$ of positive integers with $1 \le a \le 3$ and $1 \le b \le 3$. For each such pair, define $t = 3a + 2b$. Let $T$ be the set of all integers $t$ that satisfy $5 \le t \le 15$. Let $N$ be the number of elements in $T$. Now consider the set of all ordered pairs $(x,y)$ of po... | 20,388 | graphs = [
Graph(
let={
"m": Const(7),
"k": 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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tupl... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/B3/B1"
] | 5d6f3d | nt_min_crt_v1 | null | 7 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 0.01 | 2026-02-08T16:16:39.491382Z | {
"verified": true,
"answer": 20388,
"timestamp": "2026-02-08T16:16:39.501343Z"
} | ff55b5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 1895
},
"timestamp": "2026-02-17T00:00:31.411Z",
"answer": 20388
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ef2873 | sequence_fibonacci_compute_v1_124444284_8620 | Let $T$ be the set of integers $t$ such that $30 \leq t \leq 76$ and there exist positive integers $a \leq 5$, $b \leq 6$ satisfying $t = 4a + 6b + 20$. Let $n = |T|$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 17,711 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:49:29.122505Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T09:49:29.123476Z"
} | 48e9bc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 2158
},
"timestamp": "2026-02-14T19:39:21.054Z",
"answer": 17711
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
fa9d87 | nt_sum_divisors_mod_v1_458359167_3471 | Let $n$ be the number of positive integers $k$ such that $k \leq 1680$ and $13$ divides $F_k$, where $F_k$ denotes the $k$-th Fibonacci number. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by 11003. | 744 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1680)), Divides(divisor=Const(13), dividend=Fibonacci(arg=Var(name='n')))))),
"M": Const(11003),
"sigma": SumDivisors(n=Ref("n")),
... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T08:22:57.793436Z | {
"verified": true,
"answer": 744,
"timestamp": "2026-02-08T08:22:57.794518Z"
} | 5cf3c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 2324
},
"timestamp": "2026-02-13T18:02:58.059Z",
"answer": 744
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
be3fea | algebra_quadratic_discriminant_v1_1439011603_1754 | Let $a = 1$, $b = \sum_{k=1}^{3} k$, and $c = 8$. Define $\text{result} = b^2 - 4ac$. Let $Q$ be the sum of the number of positive divisors of each integer $n$ from $1$ to $|\text{result}|$ inclusive.
Compute $Q$. | 8 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1),
"b": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"c": Const(8),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Summation(var="... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.003 | 2026-02-08T16:15:14.228915Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T16:15:14.231827Z"
} | 709670 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 521
},
"timestamp": "2026-02-16T07:15:30.269Z",
"answer": 8
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
84672b | nt_count_divisible_and_v1_1456120455_86 | Let $d_1 = 6$ and $d_2 = 8$. Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 90168$, $$n \equiv \sum_{k=0}^{1} (-1)^k \binom{1}{k} \pmod{6},$$ and $n \equiv 0 \pmod{8}$. Let $c$ be the number of elements in $S$. Find the remainder when $33369c$ is divided by $78380$. | 37,713 | graphs = [
Graph(
let={
"upper": Const(90168),
"d1": Const(6),
"d2": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Summation(var="k... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 2.958 | 2026-02-08T02:53:13.812470Z | {
"verified": true,
"answer": 37713,
"timestamp": "2026-02-08T02:53:16.770953Z"
} | f5660f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1250
},
"timestamp": "2026-02-08T20:02:39.056Z",
"answer": 37713
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V... | {
"lo": 0.52,
"mid": 2,
"hi": 3.36
} | ||
44b16f | comb_bell_compute_v1_349078426_1751 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 14$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Determine the value of the $n$-th Bell number. | 4,140 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:54:04.138402Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T13:54:04.141531Z"
} | 2e152f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T19:25:11.748Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.09,
"mid": -2.97,
"hi": -0.71
} | ||
5edc25 | comb_count_partitions_v1_124444284_6948 | Let $n_2 = 0$. Define $e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $u = 6$ and $n_1 = u + 1$. Define $f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n$ be the value of $e$ multiplied by the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, \dots, 19\}$, plus $f$. Compute the number... | 26,015 | graphs = [
Graph(
let={
"n2": Const(0),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(6),
"n1": Sum(Ref("u"), Const(1)),
"f": Summation(var="k", start=Const(0)... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/BINOMIAL_ALTERNATING"
] | d0de27 | comb_count_partitions_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T08:43:33.368669Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T08:43:33.370123Z"
} | 6a5d0e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 869
},
"timestamp": "2026-02-24T09:58:36.001Z",
"answer": 26015
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemm... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
bbbca6 | algebra_poly_eval_v1_2051736721_4716 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that
$$
x \cdot y = \sum_{k=1}^{N} \varphi(k) \left\lfloor \frac{8}{k} \right\rfloor,
$$
where $N$ is the number of ordered pairs $(p,q)$ of positive integers satisfying $p < q$, $\gcd(p,q) = 1$, and $p \cdot q = 5250$.
Let $b$ be the minimum va... | 9,158 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(8),
"b": 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")), Summation(var="k", sta... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K2/B3"
] | 911cb4 | algebra_poly_eval_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"K2"
] | 3 | 0.004 | 2026-02-08T18:07:47.011353Z | {
"verified": true,
"answer": 9158,
"timestamp": "2026-02-08T18:07:47.015766Z"
} | 0e244a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 3303
},
"timestamp": "2026-02-18T14:15:03.399Z",
"answer": 9158
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
56677b | modular_min_linear_v1_124444284_548 | Let $a$ be the smallest positive integer $n$ such that $7^{1021}$ divides $n!$. Let $m = 12312$ and $b = 4341$. Determine the smallest positive integer $x$ such that $1 \leq x \leq m$ and $a \cdot x \equiv b \pmod{m}$. Let $r$ be this value of $x$. Compute $r + 2^{r \bmod 16} \bmod 86053$. | 33,599 | graphs = [
Graph(
let={
"_n": Const(86053),
"a": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(7)), Const(1021)), domain='Z_{>0}')),
"b": Const(4341),
"m": Const(12312),
"result": MinOver... | NT | null | EXTREMUM | sympy | V5 | [
"V5"
] | 79df37 | modular_min_linear_v1 | null | 6 | 0 | [
"V5"
] | 1 | 0.506 | 2026-02-08T03:21:19.611211Z | {
"verified": true,
"answer": 33599,
"timestamp": "2026-02-08T03:21:20.117555Z"
} | 36dbeb | 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": 3286
},
"timestamp": "2026-02-09T03:12:41.849Z",
"answer": 33599
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
dc957b | nt_min_coprime_above_v1_865884756_1732 | Let $m = 12100$ and $n = 70600$. Let $a = 84100$ and $b = 84386$.
Let $d_0$ be the smallest divisor of $20677$ that is at least $2$. Define
$$
\mu = \sum_{k=1}^{d_0} k.
$$
Let $r$ be the smallest integer $n$ such that $a < n \leq b$ and $\gcd(n, \mu) = 1$.
Compute the remainder when $m - r$ is divided by $n$. | 69,199 | graphs = [
Graph(
let={
"_m": Const(12100),
"_n": Const(70600),
"start": Const(84100),
"upper": Const(84386),
"modulus": Summation(var="k", start=Const(1), end=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/SUM_ARITHMETIC"
] | 487060 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 2 | 0.052 | 2026-02-08T16:14:34.392759Z | {
"verified": true,
"answer": 69199,
"timestamp": "2026-02-08T16:14:34.444776Z"
} | 82296d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 7434
},
"timestamp": "2026-02-17T00:19:55.353Z",
"answer": 69199
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1db480 | nt_count_coprime_v1_1439011603_1796 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 169$. Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 12769$ and $\gcd(n, k) = 1$. Determine the number of elements in $S$. | 5,894 | graphs = [
Graph(
let={
"upper": Const(12769),
"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(169)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.978 | 2026-02-08T16:17:11.708990Z | {
"verified": true,
"answer": 5894,
"timestamp": "2026-02-08T16:17:12.687382Z"
} | df7bbf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1046
},
"timestamp": "2026-02-17T00:39:47.524Z",
"answer": 5894
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dcc1fe | antilemma_cartesian_v1_548369836_261 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 21$ and $1 \leq j \leq 38$. Find the remainder when $128 - x$ is divided by $72324$. | 71,654 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=Const(38)))),
"Q": Mod(value=Sub(Const(128), Ref("x")), modulus=Const(72324)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T02:49:44.735424Z | {
"verified": true,
"answer": 71654,
"timestamp": "2026-02-08T02:49:44.735863Z"
} | 3a0264 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 784
},
"timestamp": "2026-02-08T20:17:02.166Z",
"answer": 71654
},
{
"i... | 2 | [
{
"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": -5.97,
"mid": -3.96,
"hi": -1.98
} | ||
c7e957_l | modular_count_residue_v1_1874849503_469 | Let $A$ be the set of all ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 10$. Let $r = \sum_{k=0}^{5} (-1)^k \binom{|A|}{k}$. Compute the number of positive integers $n$ such that $n \leq 37249$ and $n \equiv r \pmod{10}$. | 3,725 | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | modular_count_residue_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 1.31 | 2026-02-08T13:04:44.931682Z | {
"verified": false,
"answer": 3724,
"timestamp": "2026-02-08T13:04:46.241186Z"
} | 72d89c | c7e957 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 829
},
"timestamp": "2026-02-09T17:19:32.901Z",
"answer": 3724
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SU... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | |
7d772c | nt_sum_totient_over_divisors_v1_124444284_791 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 16941456$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute $$\sum_{d \mid n} \phi(d).$$ | 8,232 | 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(16941456)))), expr=Sum(Var("x"), Var("y")))),
"result": SumO... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T03:30:54.788916Z | {
"verified": true,
"answer": 8232,
"timestamp": "2026-02-08T03:30:54.796925Z"
} | 54b0ce | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1693
},
"timestamp": "2026-02-09T22:06:35.429Z",
"answer": 8232
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
9fa36c | geo_count_lattice_triangle_v1_1419126231_995 | Let $R = |128 \cdot 144 + 33 \cdot (-3)|$, $S = \gcd(128, 3) + \gcd(|128 - 33|, |144 - 3|) + \gcd(33, 144)$, and $T = \frac{R + 2 - S}{2}$. Find the remainder when $17616 \cdot T$ is divided by $86755$. | 86,340 | graphs = [
Graph(
let={
"_n": Const(33),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=144)), Mul(Const(value=33), Sub(left=Const(value=0), right=Const(value=3))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=3))), GCD(a=Abs(arg=Sub(... | GEOM | NT | COUNT | sympy | K3 | [
"K3"
] | 54c41e | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.005 | 2026-02-25T10:30:23.474828Z | {
"verified": true,
"answer": 86340,
"timestamp": "2026-02-25T10:30:23.480122Z"
} | 776bae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1697
},
"timestamp": "2026-03-30T11:02:35.054Z",
"answer": 86340
},
{
"... | 1 | [
{
"lemma": "K3",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
2db914 | comb_sum_binomial_row_v1_784195855_9970 | Let $\ell$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 32770$ and $\binom{32770}{j}$ is odd. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$, and let $M$ be the maximum value of $xy$ over all such pairs. For each integer $k$ from $1$ to $\ell$, define $... | 1,024 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32770)), Eq(Mod(value=Binom(n=Const(32770), k=Var("j")), modulus=Ref("_m")), Const(1))), domain='nonnegative_integers')),
"... | NT | null | SUM | sympy | V8 | [
"V8/K2",
"B1/K2"
] | c603b8 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"B1",
"K2",
"V8"
] | 3 | 0.003 | 2026-02-08T17:21:03.030713Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T17:21:03.033417Z"
} | 65e663 | 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": 1003
},
"timestamp": "2026-02-18T00:41:45.543Z",
"answer": 1024
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.