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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
fab3b2 | comb_catalan_compute_v1_1874849503_238 | Let $n$ be the number of integers $t$ such that $19 \leq t \leq 43$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, satisfying $t = 6a + 4b + 9$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T12:53:28.281407Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T12:53:28.284392Z"
} | 164f4f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 2211
},
"timestamp": "2026-02-09T14:59:38.182Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
a2effb | modular_mod_compute_v1_1742523217_5395 | Let $a$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 100$. Compute the remainder when $a$ is divided by $2024$. | 476 | graphs = [
Graph(
let={
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(100)))), expr=Mul(Var("x"), Var("y")))),
"m": Const(2024),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T10:57:55.450578Z | {
"verified": true,
"answer": 476,
"timestamp": "2026-02-08T10:57:55.453913Z"
} | 2dd4ab | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 528
},
"timestamp": "2026-02-15T21:06:43.258Z",
"answer": 476
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
a24963 | nt_count_coprime_and_v1_1520064083_7985 | Let $ k_1 = 9 $. Let $ k_2 $ be the minimum value of $ x + y $ over all ordered pairs $ (x, y) $ of positive integers such that $ xy = 64 $. Determine the value of the number of positive integers $ n \leq 11013 $ such that $ \gcd(n, k_1) = 1 $ and $ \gcd(n, k_2) = 1 $. | 3,671 | graphs = [
Graph(
let={
"upper": Const(11013),
"k1": Const(9),
"k2": 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(64)))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 1.121 | 2026-02-08T09:26:55.856686Z | {
"verified": true,
"answer": 3671,
"timestamp": "2026-02-08T09:26:56.977767Z"
} | bfffe3 | 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": 989
},
"timestamp": "2026-02-14T03:59:31.841Z",
"answer": 3671
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d0c3af | nt_min_crt_v1_865884756_6729 | Let $m$ be the largest prime number $n$ such that $2 \leq n \leq 8$. Let $a = 3$ and $b = 9$. Compute the smallest positive integer $n_1$ such that $1 \leq n_1 \leq 77$, $n_1 \equiv 3 \pmod{m}$, and $n_1 \equiv 9 \pmod{11}$. | 31 | graphs = [
Graph(
let={
"_n": Const(2),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"k": Const(11),
"a": Const(3),
"b": Const(9),
"upper": Const(7... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_min_crt_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.015 | 2026-02-08T19:22:22.333163Z | {
"verified": true,
"answer": 31,
"timestamp": "2026-02-08T19:22:22.348257Z"
} | 6c24a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 880
},
"timestamp": "2026-02-18T22:10:00.081Z",
"answer": 31
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6f51a3 | antilemma_k3_v1_168721529_1205 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of 13688, where $\phi$ denotes Euler's totient function. | 13,688 | graphs = [
Graph(
let={
"_n": Const(13688),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:31:40.346298Z | {
"verified": true,
"answer": 13688,
"timestamp": "2026-02-08T13:31:40.346837Z"
} | cf82a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 430
},
"timestamp": "2026-02-09T14:38:00.790Z",
"answer": 13688
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.65,
"mid": -2.15,
"hi": 1.88
} | ||
8a4397 | antilemma_k3_v1_784195855_8518 | Let $n = 79051$. Compute the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$.
Find the value of this sum. | 79,051 | graphs = [
Graph(
let={
"_n": Const(79051),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T16:08:39.378877Z | {
"verified": true,
"answer": 79051,
"timestamp": "2026-02-08T16:08:39.379310Z"
} | aa58c4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1054
},
"timestamp": "2026-02-16T07:09:28.400Z",
"answer": 26357
},
{
"id": 11... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
37afa1 | modular_mod_compute_v1_677425708_3320 | Let $ S $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 6241 $. Let $ \sigma $ be the minimum value of $ x + y $ over all pairs $ (x, y) \in S $. Let $ P $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ x + y = \sigma $. Define $ a $ to be the maximum valu... | 6,241 | 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(6241)))), expr=Sum(Var("x"), Var("y")))),
"a": MaxOverSet(s... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | modular_mod_compute_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T05:39:01.806734Z | {
"verified": true,
"answer": 6241,
"timestamp": "2026-02-08T05:39:01.809501Z"
} | 741083 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 467
},
"timestamp": "2026-02-11T22:56:24.708Z",
"answer": 1764
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
6787cb | antilemma_sum_equals_v1_898971024_82 | Let $ T $ be the set of all integers $ t $ such that there exist integers $ a $ and $ b $ satisfying $ 1 \leq a \leq 5 $, $ 1 \leq b \leq 2 $, $ 7 \leq t \leq 20 $, and $ t = 2a + 5b $. Let $ n = |T| $. Compute the number of ordered pairs $ (i, j) $ of integers with $ 1 \leq i \leq 9 $ and $ 1 \leq j \leq 9 $ such that... | 9 | 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=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.013 | 2026-02-08T15:10:49.175213Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T15:10:49.188089Z"
} | b32491 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 556
},
"timestamp": "2026-02-24T20:01:19.113Z",
"answer": 9
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -8,
"mid": -4.75,
"hi": -2.29
} | ||
368e63 | antilemma_k3_v1_1440796553_739 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $43278$, where $\phi$ denotes Euler's totient function. | 43,278 | graphs = [
Graph(
let={
"_n": Const(43278),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T11:56:50.999386Z | {
"verified": true,
"answer": 43278,
"timestamp": "2026-02-08T11:56:50.999913Z"
} | 4f3d1e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 1108
},
"timestamp": "2026-02-14T20:46:41.737Z",
"answer": 43278
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
65e1b2 | diophantine_fbi2_count_v1_548369836_326 | Let $n = 191$ and $k = 840$. Let $r$ be the number of integers $d$ such that $2 \leq d \leq n$, $d$ divides $k$, and $3 \leq k/d \leq 192$. Let $m = |r| + 2$. Compute the smallest positive integer $t$ such that the $t$-th Fibonacci number is divisible by $m$. | 21 | graphs = [
Graph(
let={
"_n": Const(191),
"k": Const(840),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(... | NT | null | COUNT | sympy | V5 | [
"MAX_PRIME_BELOW/BIG_OMEGA_ONE",
"OMEGA_ONE"
] | ea9b86 | diophantine_fbi2_count_v1 | null | 4 | 2 | [
"BIG_OMEGA_ONE",
"MAX_PRIME_BELOW",
"OMEGA_ONE",
"V5"
] | 4 | 0.142 | 2026-02-08T02:52:01.426828Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T02:52:01.569138Z"
} | 2b1483 | 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": 2461
},
"timestamp": "2026-02-08T20:19:44.513Z",
"answer": 21
},
{
"id"... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"sta... | {
"lo": -2.08,
"mid": 1.77,
"hi": 4.93
} | ||
2380a6 | sequence_count_fib_divisible_v1_2051736721_1629 | Let $d = 16$ and let $N$ be a positive integer such that $1 \leq N \leq 519$. Determine the number of such integers $N$ for which $d$ divides the $N$th Fibonacci number. Find the value of this count. | 43 | graphs = [
Graph(
let={
"upper": Const(519),
"d": Const(16),
"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_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.081 | 2026-02-08T16:08:15.101330Z | {
"verified": true,
"answer": 43,
"timestamp": "2026-02-08T16:08:15.181931Z"
} | 96c6dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 1542
},
"timestamp": "2026-02-16T21:16:39.062Z",
"answer": 43
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
50de64 | modular_count_residue_v1_153355830_1162 | Let $m$ be the number of integers $t$ such that $11 \leq t \leq 29$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 3$, $1 \leq b \leq 5$, and $t = 5a + 2b + 4$. Let $r = 4$ and $N = 66049$. Compute the number of positive integers $n \leq N$ such that $n \equiv r \pmod{m}$. Multiply this count by 69705 a... | 36,272 | graphs = [
Graph(
let={
"upper": Const(66049),
"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=3)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_count_residue_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 6.915 | 2026-02-08T05:58:15.644189Z | {
"verified": true,
"answer": 36272,
"timestamp": "2026-02-08T05:58:22.559313Z"
} | b8f478 | 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": 2095
},
"timestamp": "2026-02-12T20:28:52.181Z",
"answer": 36272
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
56bdb8 | modular_sum_quadratic_residues_v1_1978505735_2796 | Let $p$ be the largest prime number $n$ such that $2 \leq n \leq 173$. Compute $\frac{p(p-1)}{4}$. | 7,439 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(173)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T17:10:04.157440Z | {
"verified": true,
"answer": 7439,
"timestamp": "2026-02-08T17:10:04.160770Z"
} | 8f74c9 | 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": 482
},
"timestamp": "2026-02-17T21:30:47.701Z",
"answer": 7439
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
78a838 | lin_form_endings_v1_1520064083_1828 | Let $a = 8$ and $b = 6$. Let $l = \text{lcm}(a, b)$. Compute the remainder when $18100 \cdot l$ is divided by 80107. Find the value of this remainder. | 33,865 | graphs = [
Graph(
let={
"a_coeff": Const(8),
"b_coeff": Const(6),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(18100),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(80107),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:19:17.680481Z | {
"verified": true,
"answer": 33865,
"timestamp": "2026-02-08T04:19:17.681041Z"
} | e697d2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 340
},
"timestamp": "2026-02-10T16:19:39.119Z",
"answer": 33865
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
74dd43 | comb_count_partitions_v1_717093673_3139 | Let $N$ be the number of integers $n$ such that $1\le n\le M$ and the sum of the decimal digits of $n$ is even, where $M$ is defined as follows.
Consider all ordered pairs $(x,y)$ of positive integers such that $xy=1849$. For each such pair, form the sum $x+y$. Let $M$ be the minimum of all these sums.
Let $P$ be the... | 1 | graphs = [
Graph(
let={
"_c": Const(1849),
"_m": Const(2),
"_n": Const(12),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y... | NT | COMB | COUNT | sympy | LIN_FORM | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW",
"B3/L3B"
] | 7c2da4 | comb_count_partitions_v1 | bell_mod | 7 | 0 | [
"B3",
"L3B",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 4 | 0.043 | 2026-02-08T17:23:26.672275Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T17:23:26.715448Z"
} | e31a15 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 1731
},
"timestamp": "2026-02-18T01:22:08.718Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
41ba9d | algebra_quadratic_discriminant_v1_48377204_810 | Let $a = 2$, $b = -28$, and let $c$ be the number of positive integers $j$ such that $1 \leq j \leq 98$ and $j^4 \leq 92236816$. Compute the value of $b^2 - 4ac$. | 0 | graphs = [
Graph(
let={
"_n": Const(98),
"a": Const(2),
"b": Const(-28),
"c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(4)), Const(92236816))), domain='positive_integers... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"C3"
] | 8a214c | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"C3",
"MOBIUS_COPRIME"
] | 2 | 0.029 | 2026-02-08T15:42:49.484253Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T15:42:49.513130Z"
} | 02f3ac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 676
},
"timestamp": "2026-02-16T11:18:51.006Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6bc238 | nt_count_divisible_and_v1_865884756_4753 | Let $n$ be a positive integer such that $1 \leq n \leq 137280$. Suppose $n$ satisfies the following two conditions:
- $n \equiv \binom{20}{0} - 1 \pmod{12}$,
- $n \equiv \sum_{k=0}^{8} (-1)^k \binom{8}{k} \pmod{15}$.
Determine the number of such integers $n$. | 2,288 | graphs = [
Graph(
let={
"upper": Const(137280),
"d1": Const(12),
"d2": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Sub(Binom(n=C... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 7.032 | 2026-02-08T18:05:35.977854Z | {
"verified": true,
"answer": 2288,
"timestamp": "2026-02-08T18:05:43.009773Z"
} | 1d6465 | 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": 962
},
"timestamp": "2026-02-18T12:59:35.749Z",
"answer": 2288
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7"... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
f2d211 | nt_count_gcd_equals_v1_1978505735_1902 | Let $k$ be the number of integers $t$ with $14 \leq t \leq 972$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 93$, $1 \leq b \leq 38$, and $t = 8a + 6b$. Let $d = 79$ and let $\text{result}$ be the number of positive integers $n$ with $1 \leq n \leq 15625$ such that $\gcd(n, k) = d$. Comp... | 46,279 | graphs = [
Graph(
let={
"_n": Const(53597),
"upper": Const(15625),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.448 | 2026-02-08T16:31:09.591351Z | {
"verified": true,
"answer": 46279,
"timestamp": "2026-02-08T16:31:11.039323Z"
} | 8c0d89 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 4434
},
"timestamp": "2026-02-17T05:04:05.010Z",
"answer": 46279
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
269f30 | nt_count_divisible_v1_1978505735_6583 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 20$. Let $P$ be the maximum value of $xy$ over all such pairs. Let $T$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = P$. Let $d$ be the minimum value of $x_1 + y_1$ over all pairs in $T$. De... | 20,080 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(20)))), expr=Mul(Var("x"), Var("y")))),
"upper": Const(4840... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_divisible_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 1.471 | 2026-02-08T19:40:47.783421Z | {
"verified": true,
"answer": 20080,
"timestamp": "2026-02-08T19:40:49.254244Z"
} | 7c8a51 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1114
},
"timestamp": "2026-02-18T23:11:45.164Z",
"answer": 20080
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a63236 | nt_count_intersection_v1_153355830_175 | Let $S$ be the set of all integers $t$ with $21 \leq t \leq 795$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 19$, $1 \leq b \leq 85$, and $t = 15a + 6b$. Let $n$ be the number of elements in $S$.
Define $m = \mu(n)^2$. Let $a_1 = 219m$ and $b_1 = 23$. Define $w = \sum_{d\mid \gcd(a_1, b_1)} \mu... | 953 | 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=19)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MOBIUS_SQUAREFREE",
"MOBIUS_COPRIME"
] | 4a1b6a | nt_count_intersection_v1 | null | 6 | 2 | [
"LIN_FORM",
"MOBIUS_COPRIME",
"MOBIUS_SQUAREFREE"
] | 3 | 0.702 | 2026-02-08T02:55:38.663624Z | {
"verified": true,
"answer": 953,
"timestamp": "2026-02-08T02:55:39.365672Z"
} | c000f7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 1119
},
"timestamp": "2026-02-17T16:05:00.934Z",
"answer": 2857
}
] | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"sta... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
ef9215 | modular_mod_compute_v1_458359167_4090 | Let $S_1$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 100$. Let $s_1$ be the minimum value of $x + y$ over all pairs $(x, y) \in S_1$. Let $S_2$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = s_1$. Let $p_2$ be the maximum value of $xy$ over all pairs ... | 23,828 | graphs = [
Graph(
let={
"_n": Const(94649),
"a": Const(76729),
"m": 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")), MaxOverSet(set=... | NT | null | COMPUTE | sympy | B1 | [
"B1/B1",
"B3/B1"
] | 82ed59 | modular_mod_compute_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T11:30:27.790026Z | {
"verified": true,
"answer": 23828,
"timestamp": "2026-02-08T11:30:27.793302Z"
} | 0c177e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 2050
},
"timestamp": "2026-02-14T15:26:37.498Z",
"answer": 23828
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d4d8aa | geo_visible_lattice_v1_1520064083_4145 | A lattice point $(x, y)$ in the plane is said to be visible from the origin if $\gcd(x, y) = 1$. Let $V(n)$ denote the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$. Compute the remainder when $18312 \cdot V(89)$ is divided by $99485$. | 95,277 | graphs = [
Graph(
let={
"n": Const(89),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(18312), Ref("result")), modulus=Const(99485)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 0.357 | 2026-02-08T06:06:49.757732Z | {
"verified": true,
"answer": 95277,
"timestamp": "2026-02-08T06:06:50.114402Z"
} | fd2c19 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 5755
},
"timestamp": "2026-02-24T05:27:30.531Z",
"answer": 95277
},
{
"... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
20cc3c | antilemma_k3_v1_458359167_2632 | Let $n = 98462$. Compute the value of $$
\sum_{d \mid n} \phi(d),
$$ where the sum is taken over all positive divisors $d$ of $n$, and $\phi(d)$ denotes Euler's totient function. | 98,462 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=98462), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T06:23:06.880906Z | {
"verified": true,
"answer": 98462,
"timestamp": "2026-02-08T06:23:06.881179Z"
} | 5effe6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 4113
},
"timestamp": "2026-02-15T17:41:16.045Z",
"answer": null
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
8eac23 | modular_mod_compute_v1_168721529_223 | Let $a$ be the number of positive integers $n$ such that $1 \leq n \leq 27789$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Find the remainder when $a$ is divided by $50625$. | 3,969 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(27789)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
"m": Const(50625),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | modular_mod_compute_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T12:54:22.423022Z | {
"verified": true,
"answer": 3969,
"timestamp": "2026-02-08T12:54:22.424358Z"
} | e40a99 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1436
},
"timestamp": "2026-02-09T02:37:30.871Z",
"answer": 3969
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
... | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.84
} | ||
2d65c2 | sequence_count_fib_divisible_v1_1915831931_3753 | Let $s$ be the sum of all real solutions $x$ to the equation $x^2 - 486x - 13312 = 0$. Let $r$ be the number of positive integers $n \leq s$ such that the $n$th Fibonacci number is divisible by $4$. Compute the remainder when $39453r$ is divided by $91256$. | 1,733 | graphs = [
Graph(
let={
"upper": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-486), Var("x")), Const(-13312)), Const(0)))),
"d": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), C... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.022 | 2026-02-08T17:52:33.044771Z | {
"verified": true,
"answer": 1733,
"timestamp": "2026-02-08T17:52:33.066507Z"
} | eff30d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1340
},
"timestamp": "2026-02-18T09:26:35.129Z",
"answer": 1733
},
{... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cf28fd | algebra_quadratic_discriminant_v1_124444284_8387 | Let $n = 4$, $a = -4$, $b = -2$, and $c = 8$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) = 1$, and $p < q$. Compute $b^{|S|} - n \cdot a \cdot c$. | 132 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-4),
"b": Const(-2),
"c": Const(8),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(l... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.008 | 2026-02-08T09:40:40.919423Z | {
"verified": true,
"answer": 132,
"timestamp": "2026-02-08T09:40:40.927825Z"
} | c74c5e | 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": 823
},
"timestamp": "2026-02-14T05:37:14.778Z",
"answer": 132
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
127d38_n | comb_count_derangements_v1_1218484723_3489 | A teacher assigns $n$ students to $n$ seats such that no student sits in their original seat. The number $n$ is the sum of $2^0$, $2^1$, and $2^2$. In how many ways can the students be reassigned so that every student ends up in a different seat? | 1,854 | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 2 | null | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T05:09:44.388600Z | null | 28fb41 | 127d38 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 847
},
"timestamp": "2026-03-30T20:06:22.452Z",
"answer": 1854
},
{
"id... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
271e3d | alg_poly3_sum_v1_1218484723_946 | Let $T$ be the set of integers $t$ such that $t = 4a + 5b$ for some integers $a, b$ with $1 \le a \le 46$, $1 \le b \le 5$, and $9 \le t \le 209$. Let $C = |T|$. Let $D = \min\{d \ge 2 : d \mid 10930463309\}$. Compute the remainder when $$\sum_{\substack{a=1}}^{101} \sum_{\substack{b=1}}^{D} \left(54a^3 + C \cdot b^3 +... | 36,124 | graphs = [
Graph(
let={
"_m": Const(54797),
"_n": Const(369),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(101)), Geq(Var("b"), Const(1)), Leq(Var("b"), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | alg_poly3_sum_v1 | null | 7 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.03 | 2026-02-25T02:39:07.227919Z | {
"verified": true,
"answer": 36124,
"timestamp": "2026-02-25T02:39:07.257791Z"
} | 0a62be | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 28113
},
"timestamp": "2026-03-10T03:10:46.346Z",
"answer": 24167
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "o... | {
"lo": 3.81,
"mid": 5.7,
"hi": 7.82
} | ||
01b932 | geo_count_lattice_rect_v1_809748730_376 | Let $a = 28$ and $b = 107$. Define the rectangle $R$ as the set of all lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the number of lattice points in $R$. | 3,132 | graphs = [
Graph(
let={
"a": Const(28),
"b": Const(107),
"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 | 2026-02-08T11:29:32.475880Z | {
"verified": true,
"answer": 3132,
"timestamp": "2026-02-08T11:29:32.476447Z"
} | cd4458 | 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": 281
},
"timestamp": "2026-02-24T14:00:09.915Z",
"answer": 3132
},
{
"id... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
58af14 | modular_mod_compute_v1_124444284_2101 | Let $a = 47089$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 134$. Define $m$ to be the maximum value of $xy$ over all pairs $(x,y) \in S$. Let $r$ be the remainder when $a$ is divided by $m$. Compute $$\sum_{n=1}^{|r|} \tau(n),$$ where $\tau(n)$ denotes the number of positiv... | 17,256 | graphs = [
Graph(
let={
"a": Const(47089),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(134)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 6 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T04:18:11.483819Z | {
"verified": true,
"answer": 17256,
"timestamp": "2026-02-08T04:18:11.484918Z"
} | ba737e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 2908
},
"timestamp": "2026-02-10T16:31:41.772Z",
"answer": 17256
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
b7de2f | geo_visible_lattice_v1_1874849503_564 | Let $n = 64$. Define $r$ to be the number of ordered pairs $(x, y)$ of integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the sum $\sum_{k=1}^{r} \tau(k)$, where $\tau(k)$ denotes the number of positive divisors of $k$. | 20,102 | graphs = [
Graph(
let={
"n": Const(64),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Summation(var="n", start=Pow(Const(68), Mul(Const(93), Mul(Const(59), Const(0)))), end=Abs(arg=Ref(name='result')), expr=NumDivisors(n=Var("n"))),
},
goal=Ref("Q"... | GEOM | NT | COUNT | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO",
"IDENTITY_MUL_ZERO"
] | 6f21fa | geo_visible_lattice_v1 | null | 5 | 0 | [
"IDENTITY_MUL_ZERO",
"IDENTITY_POW_ZERO"
] | 2 | 0.09 | 2026-02-08T13:11:08.726566Z | {
"verified": true,
"answer": 20102,
"timestamp": "2026-02-08T13:11:08.816763Z"
} | 5d08cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 6869
},
"timestamp": "2026-02-24T17:28:56.044Z",
"answer": 20102
},
{
"... | 1 | [
{
"lemma": "IDENTITY_MUL_ZERO",
"status": "ok"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
34d853 | comb_sum_binomial_row_v1_48377204_2276 | Let $m = 37$. Let $\_n$ be the sum of all positive integers $n_1$ at most $74$ that are divisible by $m$. Now, let $n$ be the number of positive integers $n_2$ at most $\_n$ such that $n_2 \equiv \left\lfloor \frac{n_2}{2} \right\rfloor \pmod{7}$. Compute $2^n$. | 32,768 | graphs = [
Graph(
let={
"_m": Const(37),
"_n": SumOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(74)), Eq(Mod(value=Var("n1"), modulus=Ref("_m")), Const(0))))),
"n": CountOverSet(set=SolutionsSet(var=Var("n2"), conditi... | NT | null | SUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/L3C"
] | 1f6f30 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"L3C",
"SUM_DIVISIBLE"
] | 2 | 0.003 | 2026-02-08T16:42:06.860918Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T16:42:06.864096Z"
} | 02faf3 | 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": 953
},
"timestamp": "2026-02-17T10:11:27.284Z",
"answer": 32768
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a95fa3 | algebra_vieta_sum_v1_1439011603_62 | Let $P(x)$ be the polynomial $$P(x) = -x^4 + 2x^3 + cx^2 - 36x - 180,$$ where $c$ is the number of positive integers $k$ such that $1 \leq k \leq 1540$ and $44$ divides $k$. Let $S$ be the set of all real roots of $P(x) = 0$. Let $r$ be the product of all elements of $S$. Compute $67600 - r$. | 67,420 | graphs = [
Graph(
let={
"_n": Const(2),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Const(value=-1), Pow(base=Var(name='x'), exp=Const(value=4))), Mul(Ref(name='_n'), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(CountOverSet(set=Solutio... | ALG | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | algebra_vieta_sum_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.05 | 2026-02-08T15:08:32.475538Z | {
"verified": true,
"answer": 67420,
"timestamp": "2026-02-08T15:08:32.525883Z"
} | 32169e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1427
},
"timestamp": "2026-02-16T01:17:30.867Z",
"answer": 67420
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
33f467 | geo_visible_lattice_v1_1918700295_4218 | Let $n = 81$. Define $L$ to be the number of lattice points $(x, y)$ such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the Bell number of $|L| \bmod 11$. | 2 | graphs = [
Graph(
let={
"n": Const(81),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 1.604 | 2026-02-08T09:14:12.175417Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T09:14:13.778970Z"
} | 0c235d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 6126
},
"timestamp": "2026-02-24T10:52:54.449Z",
"answer": 2
},
{
"id":... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
e079bc | antilemma_sum_equals_v1_1248542787_583 | Let $ S $ be the set of all ordered pairs of integers $ (i,j) $ such that $ 1 \leq i \leq 81 $, $ 1 \leq j \leq 81 $, and $ i + j = 82 $. Compute the number of elements in $ S $. | 81 | graphs = [
Graph(
let={
"_n": Const(82),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(81)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.028 | 2026-02-08T03:14:34.168335Z | {
"verified": true,
"answer": 81,
"timestamp": "2026-02-08T03:14:34.196547Z"
} | 9b2891 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 250
},
"timestamp": "2026-02-09T05:48:11.347Z",
"answer": 81
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
7bf941 | algebra_quadratic_discriminant_v1_397696148_390 | Let $a = 2$, $b = -24$, and $c = 40$. Compute the discriminant $D = b^2 - 4ac$. Let $N$ be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Define the value
\[
\text{result} = \begin{cases}
N & \text{if } D > 0, \\
1 & \text{if } D = 0, \\
0 & \text{if } D < ... | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2),
"b": Const(-24),
"c": Const(40),
"D": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(I... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T11:27:49.552111Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T11:27:49.554515Z"
} | 91e24c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 548
},
"timestamp": "2026-02-14T14:17:44.143Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ed41e8 | antilemma_sum_equals_v1_1918700295_1369 | Let $n = 24$. Find the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 23$, $1 \leq j \leq 24$, and $i + j = n$. | 23 | graphs = [
Graph(
let={
"_n": Const(24),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.099 | 2026-02-08T05:48:30.729082Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T05:48:30.827951Z"
} | ca1f4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 346
},
"timestamp": "2026-02-24T04:30:53.219Z",
"answer": 23
},
{
"id":... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
06d594 | modular_mod_compute_v1_784195855_3914 | Let $a = -25281$. Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 14992384$. Find the value of $a \bmod m$, where the result is the unique integer $r$ with $0 \leq r < m$ such that $a \equiv r \pmod{m}$. | 5,695 | graphs = [
Graph(
let={
"a": Const(-25281),
"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(14992384)))), expr=Sum(Var("x"), Var("y"... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T06:41:51.550795Z | {
"verified": true,
"answer": 5695,
"timestamp": "2026-02-08T06:41:51.553952Z"
} | feb85b | 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": 1187
},
"timestamp": "2026-02-13T03:39:55.274Z",
"answer": 5695
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3a53fd | comb_binomial_compute_v1_784195855_2748 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 14$. Define $M$ to be the maximum value of $xy$ over all pairs in $P$. Now, let $Q$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = M$. Define $n$ to be the minimum value of $x + y$ over all pairs in $... | 3,432 | graphs = [
Graph(
let={
"_n": Const(7),
"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=MapOverSet(set=SolutionsSet(var=Tup... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3",
"K3"
] | 036957 | comb_binomial_compute_v1 | null | 6 | 0 | [
"B1",
"B3",
"K3"
] | 3 | 0.003 | 2026-02-08T05:57:35.530296Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-08T05:57:35.533437Z"
} | 45a236 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 521
},
"timestamp": "2026-02-12T17:08:48.362Z",
"answer": 3432
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
13eb94 | antilemma_k2_v1_2051736721_4448 | Let $S$ be the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 378$ and $1 \leq j \leq 10$. Define $x = \frac{8}{80} \sum_{(k,j) \in S} \phi(k) \left\lfloor \frac{378}{k} \right\rfloor$. Compute the remainder when $44121 \cdot x$ is divided by $93514$. | 32,207 | graphs = [
Graph(
let={
"_n": Const(44121),
"x": Div(Mul(Const(8), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(378)), right=IntegerRange(start=Const(1), e... | NT | COMB | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/K2",
"K2"
] | ddbc0a | antilemma_k2_v1 | null | 4 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.002 | 2026-02-08T17:59:40.626484Z | {
"verified": true,
"answer": 32207,
"timestamp": "2026-02-08T17:59:40.628223Z"
} | d31cf9 | 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": 6820
},
"timestamp": "2026-02-18T11:33:42.314Z",
"answer": 32207
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6d2e6d | antilemma_k3_v1_809748730_852 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $27499$, where $\phi$ denotes Euler's totient function. | 27,499 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=27499), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T11:47:12.628172Z | {
"verified": true,
"answer": 27499,
"timestamp": "2026-02-08T11:47:12.628716Z"
} | cc3d7c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 1668
},
"timestamp": "2026-02-14T19:03:47.101Z",
"answer": 27499
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6074b3 | alg_poly_preperiod_count_v1_1218484723_142 | Let $N = (a^5 + a^4 - 2a^3 - 2a^2 + 3a + 4) \bmod 31$, and define $M, R, S, T$ recursively by applying the same polynomial modulo 31. Let $Q$ be the number of non-negative integers $a$ with $0 \leq a \leq 14538$ such that $T = M$, $R \neq M$, and $S \neq M$. Find $Q$. | 8,911 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(5)), Pow(Var("a"), Const(4)), Mul(Const(-2), Pow(Var("a"), Const(3))), Mul(Const(-2), Pow(Var("a"), Const(2))), Mul(Const(3), Var("a")), Const(4)), modulus=Const(31)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(5)), Pow(Re... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.195 | 2026-02-25T01:51:05.414914Z | {
"verified": true,
"answer": 8911,
"timestamp": "2026-02-25T01:51:05.610108Z"
} | 259a6d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T08:36:54.947Z",
"answer": 8911
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.77,
"mid": 6.8,
"hi": 9.83
} | ||
96827f | sequence_lucas_compute_v1_601307018_7266 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ satisfying
$$
17b^4 + 68a b^k + 68a^3b + m a^4 + 102a^2b^2 = 267800337,
$$
where
$$
k = \left| \left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 15,\ -16a_1b_1 + 16a_1^2 + 29b_1^2 = 3125 \right\} \right|
$$
and
$$
m = \left| \left\{ (a_... | 5,778 | graphs = [
Graph(
let={
"_c": Const(15),
"_m": Const(3125),
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Con... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/POLY4_COUNT",
"QF_PSD_ORBIT/POLY4_COUNT"
] | 196bb5 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT",
"QF_PSD_ORBIT"
] | 3 | 0.022 | 2026-03-10T07:50:29.831456Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-03-10T07:50:29.853104Z"
} | 272544 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 358,
"completion_tokens": 2919
},
"timestamp": "2026-04-19T06:16:45.946Z",
"answer": 5778
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
6441c5 | lin_form_endings_v1_1742523217_134 | Let $a = 14$ and $b = 35$. Let $k = 20$. Define $d = \gcd(a, b)$, and let $m = \gcd(k, d)$. Let $t = \left\lfloor \frac{k}{m} \right\rfloor$. Compute the remainder when $17089 \cdot t$ is divided by $99838$. | 42,266 | graphs = [
Graph(
let={
"a_coeff": Const(14),
"b_coeff": Const(35),
"k_val": Const(20),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(17... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:53:21.641726Z | {
"verified": true,
"answer": 42266,
"timestamp": "2026-02-08T02:53:21.642472Z"
} | 79b071 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 418
},
"timestamp": "2026-02-09T14:00:30.657Z",
"answer": 42266
},
{
"i... | 1 | [
{
"lemma": "C2",
"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",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.06,
"hi": -0.47
} | ||
824d76 | nt_count_divisible_and_v1_458359167_3359 | Let $d_1$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Let $d_2 = 6$. Determine the number of positive integers $n$ such that $1 \leq n \leq 10680$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 890 | graphs = [
Graph(
let={
"upper": Const(10680),
"d1": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(4)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 2 | 0 | [
"B3"
] | 1 | 5.12 | 2026-02-08T08:18:18.683358Z | {
"verified": true,
"answer": 890,
"timestamp": "2026-02-08T08:18:23.803665Z"
} | 2e9362 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 510
},
"timestamp": "2026-02-13T17:09:32.497Z",
"answer": 890
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
f8607d | modular_min_modexp_v1_151522320_1988 | Let $a = 7$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 10201$. Let $m$ be the largest prime number less than or equal to $444$. Find the smallest positive integer $x \leq 442$ such that $a^x \equiv b \pmod{m}$. | 122 | graphs = [
Graph(
let={
"a": Const(7),
"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")), Const(10201)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | modular_min_modexp_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.095 | 2026-02-08T04:30:19.403430Z | {
"verified": true,
"answer": 122,
"timestamp": "2026-02-08T04:30:19.498913Z"
} | 621baa | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 5507
},
"timestamp": "2026-02-10T16:49:54.486Z",
"answer": 122
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
059087 | nt_gcd_compute_v1_168721529_1084 | Let $ p_1 = 31 $, $ q_1 = 83 $, and $ r $ be the smallest prime divisor of $ 19343 $. Define $ n_1 = p_1^2 \cdot q_1 \cdot r $. Let $ v = \mu(n_1)^2 $, where $ \mu $ is the M\"obius function. Define $ p = 73 + v $ and $ q = 23 $. Let $ n = p^2 \cdot (q + 1) $. Let $ e = \mu(n)^2 $. Let $ a = 419335 $ and $ b = 778765 +... | 42,543 | graphs = [
Graph(
let={
"p1": Const(31),
"q1": Const(83),
"r": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(19343))))),
"n1": Mul(Pow(Ref("p1"), Const(2)), Ref("q1"), Ref("r")),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_SQUAREFREE"
] | 9851d7 | nt_gcd_compute_v1 | null | 4 | 2 | [
"MIN_PRIME_FACTOR",
"MOBIUS_SQUAREFREE"
] | 2 | 0.007 | 2026-02-08T13:27:41.290229Z | {
"verified": true,
"answer": 42543,
"timestamp": "2026-02-08T13:27:41.297142Z"
} | 281245 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 2745
},
"timestamp": "2026-02-09T13:38:41.499Z",
"answer": 42543
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status":... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
ab65f2 | antilemma_sum_equals_v1_1520064083_9567 | Let $ T $ be the set of all integers $ t $ such that $ 22 \leq t \leq 222 $ and there exist positive integers $ a $ and $ b $ with $ 1 \leq a \leq 19 $, $ 1 \leq b \leq 5 $, and $ t = 8a + 14b $. Let $ n $ be the number of elements in $ T $. Determine the number of ordered pairs $ (i, j) $ of positive integers such tha... | 80 | 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=19)), 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 | 0.005 | 2026-02-08T10:52:56.826847Z | {
"verified": true,
"answer": 80,
"timestamp": "2026-02-08T10:52:56.831760Z"
} | 7c29c7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 1620
},
"timestamp": "2026-02-24T12:29:52.419Z",
"answer": 80
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
2ac1da | nt_count_digit_sum_v1_1915831931_2036 | Let $S$ be the set of all real solutions to the equation $x^2 - 9999x + 159728 = 0$. Define $U$ to be the sum of all elements in $S$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq U$ and the sum of the decimal digits of $n$ is 14. | 540 | graphs = [
Graph(
let={
"upper": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-9999), Var("x")), Const(159728)), Const(0)))),
"target_sum": Const(14),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_digit_sum_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.387 | 2026-02-08T16:35:48.687105Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T16:35:49.074513Z"
} | 5212b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 2704
},
"timestamp": "2026-02-17T07:36:33.367Z",
"answer": 540
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
72d2a5 | nt_sum_gcd_range_mod_v1_1918700295_176 | Let $N$ be the number of positive integers $t$ with $16 \le t \le 2040$ for which there exist positive integers $a$ and $b$, $1 \le a \le 259$, $1 \le b \le 368$, such that
$$
t = 5a + 2b + 9.
$$Let $k = 180$. Compute the remainder when
$$
\sum_{n=1}^N \gcd(n, k)
$$is divided by $10501$. | 6,398 | 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=259)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.304 | 2026-02-08T03:02:49.387900Z | {
"verified": true,
"answer": 6398,
"timestamp": "2026-02-08T03:02:49.691830Z"
} | f3e3b6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 7855
},
"timestamp": "2026-02-10T12:36:08.083Z",
"answer": 6398
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": 2.27,
"mid": 4.73,
"hi": 7.05
} | ||
63695e | geo_count_lattice_rect_v1_349078426_660 | Compute the number of lattice points $(x,y)$ such that $0 \leq x \leq 99$ and $0 \leq y \leq 101$. | 10,200 | graphs = [
Graph(
let={
"a": Const(99),
"b": Const(101),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T13:12:14.176213Z | {
"verified": true,
"answer": 10200,
"timestamp": "2026-02-08T13:12:14.176916Z"
} | 62651d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 159
},
"timestamp": "2026-02-24T17:32:58.847Z",
"answer": 10200
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
eccb1d | sequence_count_fib_divisible_v1_1520064083_10047 | Let $n$ be a positive integer. Determine the number of positive integers $n \leq 881$ for which the $n$th Fibonacci number is divisible by 2. | 293 | graphs = [
Graph(
let={
"upper": Const(881),
"d": Const(2),
"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')))))),
},
go... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/C3",
"MOBIUS_COPRIME",
"C3/C3"
] | b322bc | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"C3",
"LIN_FORM",
"MOBIUS_COPRIME"
] | 3 | 0.3 | 2026-02-08T11:10:54.158191Z | {
"verified": true,
"answer": 293,
"timestamp": "2026-02-08T11:10:54.457870Z"
} | ac29d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 755
},
"timestamp": "2026-02-14T10:47:33.028Z",
"answer": 293
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
450f30 | nt_sum_over_divisible_v1_168721529_883 | Let $S$ be the set of all positive integers $n$ such that $n \le 63504$ and $n$ is divisible by 43. Let $T$ be the sum of all elements in $S$. Compute the Bell number $B_r$, where $r$ is the remainder when $|T|$ is divided by 11. | 4,140 | graphs = [
Graph(
let={
"upper": Const(63504),
"divisor": Const(43),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"Q": Bell... | COMB | null | SUM | sympy | K3 | [
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 26ae4b | nt_sum_over_divisible_v1 | bell_mod | 4 | 0 | [
"K3",
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 3 | 3.776 | 2026-02-08T13:20:06.419700Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T13:20:10.196136Z"
} | 28ef77 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1130
},
"timestamp": "2026-02-09T10:13:58.664Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"... | {
"lo": -2.77,
"mid": -0.49,
"hi": 2.44
} | ||
694c45 | sequence_fibonacci_compute_v1_238844314_1166 | Let $n$ be the largest prime number such that $2 \leq n \leq 23$. Compute the $n$th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_n": Const(23),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T14:00:57.556247Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T14:00:57.558579Z"
} | fd96e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 524
},
"timestamp": "2026-02-15T22:54:11.557Z",
"answer": 28657
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
cd566a | sequence_count_fib_divisible_v1_458359167_1265 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x \cdot y = 225$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the number of positive integers $n \leq 11580$ such that $s$ divides the $n$-th Fibonacci number. Let $U$ be the number of positive integers $n \leq ... | 48,979 | graphs = [
Graph(
let={
"_m": Const(56383),
"_n": Const(11580),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), V... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.023 | 2026-02-08T04:31:28.460796Z | {
"verified": true,
"answer": 48979,
"timestamp": "2026-02-08T04:31:28.484019Z"
} | 014a5c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 3511
},
"timestamp": "2026-02-10T16:55:04.654Z",
"answer": 48979
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
d8c1f0 | sequence_count_fib_divisible_v1_1742523217_4581 | Let $p$ be the largest prime number not exceeding 543. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq p$ and the $n$-th Fibonacci number is divisible by 11. Compute the number of elements in $S$. | 54 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(543)), IsPrime(Var("n"))))),
"d": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=... | NT | null | COUNT | sympy | B3 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.115 | 2026-02-08T08:58:28.720350Z | {
"verified": true,
"answer": 54,
"timestamp": "2026-02-08T08:58:28.834991Z"
} | 251d16 | 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": 1197
},
"timestamp": "2026-02-13T22:40:46.577Z",
"answer": 54
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
36be44 | geo_count_lattice_triangle_v1_1742523217_1237 | Let $n = 111$. The twice the area of a triangle with vertices at $(111, 120)$, $(22, 300)$, and $(0, 0)$ is given by
$$
|111 \cdot 120 + 22 \cdot (0 - 300) + 0 \cdot (300 - 120)|.
$$
Let $\text{area\_2x}$ denote this value. Define $\text{boundary}$ as the sum
$$
\gcd(|111|, |1 + 2 + \cdots + 24|) + \gcd(|22 - 111|, |12... | 83,110 | graphs = [
Graph(
let={
"_n": Const(111),
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=120)), Mul(Const(value=22), Sub(left=Const(value=0), right=Const(value=300))))),
"boundary": Sum(GCD(a=Abs(arg=Ref(name='_n')), b=Abs(arg=Summation(expr=Var(name='k'), var='... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.007 | 2026-02-08T03:34:41.310969Z | {
"verified": true,
"answer": 83110,
"timestamp": "2026-02-08T03:34:41.318157Z"
} | 6c5ba7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 1353
},
"timestamp": "2026-02-10T05:27:15.273Z",
"answer": 83110
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": ... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
987a8f | nt_gcd_compute_v1_865884756_997 | Let $a = 1036906$ and $b = 1675002$. Define $d = \gcd(a, b)$. Let $p$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 42$. Compute the remainder when $p - d$ is divided by $67944$. | 56,567 | graphs = [
Graph(
let={
"_n": Const(67944),
"a": Const(1036906),
"b": Const(1675002),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | nt_gcd_compute_v1 | negation_mod | 3 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T15:43:19.095060Z | {
"verified": true,
"answer": 56567,
"timestamp": "2026-02-08T15:43:19.096691Z"
} | 968225 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1192
},
"timestamp": "2026-02-16T06:17:04.854Z",
"answer": 322
},
{
"id": 11,... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
3d6bdf | modular_count_residue_v1_124444284_6532 | Let $m$ be the largest prime number less than or equal to 18. Compute the number of positive integers $n$ such that $1 \leq n \leq 88888$ and $n \equiv 2 \pmod{m}$. | 5,229 | graphs = [
Graph(
let={
"upper": Const(88888),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(18)), IsPrime(Var("n"))))),
"r": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.316 | 2026-02-08T08:30:18.361166Z | {
"verified": true,
"answer": 5229,
"timestamp": "2026-02-08T08:30:21.677020Z"
} | a52249 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 993
},
"timestamp": "2026-02-13T19:14:49.349Z",
"answer": 5229
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
608491 | comb_count_derangements_v1_784195855_3001 | Let $n = 7$. Compute $!n$, the number of derangements of $n$ elements. Let $m$ be the largest prime number less than or equal to 11. Compute $!n \bmod m$, take the absolute value, and use this as the index for the Bell number $B_k$, which counts the number of partitions of a set of size $k$. Determine the value of $B_k... | 203 | graphs = [
Graph(
let={
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))))),
... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | comb_count_derangements_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T06:11:03.555790Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T06:11:03.556678Z"
} | 640d8c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1151
},
"timestamp": "2026-02-12T20:56:51.623Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
4b2fcc | modular_sum_quadratic_residues_v1_153355830_786 | Let $p$ be the smallest prime divisor of $98824109$ that is at least $2$. Compute $\frac{p(p-1)}{4}$. | 53,015 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(98824109))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
},
goal=... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T04:10:41.369551Z | {
"verified": true,
"answer": 53015,
"timestamp": "2026-02-08T04:10:41.371394Z"
} | b07f0e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 79,
"completion_tokens": 5483
},
"timestamp": "2026-02-11T22:26:33.094Z",
"answer": 53015
},
{... | 1 | [
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d1222a | modular_mod_compute_v1_1820931509_417 | Let $a = 25200$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2140369$. Let $m$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the remainder when $a$ is divided by $m$. | 1,792 | graphs = [
Graph(
let={
"a": Const(25200),
"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(2140369)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T11:35:16.877693Z | {
"verified": true,
"answer": 1792,
"timestamp": "2026-02-08T11:35:16.881030Z"
} | 80b498 | 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": 964
},
"timestamp": "2026-02-14T16:10:25.148Z",
"answer": 1792
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a0ffe8 | antilemma_sum_equals_v1_1742523217_1850 | Let $m = 40$. Define $k$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the number of ordered pairs $(i,j)$ with $1 \leq i \leq 18$ and $1 \leq j \leq 19$ such that $i + j = k$. | 18 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.251 | 2026-02-08T04:18:44.650096Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T04:18:44.900760Z"
} | 64ad02 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 959
},
"timestamp": "2026-02-24T00:14:24.148Z",
"answer": 18
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
acf5a3 | nt_sum_totient_over_divisors_v1_151522320_270 | Let $n = 56572$. Let $f(n)$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Let $A = f(n)$. Define $s$ to be the sum of $d_i \cdot (i+1)^2$ for $i = 0$ to $k-1$, where $d_i$ is the $i$-th decimal digit of $|A|$ (starting from the units digit as $i=0$) and $k$ is the number of digits in $|A|$. Let $P$ be ... | 620 | graphs = [
Graph(
let={
"n": Const(56572),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 51a773 | nt_sum_totient_over_divisors_v1 | digits_weighted_mod | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T03:07:07.428566Z | {
"verified": true,
"answer": 620,
"timestamp": "2026-02-08T03:07:07.430652Z"
} | 96d356 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 678
},
"timestamp": "2026-02-09T01:01:56.374Z",
"answer": 620
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
1418af | modular_min_modexp_v1_809748730_1628 | Find the smallest positive integer $x$ such that $1 \leq x \leq 820$ and $13^x \equiv 599 \pmod{821}$. | 502 | graphs = [
Graph(
let={
"a": Const(13),
"b": Const(599),
"m": Const(821),
"upper": Const(820),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(ModExp(base=Ref("a"), exp=Var(... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COUNT_PRIMES"
] | 4bb206 | modular_min_modexp_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"MIN_PRIME_FACTOR"
] | 2 | 0.089 | 2026-02-08T12:35:16.701382Z | {
"verified": true,
"answer": 502,
"timestamp": "2026-02-08T12:35:16.790628Z"
} | fdbc59 | 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": 5269
},
"timestamp": "2026-02-15T02:54:33.205Z",
"answer": 502
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c6da97_n | comb_count_permutations_fixed_v1_1218484723_9 | A theater group has $9$ actors, each assigned a unique role. They decide to reshuffle the roles such that exactly $k$ actors keep their original roles, where $k$ is the sum of $2^0$, $2^1$, and $2^2$. The remaining $9-k$ actors must receive roles different from their original ones. In how many ways can this assignment ... | 36 | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_permutations_fixed_v1 | null | 4 | null | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 2 | 0.002 | 2026-02-25T01:41:20.834904Z | null | 804c00 | c6da97 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 975
},
"timestamp": "2026-03-30T14:37:27.750Z",
"answer": 36
},
{
"id":... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
0cb55a | comb_factorial_compute_v1_717093673_1659 | Let $n'$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the smallest divisor of 637637 that is greater than or equal to $n'$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_factorial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T16:14:20.208728Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T16:14:20.211390Z"
} | 652ea5 | 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": 1924
},
"timestamp": "2026-02-16T23:19:21.141Z",
"answer": 5040
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9ac616 | lin_form_endings_v1_153355830_2041 | Let $t$ be a positive integer. A number $t$ is said to be expressible if there exist integers $a$ and $b$ with $1 \leq a \leq 17$, $1 \leq b \leq 42$, and $112 \leq t \leq 3654$ such that $t = 42a + 70b$. Let $r$ be the number of such expressible values of $t$. Compute the remainder when $13594 \cdot r$ is divided by $... | 57,904 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=17)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:52:53.137199Z | {
"verified": true,
"answer": 57904,
"timestamp": "2026-02-08T06:52:53.138367Z"
} | 26b96f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1728
},
"timestamp": "2026-02-24T07:12:40.315Z",
"answer": 72764
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
fd1d7f | nt_count_divisors_in_range_v1_1520064083_2311 | Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6350400$. Let $S$ be the set of all values of $x + y$ as $(x,y)$ ranges over these pairs. Let $n$ be the minimum element of $S$. Let $a = 5$. Let $b$ be the number of positive integers $p$ for which there exists a positive integer $q$ su... | 41 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(5),
... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | nt_count_divisors_in_range_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 3 | 0.21 | 2026-02-08T04:38:39.350827Z | {
"verified": true,
"answer": 41,
"timestamp": "2026-02-08T04:38:39.561129Z"
} | edf0cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 4745
},
"timestamp": "2026-02-12T02:08:53.757Z",
"answer": 41
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f57f2b | comb_bell_compute_v1_601307018_5339 | Let $B_n$ denote the $n$-th Bell number. Let $S = \left(3a^4 - 4a^3 - a^2 + 4a - 5\right) \bmod c$, where $a$ is a variable and $c$ is the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 722$. Define $T = \left(3S^4 - 4S^3 - S^2 + 4S - 5\right) \bmod d$, where $d$ is the number of i... | 4,140 | graphs = [
Graph(
let={
"_c": Const(3),
"_m": Const(3),
"_n": Const(361),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(360)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/POLY_ORBIT_HENSEL",
"COMB1/POLY_ORBIT_HENSEL"
] | 78f47d | comb_bell_compute_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 3 | 0.014 | 2026-03-10T06:00:27.749492Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-03-10T06:00:27.763191Z"
} | 043604 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 428,
"completion_tokens": 7365
},
"timestamp": "2026-04-19T01:50:28.903Z",
"answer": 4140
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"st... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
2c23dc | diophantine_sum_product_min_v1_124444284_2944 | Let $S = 111$. Let $P$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 2325625$. Let $r$ be the smallest positive integer $x$ such that $1 \leq x \leq 110$ and $x(S - x) = P$. Let $c$ be the number of positive integers $j$ such that $j \leq m$, where $m$ is the minim... | 95,000 | graphs = [
Graph(
let={
"S": Const(111),
"P": 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(2325625)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | EXTREMUM | sympy | B3 | [
"B3/C3"
] | 9e51bc | diophantine_sum_product_min_v1 | affine_mod | 7 | 0 | [
"B3",
"C3"
] | 2 | 0.028 | 2026-02-08T05:05:18.113259Z | {
"verified": true,
"answer": 95000,
"timestamp": "2026-02-08T05:05:18.140860Z"
} | 30b1e4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 2431
},
"timestamp": "2026-02-11T22:52:17.956Z",
"answer": 95000
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
8d85a5 | antilemma_sum_primes_v1_1125832087_41 | Compute the sum of all prime numbers $n$ such that $2 \leq n \leq 75$. | 712 | graphs = [
Graph(
let={
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(75)), IsPrime(Var("n"))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | SUM_PRIMES | [
"SUM_PRIMES"
] | 83231d | antilemma_sum_primes_v1 | null | 3 | 0 | [
"SUM_PRIMES"
] | 1 | 0.001 | 2026-02-08T02:50:48.160301Z | {
"verified": true,
"answer": 712,
"timestamp": "2026-02-08T02:50:48.161551Z"
} | 7d8033 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 636
},
"timestamp": "2026-02-17T14:50:43.800Z",
"answer": 712
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
3b3a88 | nt_euler_phi_compute_v1_677425708_150 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 2395$ and $\gcd(n, 12) = 1$. Let $B = 32400$. Define $R = \phi(B)$, where $\phi$ is Euler's totient function. Let $S$ be the set of all real solutions $x$ to the equation $x^2 - 64x + A = 0$. Compute the remainder when $R^2 + 10R + \sum S$ is divid... | 43,810 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2395)), Eq(GCD(a=Var("n"), b=Const(12)), Const(1))))),
"n": Const(32400),
"result": EulerPhi(n=Ref("n")),
... | NT | null | COMPUTE | sympy | C4 | [
"C4/VIETA_SUM"
] | bb0541 | nt_euler_phi_compute_v1 | quadratic_mod | 6 | 0 | [
"C4",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T03:06:42.409359Z | {
"verified": true,
"answer": 43810,
"timestamp": "2026-02-08T03:06:42.411453Z"
} | 33aae9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1784
},
"timestamp": "2026-02-08T20:20:09.415Z",
"answer": 43810
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_... | {
"lo": -3.78,
"mid": -1.03,
"hi": 1.58
} | ||
14541f | sequence_lucas_compute_v1_601307018_1714 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 35$ such that $$\left|\left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 35,\ -32a_1b_1 + 16a_1^2 + 16b_1^2 = 16 \right\}\right| \cdot ab^3 + 68a^3b + 17b^4 + 17a^4 + 102a^2b^2 = 134138177.$$ Let $S = L_n$, the $n$-th Lucas number. Find the ... | 32,562 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(68),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_m")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Eq(Sum(Mul(CountOverS... | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"QF_PSD_COUNT/POLY4_COUNT"
] | 84aa99 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT",
"SUM_GEOM"
] | 3 | 0.063 | 2026-03-10T02:27:50.062164Z | {
"verified": true,
"answer": 32562,
"timestamp": "2026-03-10T02:27:50.125026Z"
} | ce91dd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 6425
},
"timestamp": "2026-03-29T03:11:35.549Z",
"answer": 32562
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -2.48,
"mid": 1.07,
"hi": 4.5
} | ||
7a0f84 | algebra_poly_eval_v1_1218484723_1528 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 20$ such that
$$
17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 5640192.
$$
Let $t$ be the number of ordered pairs $(a_1, b_1)$ with $1 \le a_1, b_1 \le 40$ such that
$$
5a_1^2 + C a_1 b_1 + 5b_1^2 = 14580,
$$
where $C = \left| \le... | 47,994 | graphs = [
Graph(
let={
"_c": Const(99313),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Eq(Sum(Mul(Const(17), Pow(Var("a"), Const(4)))... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/POLY4_COUNT/QF_PSD_COUNT",
"POLY4_COUNT/POLY4_COUNT/QF_PSD_COUNT"
] | 8871bd | algebra_poly_eval_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT"
] | 2 | 0.213 | 2026-02-25T03:13:23.755175Z | {
"verified": true,
"answer": 47994,
"timestamp": "2026-02-25T03:13:23.967769Z"
} | f0a914 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 458,
"completion_tokens": 2084
},
"timestamp": "2026-03-10T04:34:30.133Z",
"answer": 47994
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
974707 | modular_product_range_v1_601307018_3246 | Let $S = \{ (a, b) : 1 \le a, b \le 40 \}$ and let $T = \left| \{ (a_1, b_1) : 1 \le a_1, b_1 \le 35,\ 64a_1^3 + 108a_1b_1^2 + 144a_1^2b_1 + 27b_1^3 = 1367631 \} \right|$. Let $k$ be the number of pairs $(a, b) \in S$ such that $ -9a^3 + 27a^2b - 27ab^2 + Tb^3 = -1944 $. Define $R = \prod_{i=k}^{84} i$. Find the remain... | 5,712 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(11497),
"prod": MathProduct(expr=Var("i"), var="i", start=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)),... | NT | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY3_COUNT/POLY3_COUNT"
] | 032cc9 | modular_product_range_v1 | null | 8 | 0 | [
"POLY3_COUNT",
"POLY_ORBIT_HENSEL"
] | 2 | 0.23 | 2026-03-10T03:46:57.390443Z | {
"verified": true,
"answer": 5712,
"timestamp": "2026-03-10T03:46:57.620819Z"
} | ab1f5f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 9571
},
"timestamp": "2026-04-18T23:20:39.567Z",
"answer": 5712
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
7a712e | modular_sum_quadratic_residues_v1_601307018_4834 | Let $p$ be the largest prime number $n$ satisfying $$\left|\left\{ d \mid d > 0,\ d \mid 72,\ \gcd(d, 72/d) = 1,\ d < 72/d \right\}\right| \leq n \leq \min\left\{ |x - y| : x, y > 0,\ xy = 428275 \right\}.$$ Let $R = \frac{p(p - 1)}{4}$. Find the remainder when $44121 \cdot R$ is divided by $69994$. | 15,323 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p1"), condition=And(IsPositive(arg=Var(name='p1')), Exists(var=Var(name='q'), condition=And(Eq(lef... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B3_DIFF/MAX_PRIME_BELOW"
] | bc154a | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"B3_DIFF",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.01 | 2026-03-10T05:31:20.927174Z | {
"verified": true,
"answer": 15323,
"timestamp": "2026-03-10T05:31:20.936980Z"
} | 529f37 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 28010
},
"timestamp": "2026-03-29T13:36:55.182Z",
"answer": 61321
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
},... | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
e31f6a | algebra_quadratic_discriminant_v1_655260480_5052 | Let $m = 4$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 72$, and $\gcd(p, q) = 1$. Let $a = 1$. Let $b$ be the number of positive integers $p_1$ for which there exists a positive integer $q$ such that $p_1 < q$, $p_1 q = 18$, and $\gcd(p_1, q) =... | 100 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COMPUTE | sympy | K3 | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"K3"
] | 2 | 0.023 | 2026-02-08T18:15:50.516000Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T18:15:50.539312Z"
} | c8033c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 2509
},
"timestamp": "2026-02-18T15:40:11.536Z",
"answer": 100
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
957744 | nt_count_phi_equals_v1_349078426_1370 | Let $n = 126$. Consider all pairs of positive integers $(x, y)$ such that $x + y = n$. Let $P$ be the maximum value of $x \cdot y$ over all such pairs. Let $k = 3792$. Determine the number of positive integers $m$ such that $1 \leq m \leq P$ and $\phi(m) = k$. Compute $19$ minus this number. | 18 | graphs = [
Graph(
let={
"_n": Const(126),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B1"
] | 1 | 0.404 | 2026-02-08T13:34:29.189644Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T13:34:29.593744Z"
} | bf0c11 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 4777
},
"timestamp": "2026-02-15T17:59:14.518Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
45d061 | nt_count_coprime_and_v1_151522320_192 | Let $\text{upper} = \sum_{d \mid 3116} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $k_1 = 11$ and $k_2 = 13$. Compute the number of positive integers $n$ such that $1 \le n \le \text{upper}$, $\gcd(n, 11) = 1$, and $\gcd(n, 13) = 1$. | 2,615 | graphs = [
Graph(
let={
"upper": SumOverDivisors(n=Const(value=3116), var='d', expr=EulerPhi(n=Var(name='d'))),
"k1": Const(11),
"k2": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("up... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | nt_count_coprime_and_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.338 | 2026-02-08T03:02:12.003183Z | {
"verified": true,
"answer": 2615,
"timestamp": "2026-02-08T03:02:12.341017Z"
} | fb4221 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1114
},
"timestamp": "2026-02-10T12:30:06.420Z",
"answer": 2615
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
846989 | modular_count_residue_v1_1520064083_8655 | Let $m = 28$. Let $T$ be the set of integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \le a \le 2$, $1 \le b \le 4$, $18 \le t \le 27$, and $t = 3a + 2b + 13$. Let $c$ be the number of elements in $T$. Define
\[
r = \sum_{k=0}^{8} (-1)^k \binom{c}{k}.
\]
Let $S$ be the set of all positive integers $... | 27,226 | graphs = [
Graph(
let={
"upper": Const(37249),
"m": Const(28),
"r": Summation(var="k", start=Const(0), end=Const(8), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | modular_count_residue_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 1.329 | 2026-02-08T10:17:24.952555Z | {
"verified": true,
"answer": 27226,
"timestamp": "2026-02-08T10:17:26.281761Z"
} | f3d31d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 2504
},
"timestamp": "2026-02-24T11:55:24.080Z",
"answer": 27226
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
fab66b | algebra_quadratic_discriminant_v1_1520064083_1654 | Let $a = 1$, $b = 16$, and let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1365154791000$, $\gcd(p, q) = 1$, and $p < q$. Let $D = b^2 - 4ac$. Define $\alpha = 2$ if $D > 0$, $\alpha = 1$ if $D = 0$, and $\alpha = 0$ otherwise. Compute $|\alpha|$. | 1 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1),
"b": Const(16),
"c": 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(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.094 | 2026-02-08T04:11:05.741829Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T04:11:05.835863Z"
} | 062aba | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 2484
},
"timestamp": "2026-02-10T15:48:13.806Z",
"answer": 1
},
{
"id"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4cfda1 | comb_catalan_compute_v1_677425708_1908 | Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = s$, where $s$ is the number of ordered pairs $(x_1, x_2)$ of positive odd integers satisfying $x_1 + x_2 = 18$.
Let $C_n$ denote the $n$-th Catalan number.
Compute $84681 - C_n$. | 67,885 | graphs = [
Graph(
let={
"_n": Const(18),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(na... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/COMB1"
] | b2c526 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T04:37:55.525592Z | {
"verified": true,
"answer": 67885,
"timestamp": "2026-02-08T04:37:55.529178Z"
} | 5e8eeb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 951
},
"timestamp": "2026-02-10T02:56:49.615Z",
"answer": 67885
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
1b3e24 | modular_sum_quadratic_residues_v1_2051736721_1912 | Let $p$ be the sum of all real solutions $x$ to the equation $x^2 - 229x - 28302 = 0$. Define $\text{result} = \frac{p(p-1)}{4}$. Compute the remainder when $44121 \cdot \text{result}$ is divided by $50791$. | 43,055 | graphs = [
Graph(
let={
"_n": Const(4),
"p": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-229), Var("x")), Const(-28302)), Const(0)))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
"Q": Mod... | NT | null | SUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T16:19:10.799520Z | {
"verified": true,
"answer": 43055,
"timestamp": "2026-02-08T16:19:10.801038Z"
} | 215fc4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 982
},
"timestamp": "2026-02-17T02:33:26.750Z",
"answer": 43055
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
887ec2 | nt_count_primes_v1_124444284_9154 | Let $P$ be the number of ordered pairs $(p, q)$ of positive integers such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of prime numbers $n$ such that $P \leq n \leq 65536$. Compute the remainder when $60551 \cdot |S|$ is divided by $80064$. | 48,034 | graphs = [
Graph(
let={
"_n": Const(80064),
"upper": Const(65536),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.832 | 2026-02-08T12:15:01.226478Z | {
"verified": true,
"answer": 48034,
"timestamp": "2026-02-08T12:15:03.058892Z"
} | ac433b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 2406
},
"timestamp": "2026-02-14T23:28:36.964Z",
"answer": 48034
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3e01d0_n | alg_telescope_v1_1218484723_3861 | A robot moves along a number line, starting at 0. On step $k$ (for $k = 0$ to $1478$), it jumps forward by $(k+1)^2 - k^2$ units. After completing all jumps, it reports its total position modulo the number of distinct signal strengths $t$ in the range $[7, 9928]$ that can be generated using combinations of 3-unit and 4... | 5,921 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_telescope_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.081 | 2026-02-25T05:30:23.480997Z | null | d449f5 | 3e01d0 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 8889
},
"timestamp": "2026-03-30T20:42:59.106Z",
"answer": 5921
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
f52eff | comb_count_permutations_fixed_v1_1218484723_4514 | Let $D_n$ denote the number of derangements of $n$ elements. Let $n = \sum_{k=0}^{2} 2^k$. Compute $77777 - \binom{n}{2} D_{n-2}$. | 76,853 | graphs = [
Graph(
let={
"n": Summation(var="k1", start=Const(0), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"_c": Const(77777),
... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.002 | 2026-02-25T06:11:07.334310Z | {
"verified": true,
"answer": 76853,
"timestamp": "2026-02-25T06:11:07.335961Z"
} | 32d295 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 684
},
"timestamp": "2026-03-29T15:59:27.422Z",
"answer": 76853
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
33add5 | comb_count_permutations_fixed_v1_1918700295_2512 | Let $n = 9$ and let $k$ be the largest prime number satisfying $2 \leq k \leq 5$. Compute the remainder when $64837 \cdot \binom{n}{k} \cdot !(n - k)$ is divided by $87340$, where $!m$ denotes the number of derangements of $m$ elements. | 72,218 | graphs = [
Graph(
let={
"n": Const(9),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T07:56:19.929776Z | {
"verified": true,
"answer": 72218,
"timestamp": "2026-02-08T07:56:19.932434Z"
} | dd6f1a | 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": 2576
},
"timestamp": "2026-02-13T13:49:11.885Z",
"answer": 72218
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9af9b8 | sequence_lucas_compute_v1_1918700295_3751 | Let $c = 6$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = c$. Let $m$ be the maximum value of $xy$ over all such pairs. Let $Q$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $n$ be the minimum value of $x + y$ over all such pairs. Defin... | 24,476 | graphs = [
Graph(
let={
"_c": Const(6),
"_m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_c")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3/SUM_ARITHMETIC"
] | 314b38 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"B1",
"B3",
"SUM_ARITHMETIC"
] | 3 | 0.002 | 2026-02-08T08:51:18.744521Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T08:51:18.746541Z"
} | b63fce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 803
},
"timestamp": "2026-02-13T22:40:26.312Z",
"answer": 24476
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
8314cf | antilemma_k2_v1_898971024_1382 | Let $m = 320$ and let $n = \sum_{d \mid m} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $r_1$ and $r_2$ be the roots of the quadratic equation $x^2 - 320x + 17319 = 0$. Define $s = r_1 + r_2$. Compute
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{s}{k} \right\rfloor.
$$Find the remainder when $34431x... | 78,308 | graphs = [
Graph(
let={
"_m": Const(320),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverSet(set=SolutionsSet(var=Var("x1"), condition... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/VIETA_SUM/K2",
"K2"
] | 871991 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"K3",
"VIETA_SUM"
] | 3 | 0.003 | 2026-02-08T16:05:52.056693Z | {
"verified": true,
"answer": 78308,
"timestamp": "2026-02-08T16:05:52.059398Z"
} | 89edc2 | 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": 2643
},
"timestamp": "2026-02-16T20:24:13.376Z",
"answer": 78308
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a5a087 | geo_count_lattice_rect_v1_1520064083_7916 | Let $a = 60$ and $b = 133$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries. Let $m$ be the smallest positive integer such that the $m$th Fibonacci number is divisible by the sum of this lattice point count and $2$. Find $m$. | 888 | graphs = [
Graph(
let={
"a": Const(60),
"b": Const(133),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T09:22:39.657754Z | {
"verified": true,
"answer": 888,
"timestamp": "2026-02-08T09:22:39.659600Z"
} | c2b184 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 7408
},
"timestamp": "2026-02-24T11:17:26.623Z",
"answer": 888
},
{
"id... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
2020a6 | nt_count_divisible_and_v1_784195855_9731 | Let $x$ and $y$ be positive integers such that $xy = 36$. Define $d_2$ to be the minimum value of $x + y$ over all such pairs. Let $N$ be the number of positive integers $n$ with $1 \leq n \leq 252660$ such that $n$ is divisible by both $10$ and $d_2$. Compute $N$. | 4,211 | graphs = [
Graph(
let={
"_n": Const(36),
"upper": Const(252660),
"d1": Const(10),
"d2": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var(... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 18.315 | 2026-02-08T17:00:44.156822Z | {
"verified": true,
"answer": 4211,
"timestamp": "2026-02-08T17:01:02.471689Z"
} | cb59c2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 449
},
"timestamp": "2026-02-16T08:41:53.063Z",
"answer": 4211
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
d02048 | geo_count_lattice_triangle_v1_1520064083_9579 | Let $A$ be $120$ times the number of positive integers $t$ such that there exist integers $a$ and $b$ with $1 \le a \le 13$, $1 \le b \le 96$, $5 \le t \le 231$, and $t = 3a + 2b$. Let $B = 80 \cdot 100$. Define $\text{area}_2 = |A - B|$. Let $P$ be the sum of the following three greatest common divisors: $\gcd(120, 10... | 9,486 | graphs = [
Graph(
let={
"_m": Const(100),
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Cons... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.009 | 2026-02-08T10:53:08.020469Z | {
"verified": true,
"answer": 9486,
"timestamp": "2026-02-08T10:53:08.029221Z"
} | 25f9c1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 5694
},
"timestamp": "2026-02-14T09:24:38.471Z",
"answer": 9486
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
837b8a | modular_modexp_compute_v1_601307018_9600 | Let $e$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 915981$. Compute $5^e \bmod 45753$. | 15,256 | graphs = [
Graph(
let={
"a": Const(5),
"e": 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(915981)))), expr=Abs(arg=Sub(left=Var(name='x... | NT | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"B3_DIFF"
] | b47ea7 | modular_modexp_compute_v1 | null | 3 | 0 | [
"B3_DIFF",
"POLY_ORBIT_HENSEL"
] | 2 | 12.455 | 2026-03-10T10:02:32.877042Z | {
"verified": true,
"answer": 15256,
"timestamp": "2026-03-10T10:02:45.332432Z"
} | 2a12b2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 4172
},
"timestamp": "2026-04-19T11:36:57.686Z",
"answer": 15256
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
96c975 | algebra_quadratic_discriminant_v1_717093673_1660 | Let $a = 3$, $b = 5$, and $c = 8$. Let $M$ be the maximum value of $xy$ over all positive integers $x$ and $y$ such that $x + y = 4$. Compute the remainder when $44121 \cdot (b^2 - a \cdot M \cdot c)$ is divided by 97486. | 84,447 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(3),
"b": Const(5),
"c": Const(8),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(n... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"B1"
] | 1 | 0.005 | 2026-02-08T16:14:20.222475Z | {
"verified": true,
"answer": 84447,
"timestamp": "2026-02-08T16:14:20.227439Z"
} | 7f9637 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 933
},
"timestamp": "2026-02-16T23:18:37.891Z",
"answer": 84447
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c64c56 | nt_sum_over_divisible_v1_677425708_3598 | Let $N = 44121$ and $U = 41616$. Let $D$ be the smallest divisor of $70362495139$ that is at least $2$. Define $T$ to be the sum of all positive integers $n$ such that $n \leq U$ and $n$ is divisible by $D$. Compute the value of $N \cdot T \mod 71987$. | 4,175 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(41616),
"divisor": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(70362495139))))),
"result": SumOverSet(set=SolutionsSet(var=... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.327 | 2026-02-08T05:51:19.494229Z | {
"verified": true,
"answer": 4175,
"timestamp": "2026-02-08T05:51:20.820885Z"
} | a32d7c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 4936
},
"timestamp": "2026-02-12T15:18:00.739Z",
"answer": 4175
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5edd18 | comb_count_derangements_v1_601307018_9091 | Let $n = \sum_{k=0}^{2} 2^k$. Compute the number of derangements $D_n$ of $n$ elements, and let $M = D_n$. Find the remainder when $44121M$ is divided by $79139$. | 49,747 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(0), end=Ref("_n"), expr=Pow(Const(2), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(79139)),
},
... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 3 | 0 | [
"POLY_ORBIT_LEGENDRE",
"SUM_GEOM"
] | 2 | 0.183 | 2026-03-10T09:29:17.535542Z | {
"verified": true,
"answer": 49747,
"timestamp": "2026-03-10T09:29:17.718396Z"
} | 8425da | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 1781
},
"timestamp": "2026-04-19T10:39:35.544Z",
"answer": 49747
},
{
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
8667d5 | algebra_quadratic_discriminant_v1_124444284_2889 | Let $n = 400$. Define $c$ to be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = n$. Compute $(-2)^2 - 4(-2)(c)$. | 324 | graphs = [
Graph(
let={
"_n": Const(400),
"a": Const(-2),
"b": Const(-2),
"c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var... | NT | null | COMPUTE | sympy | L3B | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B3",
"L3B"
] | 2 | 0.014 | 2026-02-08T05:03:40.916167Z | {
"verified": true,
"answer": 324,
"timestamp": "2026-02-08T05:03:40.929879Z"
} | 0146f1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 267
},
"timestamp": "2026-02-11T22:12:45.016Z",
"answer": 324
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
5b006e | diophantine_product_count_v1_2051736721_4325 | Let $k$ be the number of integers $t$ such that $9 \leq t \leq 194$ and there exist positive integers $a \leq 20$ and $b \leq 22$ for which $t = 2a + 7b$. Let $N = 76$. Compute the number of positive integers $x$ such that $1 \leq x \leq N$, $x$ divides $k$, and $\frac{k}{x} \leq N$. | 14 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=20)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.023 | 2026-02-08T17:54:55.785983Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T17:54:55.809351Z"
} | 4f8695 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 3479
},
"timestamp": "2026-02-18T10:07:03.053Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
61c389 | nt_sum_over_divisible_v1_1742523217_5409 | Let $d$ be the smallest divisor of 17947 that is at least 2. Compute the sum of all positive integers $n \leq 12769$ such that $d$ divides $n$. Then, find the remainder when this sum is multiplied by 71507 and divided by 98826. | 45,829 | graphs = [
Graph(
let={
"upper": Const(12769),
"divisor": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(17947))))),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), ... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.41 | 2026-02-08T10:58:59.927850Z | {
"verified": true,
"answer": 45829,
"timestamp": "2026-02-08T10:59:00.337904Z"
} | 56611b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 3351
},
"timestamp": "2026-02-14T09:43:43.998Z",
"answer": 45829
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} |
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