id stringlengths 30 68 | messages listlengths 2 2 | category stringclasses 113
values | model stringclasses 1
value | text stringlengths 59 13.6k | token_count int64 18 7.69k |
|---|---|---|---|---|---|
landformgenerationcounting_diff_2_35_241fe9e539_YzOa02 | [
{
"content": "You are given two arrays `H` and `C`, each of length 5:\nH: H[0]=2 H[1]=3 H[2]=3 H[3]=5 H[4]=2\nC: C[0]=4 C[1]=2 C[2]=2 C[3]=1 C[4]=4\n\nA permutation `p` of the indices `0` to `4` (i.e., `p[0], p[1], ..., p[4]`) is considered **valid** if and only if the following condition holds for every index ... | landformgenerationcounting | o4-mini-high | You are given two arrays `H` and `C`, each of length 5:
H: H[0]=2 H[1]=3 H[2]=3 H[3]=5 H[4]=2
C: C[0]=4 C[1]=2 C[2]=2 C[3]=1 C[4]=4
A permutation `p` of the indices `0` to `4` (i.e., `p[0], p[1], ..., p[4]`) is considered **valid** if and only if the following condition holds for every index `i` from `0` to `4`: there... | 576 |
gridbfs_diff_2_4_62d52d4c4f_N0kWpG | [
{
"content": "You are given a 5 × 6 grid. Each cell contains `0`, `1`, or `X`. For each cell, compute its **shortest distance** to any cell containing `1`, where distance is defined as the minimum number of steps required to move from one cell to another under the following rules:\n1. You may move **up**, **dow... | gridbfs | o4-mini-high | You are given a 5 × 6 grid. Each cell contains `0`, `1`, or `X`. For each cell, compute its **shortest distance** to any cell containing `1`, where distance is defined as the minimum number of steps required to move from one cell to another under the following rules:
1. You may move **up**, **down**, **left**, or **rig... | 650 |
gridbfs_diff_1_13_de4d0c2c03_6muarb | [
{
"content": "You are given a 3 × 2 grid. Each cell contains `0`, `1`, or `X`. For each cell, compute its **shortest distance** to any cell containing `1`, where distance is defined as the minimum number of steps required to move from one cell to another under the following rules:\n1. You may move **up**, **dow... | gridbfs | o4-mini-high | You are given a 3 × 2 grid. Each cell contains `0`, `1`, or `X`. For each cell, compute its **shortest distance** to any cell containing `1`, where distance is defined as the minimum number of steps required to move from one cell to another under the following rules:
1. You may move **up**, **down**, **left**, or **rig... | 267 |
multiplication_diff_9_25_aaeb7a4275_Lb7Zoq | [
{
"content": "What is the multiplication of 3622576170 and 42398663501?",
"role": "user"
},
{
"content": "We use high-precision multiplication by splitting one factor into manageable parts (e.g. 42 398 663 501 = 42 398 663×1 000 + 501), multiply each part by 3 622 576 170, and add the partial produc... | multiplication | o4-mini-high | What is the multiplication of 3622576170 and 42398663501?
We use high-precision multiplication by splitting one factor into manageable parts (e.g. 42 398 663 501 = 42 398 663×1 000 + 501), multiply each part by 3 622 576 170, and add the partial products.
Therefore the answer is: 153592388038571371170 | 93 |
gridbfs_diff_3_10_c4ede2e7f5_ScwFQx | [
{
"content": "You are given a 6 × 6 grid. Each cell contains `0`, `1`, or `X`. For each cell, compute its **shortest distance** to any cell containing `1`, where distance is defined as the minimum number of steps required to move from one cell to another under the following rules:\n1. You may move **up**, **dow... | gridbfs | o4-mini-high | You are given a 6 × 6 grid. Each cell contains `0`, `1`, or `X`. For each cell, compute its **shortest distance** to any cell containing `1`, where distance is defined as the minimum number of steps required to move from one cell to another under the following rules:
1. You may move **up**, **down**, **left**, or **rig... | 422 |
tournament_longestpath_diff_7_22_33d2e66901_phTbpr | [
{
"content": "You are given a **directed graph** with 10 vertices labeled from `0` to `9`. The graph contains the following directed edges. Each edge is represented as a tuple `(s, t)`, meaning there is a directed edge **from vertex `s` to vertex `t`**:\n(0, 1)\n(0, 2)\n(0, 4)\n(0, 5)\n(0, 6)\n(0, 7)\n(0, 8)\n(... | tournament | o4-mini-high | You are given a **directed graph** with 10 vertices labeled from `0` to `9`. The graph contains the following directed edges. Each edge is represented as a tuple `(s, t)`, meaning there is a directed edge **from vertex `s` to vertex `t`**:
(0, 1)
(0, 2)
(0, 4)
(0, 5)
(0, 6)
(0, 7)
(0, 8)
(0, 9)
(1, 3)
(1, 4)
(1, 5)
(1,... | 595 |
discretelogarithm_diff_9_23_fa80b50f81_4bGXtR | [
{
"content": "Please find the **smallest** non-negative integer **y** such that **(23^y) MOD 27 = 7 MOD 27**.\n\n**Output Format:** Your final answer should be a single non-negative integer — the smallest **y** satisfying the equation.",
"role": "user"
},
{
"content": "I’m sorry, but I can’t share ... | discretelogarithm | o4-mini-high | Please find the **smallest** non-negative integer **y** such that **(23^y) MOD 27 = 7 MOD 27**.
**Output Format:** Your final answer should be a single non-negative integer — the smallest **y** satisfying the equation.
. Here’s a concise solution:
Compute 23^y mod 27 for y = 0, 1, 2, … until it equals 7. You find:
... | 208 |
bridge_diff_6_47_03dd0a6344_OuNOb7 | [
{
"content": "You are given an **undirected graph** with 10 vertices labeled from 0 to 9. The graph contains the following undirected edges:\n(4, 6)\n(7, 8)\n(0, 7)\n(1, 3)\n(3, 7)\n(2, 4)\n(0, 8)\n(8, 9)\n(2, 5)\n(0, 3)\n(4, 5)\n\nYour task is to find all edges (u, v) such that removing the edge (u, v) from th... | bridge | o4-mini-high | You are given an **undirected graph** with 10 vertices labeled from 0 to 9. The graph contains the following undirected edges:
(4, 6)
(7, 8)
(0, 7)
(1, 3)
(3, 7)
(2, 4)
(0, 8)
(8, 9)
(2, 5)
(0, 3)
(4, 5)
Your task is to find all edges (u, v) such that removing the edge (u, v) from the graph would disconnect vertices u... | 361 |
addmultiple_divisible_counting_diff_8_12_9b698809df_eowDMo | [
{
"content": "Please compute the number of pairs (a, b) such that:\n- 1 ≤ a < b ≤ 112\n- a × b is divisible by a + b\n\n**Output Format:** Your final answer should be a single integer — the number of such pairs (a, b).",
"role": "user"
},
{
"content": "Here is a concise solution outline (omitting th... | addmultiple | o4-mini-high | Please compute the number of pairs (a, b) such that:
- 1 ≤ a < b ≤ 112
- a × b is divisible by a + b
**Output Format:** Your final answer should be a single integer — the number of such pairs (a, b).
Here is a concise solution outline (omitting the full internal search details):
We look for 1 ≤ a < b ≤ 112 with (a·b)... | 245 |
stoneintervalsgame_diff_8_81_75158d1945_hLqyBP | [
{
"content": "There are 12 piles of stones. Initially, the i-th pile contains A[i] stones, given as: A[0]=0 A[1]=0 A[2]=0 A[3]=0 A[4]=0 A[5]=0 A[6]=16 A[7]=0 A[8]=0 A[9]=5 A[10]=0 A[11]=0\nAlice and Bob play a game with the following rules:\n- Alice goes first. They alternate turns.\n- On each turn, a player se... | stoneintervalsgame | o4-mini-high | There are 12 piles of stones. Initially, the i-th pile contains A[i] stones, given as: A[0]=0 A[1]=0 A[2]=0 A[3]=0 A[4]=0 A[5]=0 A[6]=16 A[7]=0 A[8]=0 A[9]=5 A[10]=0 A[11]=0
Alice and Bob play a game with the following rules:
- Alice goes first. They alternate turns.
- On each turn, a player selects a pile `i` such tha... | 311 |
mostcomponenttreeremovingtwopaths_diff_7_52_c0c7fdd88b_TXY2UJ | [
{
"content": "You are given a **tree** with 12 vertices labeled from 1 to 12, where vertex 1 is the **root**. The tree contains the following 11 undirected edges:\n(6, 12)\n(3, 10)\n(7, 10)\n(3, 11)\n(3, 9)\n(1, 12)\n(2, 4)\n(2, 3)\n(6, 8)\n(5, 10)\n(7, 12)\n\nYour task is to choose two paths (each from any ver... | mostcomponenttreeremovingtwopaths | o4-mini-high | You are given a **tree** with 12 vertices labeled from 1 to 12, where vertex 1 is the **root**. The tree contains the following 11 undirected edges:
(6, 12)
(3, 10)
(7, 10)
(3, 11)
(3, 9)
(1, 12)
(2, 4)
(2, 3)
(6, 8)
(5, 10)
(7, 12)
Your task is to choose two paths (each from any vertex to any vertex; a path could be ... | 629 |
setsplitting_diff_4_24_8c5465cc1c_Eqle3G | [
{
"content": "Define the full set `S` as all 7 integers from `0` to `6`.\n\nYour task is to partition `S` into two **disjoint subsets** `S1` and `S2` such that:\n- `S1 ∪ S2 = S` and `S1 ∩ S2 = ∅`\n- For each of the following 15 subsets (each a subset of `S`), the subset is **not fully contained** in either `S1`... | setsplitting | o4-mini-high | Define the full set `S` as all 7 integers from `0` to `6`.
Your task is to partition `S` into two **disjoint subsets** `S1` and `S2` such that:
- `S1 ∪ S2 = S` and `S1 ∩ S2 = ∅`
- For each of the following 15 subsets (each a subset of `S`), the subset is **not fully contained** in either `S1` or `S2`. That is, each su... | 651 |
stoneintervalsgame_diff_1_52_3a16ebc38e_1mUYpP | [
{
"content": "There are 4 piles of stones. Initially, the i-th pile contains A[i] stones, given as: A[0]=0 A[1]=5 A[2]=2 A[3]=0\nAlice and Bob play a game with the following rules:\n- Alice goes first. They alternate turns.\n- On each turn, a player selects a pile `i` such that **at least one of its adjacent pi... | stoneintervalsgame | o4-mini-high | There are 4 piles of stones. Initially, the i-th pile contains A[i] stones, given as: A[0]=0 A[1]=5 A[2]=2 A[3]=0
Alice and Bob play a game with the following rules:
- Alice goes first. They alternate turns.
- On each turn, a player selects a pile `i` such that **at least one of its adjacent piles** (`i - 1` or `i + 1`... | 408 |
tournament_longestpath_diff_1_35_1899aff341_tapMM2 | [
{
"content": "You are given a **directed graph** with 4 vertices labeled from `0` to `3`. The graph contains the following directed edges. Each edge is represented as a tuple `(s, t)`, meaning there is a directed edge **from vertex `s` to vertex `t`**:\n(0, 3)\n(1, 0)\n(1, 2)\n(1, 3)\n(2, 0)\n(2, 3)\n\nIt is gu... | tournament | o4-mini-high | You are given a **directed graph** with 4 vertices labeled from `0` to `3`. The graph contains the following directed edges. Each edge is represented as a tuple `(s, t)`, meaning there is a directed edge **from vertex `s` to vertex `t`**:
(0, 3)
(1, 0)
(1, 2)
(1, 3)
(2, 0)
(2, 3)
It is guaranteed that there is **exact... | 222 |
knightsandknaves_diff_4_38_c3488ff095_c32MyW | [
{
"content": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: James, Matthew, Mason, Amelia, Avery, Alexander, and Jacob. James noted, \"Avery is a knave and Mason is a knave\". Matthew commented, \"Avery is not a knave... | knightsandknaves | o4-mini-high | A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: James, Matthew, Mason, Amelia, Avery, Alexander, and Jacob. James noted, "Avery is a knave and Mason is a knave". Matthew commented, "Avery is not a knave". "Alexander is a knave ... | 362 |
jugpuzzle_diff_0_37_b1f49d7284_CgmRgR | [
{
"content": "You are given 3 jugs (initially empty) with the following capacities:\nJug 0's capacity: 20 liters\nJug 1's capacity: 29 liters\nJug 2's capacity: 8 liters\n\nPlease fill a jug (you pick the one) with exactly 16 liters of water. You may perform the following actions:\n- `Fill i` — Fill jug `i` to ... | jugpuzzle | o4-mini-high | You are given 3 jugs (initially empty) with the following capacities:
Jug 0's capacity: 20 liters
Jug 1's capacity: 29 liters
Jug 2's capacity: 8 liters
Please fill a jug (you pick the one) with exactly 16 liters of water. You may perform the following actions:
- `Fill i` — Fill jug `i` to its full capacity.
- `Empty ... | 243 |
palindromicsubstringnumbercounting_diff_3_60_f20d83cc44_nzNkUi | [
{
"content": "We treat every positive integer as a string of digits (without leading zeros). A number is called a `good number` if it contains at least one palindromic substring of length **greater than 1**.\n\nFor example:\n- 101 is a good number because it contains the substring \"101\",\n- 110 is a good numb... | palindromicsubstringnumbercounting | o4-mini-high | We treat every positive integer as a string of digits (without leading zeros). A number is called a `good number` if it contains at least one palindromic substring of length **greater than 1**.
For example:
- 101 is a good number because it contains the substring "101",
- 110 is a good number because it contains the s... | 253 |
fireworkshow_diff_8_122_0137edb964_shZuVo | [
{
"content": "You are given a **tree** with 11 vertices labeled from `1` to `11`, where vertex `1` is the **root**. Each vertex (except the root) has a parent `p`, and the edge connecting the vertex to its parent has length `w`. The list of (parent, weight) pairs for each non-root vertex is given as:\nVertex 2:... | fireworkshow | o4-mini-high | You are given a **tree** with 11 vertices labeled from `1` to `11`, where vertex `1` is the **root**. Each vertex (except the root) has a parent `p`, and the edge connecting the vertex to its parent has length `w`. The list of (parent, weight) pairs for each non-root vertex is given as:
Vertex 2: (1, 10)
Vertex 3: (2, ... | 548 |
minimumintervalcoverage_diff_0_63_92be382806_HaeHxU | [
{
"content": "You are given 3 intervals within [1, 3]. Each interval is defined as [L[i], R[i]] with an associated cost C[i]. The intervals are provided as:\nL[1]=1 R[1]=3 C[1]=2\nL[2]=1 R[2]=1 C[2]=2\nL[3]=1 R[3]=2 C[3]=2\n\nYou can select each interval any number of times (including 0). For each point i in [1... | minimumintervalcoverage | o4-mini-high | You are given 3 intervals within [1, 3]. Each interval is defined as [L[i], R[i]] with an associated cost C[i]. The intervals are provided as:
L[1]=1 R[1]=3 C[1]=2
L[2]=1 R[2]=1 C[2]=2
L[3]=1 R[3]=2 C[3]=2
You can select each interval any number of times (including 0). For each point i in [1, 3], you must ensure it is... | 279 |
maze_diff_2_22_c811727e62_LmDs7m | [
{
"content": "You are given a 6×6 grid representing a maze. Each cell in the grid is either a wall (`#`) or an open space (`.`). The maze is provided in the following format:\n.#..##\n......\n#.....\n#...#.\n......\n......\n\nYour task is to find the **shortest path** from the top-left corner `(0, 0)` to the bo... | maze | o4-mini-high | You are given a 6×6 grid representing a maze. Each cell in the grid is either a wall (`#`) or an open space (`.`). The maze is provided in the following format:
.#..##
......
#.....
#...#.
......
......
Your task is to find the **shortest path** from the top-left corner `(0, 0)` to the bottom-right corner `(5, 5)`.
Yo... | 243 |
las_diff_2_85_2d388a6611_rotX07 | [
{
"content": "There are 5 people labeled from 1 to 5, and 5 foods also labeled from 1 to 5. The i-th food has C[i] calories, and the array C is: C[1]=4, C[2]=10, C[3]=2, C[4]=6, C[5]=4\n\nEach person chooses one food as follows:\n- Person i (1 ≤ i < 5) can choose either food i or food i+1.\n- Person 5 can choos... | las | o4-mini-high | There are 5 people labeled from 1 to 5, and 5 foods also labeled from 1 to 5. The i-th food has C[i] calories, and the array C is: C[1]=4, C[2]=10, C[3]=2, C[4]=6, C[5]=4
Each person chooses one food as follows:
- Person i (1 ≤ i < 5) can choose either food i or food i+1.
- Person 5 can choose either food 5 or food 1.... | 724 |
bridge_diff_8_95_111fd8eb00_5wGKDt | [
{
"content": "You are given an **undirected graph** with 14 vertices labeled from 0 to 13. The graph contains the following undirected edges:\n(1, 2)\n(1, 12)\n(5, 7)\n(7, 11)\n(6, 9)\n(6, 11)\n(6, 13)\n(4, 11)\n(5, 11)\n(0, 12)\n(0, 2)\n(0, 1)\n(2, 10)\n(2, 12)\n(8, 11)\n(10, 13)\n(3, 6)\n\nYour task is to fin... | bridge | o4-mini-high | You are given an **undirected graph** with 14 vertices labeled from 0 to 13. The graph contains the following undirected edges:
(1, 2)
(1, 12)
(5, 7)
(7, 11)
(6, 9)
(6, 11)
(6, 13)
(4, 11)
(5, 11)
(0, 12)
(0, 2)
(0, 1)
(2, 10)
(2, 12)
(8, 11)
(10, 13)
(3, 6)
Your task is to find all edges (u, v) such that removing the... | 484 |
tree_distanceequaltriad_counting_diff_2_45_a88ff5b4a9_amus4Y | [
{
"content": "You are given a **tree** (i.e., a connected undirected graph with no cycles) with 6 vertices, labeled from `1` to `6`. It contains the following 5 undirected edges:\n5 6\n4 6\n1 2\n3 5\n1 6\n\nPlease compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤... | tree | o4-mini-high | You are given a **tree** (i.e., a connected undirected graph with no cycles) with 6 vertices, labeled from `1` to `6`. It contains the following 5 undirected edges:
5 6
4 6
1 2
3 5
1 6
Please compute the number of three-vertex sets (a triad of vertices A, B, and C such that 1 ≤ A < B < C ≤ 6) for which the **pairwise ... | 599 |
palindromicsubstringnumbercounting_diff_8_106_4045c1feff_9Vd8LD | [
{
"content": "We treat every positive integer as a string of digits (without leading zeros). A number is called a `good number` if it contains at least one palindromic substring of length **greater than 1**.\n\nFor example:\n- 101 is a good number because it contains the substring \"101\",\n- 110 is a good numb... | palindromicsubstringnumbercounting | o4-mini-high | We treat every positive integer as a string of digits (without leading zeros). A number is called a `good number` if it contains at least one palindromic substring of length **greater than 1**.
For example:
- 101 is a good number because it contains the substring "101",
- 110 is a good number because it contains the s... | 594 |
abprogramsimulation_diff_2_12_4001a984ee_zoZCfU | [
{
"content": "A::B is a system with 4 tokens: `A#`, `#A`, `B#` and `#B`.\n\nAn A::B program is a sequence of tokens, e.g., `B# A# #B #A B#`.\n\nTo *compute* a program, we must rewrite neighbor tokens, using the rules (whenever two neighbor tokens have their `#` facing each-other, they must be rewritten accordin... | abprogramsimulation | o4-mini-high | A::B is a system with 4 tokens: `A#`, `#A`, `B#` and `#B`.
An A::B program is a sequence of tokens, e.g., `B# A# #B #A B#`.
To *compute* a program, we must rewrite neighbor tokens, using the rules (whenever two neighbor tokens have their `#` facing each-other, they must be rewritten according to the corresponding rul... | 262 |
abprogramsimulation_diff_4_29_bb7dd2064c_6InxAC | [
{
"content": "A::B is a system with 4 tokens: `A#`, `#A`, `B#` and `#B`.\n\nAn A::B program is a sequence of tokens, e.g., `B# A# #B #A B#`.\n\nTo *compute* a program, we must rewrite neighbor tokens, using the rules (whenever two neighbor tokens have their `#` facing each-other, they must be rewritten accordin... | abprogramsimulation | o4-mini-high | A::B is a system with 4 tokens: `A#`, `#A`, `B#` and `#B`.
An A::B program is a sequence of tokens, e.g., `B# A# #B #A B#`.
To *compute* a program, we must rewrite neighbor tokens, using the rules (whenever two neighbor tokens have their `#` facing each-other, they must be rewritten according to the corresponding rul... | 401 |
mostcomponenttreeremovingtwopaths_diff_2_13_1c3b2883c4_L42DcA | [
{
"content": "You are given a **tree** with 6 vertices labeled from 1 to 6, where vertex 1 is the **root**. The tree contains the following 5 undirected edges:\n(2, 5)\n(5, 6)\n(1, 5)\n(4, 5)\n(3, 5)\n\nYour task is to choose two paths (each from any vertex to any vertex; a path could be just one single vertex)... | mostcomponenttreeremovingtwopaths | o4-mini-high | You are given a **tree** with 6 vertices labeled from 1 to 6, where vertex 1 is the **root**. The tree contains the following 5 undirected edges:
(2, 5)
(5, 6)
(1, 5)
(4, 5)
(3, 5)
Your task is to choose two paths (each from any vertex to any vertex; a path could be just one single vertex) such that:
- The two paths d... | 268 |
axis_kcenter_diff_7_81_fece5610be_BgWhkh | [
{
"content": "You are given 12 points on a line, labeled from 0 to 11. Their positions (from left to right) are: 1 9 10 21 24 28 29 30 34 35 53 60\n\nPlease select a set of 9 distinct points. Try your best to minimize the total distance from all points to their nearest selected point (the distance is the absolu... | axis | o4-mini-high | You are given 12 points on a line, labeled from 0 to 11. Their positions (from left to right) are: 1 9 10 21 24 28 29 30 34 35 53 60
Please select a set of 9 distinct points. Try your best to minimize the total distance from all points to their nearest selected point (the distance is the absolute difference between po... | 178 |
polynomialinterpolation_diff_4_43_c43aeb99a5_Ayn4uC | [
{
"content": "You are given a polynomial of degree 6 in the form: f(x) = a_0 * x^0 + a_1 * x^1 + ... + a_6 * x^6, where the coefficients `a_0, a_1, ..., a_6` are integers.\n\nIt is known that the polynomial passes through the following 7 points: \nf(-4) = 10222\nf(0) = -2\nf(2) = 334\nf(-5) = 40703\nf(-2) = 11... | polynomialinterpolation | o4-mini-high | You are given a polynomial of degree 6 in the form: f(x) = a_0 * x^0 + a_1 * x^1 + ... + a_6 * x^6, where the coefficients `a_0, a_1, ..., a_6` are integers.
It is known that the polynomial passes through the following 7 points:
f(-4) = 10222
f(0) = -2
f(2) = 334
f(-5) = 40703
f(-2) = 110
f(4) = 14990
f(1) = 17
Ple... | 423 |
clearsymmetry_diff_8_35_2a034cb643_Ecy9JH | [
{
"content": "Consider some square matrix A with side n consisting of zeros and ones. There are n rows numbered from 1 to n from top to bottom and n columns numbered from 1 to n from left to right in this matrix. We'll denote the element of the matrix which is located at the intersection of the i-row and the j-... | clearsymmetry | o4-mini-high | Consider some square matrix A with side n consisting of zeros and ones. There are n rows numbered from 1 to n from top to bottom and n columns numbered from 1 to n from left to right in this matrix. We'll denote the element of the matrix which is located at the intersection of the i-row and the j-th column as A(i, j).
... | 514 |
setsplitting_diff_3_8_08638245a3_iFFKz5 | [
{
"content": "Define the full set `S` as all 6 integers from `0` to `5`.\n\nYour task is to partition `S` into two **disjoint subsets** `S1` and `S2` such that:\n- `S1 ∪ S2 = S` and `S1 ∩ S2 = ∅`\n- For each of the following 7 subsets (each a subset of `S`), the subset is **not fully contained** in either `S1` ... | setsplitting | o4-mini-high | Define the full set `S` as all 6 integers from `0` to `5`.
Your task is to partition `S` into two **disjoint subsets** `S1` and `S2` such that:
- `S1 ∪ S2 = S` and `S1 ∩ S2 = ∅`
- For each of the following 7 subsets (each a subset of `S`), the subset is **not fully contained** in either `S1` or `S2`. That is, each sub... | 490 |
integral_diff_8_15_82e09dee14_5Aprux | [
{
"content": "You are given the derivative of a function: F'(x) = 1 + sqrt(3)/(4*(-x)**(3/2))\n\nYour task is to find **an antiderivative** F(x) such that its derivative is equal to the given expression.\n\n**Output Format:** Your answer should be the expression for F(x), written in **SymPy syntax**. Do not omi... | integral | o4-mini-high | You are given the derivative of a function: F'(x) = 1 + sqrt(3)/(4*(-x)**(3/2))
Your task is to find **an antiderivative** F(x) such that its derivative is equal to the given expression.
**Output Format:** Your answer should be the expression for F(x), written in **SymPy syntax**. Do not omit any symbols (e.g., alway... | 247 |
gridcoloringcounting_diff_0_14_766c74df8d_4OvKkj | [
{
"content": "You are given a grid of size 2 × 3. You may color some cells (and leave others uncolored) using 1 colors labeled from 0 to 0, such that:\n1. No two different colors appear in the same row or the same column.\n2. Color `i` is used exactly X[i] times. The array X is given as: X[0]=6\n\nPlease comput... | gridcoloringcounting | o4-mini-high | You are given a grid of size 2 × 3. You may color some cells (and leave others uncolored) using 1 colors labeled from 0 to 0, such that:
1. No two different colors appear in the same row or the same column.
2. Color `i` is used exactly X[i] times. The array X is given as: X[0]=6
Please compute the number of valid colo... | 201 |
pipelinearrangement_diff_5_51_8b7cda0f73_64CtS4 | [
{
"content": "You need to process 8 products labeled from `0` to `7`. Each product must go through **two machines**, A and B, **in order**.\n\nThe processing times for each product on machines A and B are given as:\nA[0]=5, B[0]=8\nA[1]=4, B[1]=1\nA[2]=2, B[2]=3\nA[3]=2, B[3]=3\nA[4]=6, B[4]=1\nA[5]=5, B[5]=5\n... | pipelinearrangement | o4-mini-high | You need to process 8 products labeled from `0` to `7`. Each product must go through **two machines**, A and B, **in order**.
The processing times for each product on machines A and B are given as:
A[0]=5, B[0]=8
A[1]=4, B[1]=1
A[2]=2, B[2]=3
A[3]=2, B[3]=3
A[4]=6, B[4]=1
A[5]=5, B[5]=5
A[6]=5, B[6]=3
A[7]=6, B[7]=8
... | 752 |
fireworkshow_diff_2_63_82a75dc606_FVfzf8 | [
{
"content": "You are given a **tree** with 5 vertices labeled from `1` to `5`, where vertex `1` is the **root**. Each vertex (except the root) has a parent `p`, and the edge connecting the vertex to its parent has length `w`. The list of (parent, weight) pairs for each non-root vertex is given as:\nVertex 2: (... | fireworkshow | o4-mini-high | You are given a **tree** with 5 vertices labeled from `1` to `5`, where vertex `1` is the **root**. Each vertex (except the root) has a parent `p`, and the edge connecting the vertex to its parent has length `w`. The list of (parent, weight) pairs for each non-root vertex is given as:
Vertex 2: (1, 4)
Vertex 3: (2, 3)
... | 423 |
axis_kcenter_diff_8_118_0d3c28537f_DhsFH8 | [
{
"content": "You are given 14 points on a line, labeled from 0 to 13. Their positions (from left to right) are: 1 2 12 23 31 32 37 38 39 42 46 56 60 64\n\nPlease select a set of 12 distinct points. Try your best to minimize the total distance from all points to their nearest selected point (the distance is the... | axis | o4-mini-high | You are given 14 points on a line, labeled from 0 to 13. Their positions (from left to right) are: 1 2 12 23 31 32 37 38 39 42 46 56 60 64
Please select a set of 12 distinct points. Try your best to minimize the total distance from all points to their nearest selected point (the distance is the absolute difference bet... | 395 |
tournament_longestpath_diff_5_80_3c99a02a6f_HVDNMb | [
{
"content": "You are given a **directed graph** with 8 vertices labeled from `0` to `7`. The graph contains the following directed edges. Each edge is represented as a tuple `(s, t)`, meaning there is a directed edge **from vertex `s` to vertex `t`**:\n(0, 1)\n(0, 3)\n(0, 5)\n(0, 6)\n(1, 4)\n(1, 5)\n(1, 6)\n(1... | tournament | o4-mini-high | You are given a **directed graph** with 8 vertices labeled from `0` to `7`. The graph contains the following directed edges. Each edge is represented as a tuple `(s, t)`, meaning there is a directed edge **from vertex `s` to vertex `t`**:
(0, 1)
(0, 3)
(0, 5)
(0, 6)
(1, 4)
(1, 5)
(1, 6)
(1, 7)
(2, 0)
(2, 1)
(2, 3)
(2, ... | 545 |
sat_diff_5_33_7ff2139c55_WOqy9Q | [
{
"content": "There are 8 boolean (0/1) values x[0], x[1], ..., x[7]. Each of the following 21 expressions (`|` means OR, `!` means NOT) must equal 1:\n(!x[4]) | (x[5])\n(!x[0]) | (!x[2]) | (!x[5])\n(!x[0]) | (!x[3]) | (!x[5])\n(x[1]) | (x[7])\n(x[2]) | (x[7])\n(!x[1]) | (!x[3]) | (x[7])\n(x[2]) | (x[7])\n(!x[4... | sat | o4-mini-high | There are 8 boolean (0/1) values x[0], x[1], ..., x[7]. Each of the following 21 expressions (`|` means OR, `!` means NOT) must equal 1:
(!x[4]) | (x[5])
(!x[0]) | (!x[2]) | (!x[5])
(!x[0]) | (!x[3]) | (!x[5])
(x[1]) | (x[7])
(x[2]) | (x[7])
(!x[1]) | (!x[3]) | (x[7])
(x[2]) | (x[7])
(!x[4]) | (x[5])
(x[0]) | (!x[3]) |... | 807 |
graphisomorphism_diff_8_90_42e580f274_SMtery | [
{
"content": "You are given two **undirected graphs**, G1 and G2, each with 11 vertices labeled from `0` to `10`. Both graphs contain exactly 19 **undirected** edges.\n\n- Graph G1 has the following (undirected) edge set E1:\n(3, 7)\n(1, 8)\n(2, 6)\n(4, 5)\n(4, 8)\n(3, 8)\n(4, 7)\n(1, 5)\n(1, 9)\n(3, 5)\n(5, 6)... | graphisomorphism | o4-mini-high | You are given two **undirected graphs**, G1 and G2, each with 11 vertices labeled from `0` to `10`. Both graphs contain exactly 19 **undirected** edges.
- Graph G1 has the following (undirected) edge set E1:
(3, 7)
(1, 8)
(2, 6)
(4, 5)
(4, 8)
(3, 8)
(4, 7)
(1, 5)
(1, 9)
(3, 5)
(5, 6)
(0, 6)
(0, 5)
(2, 7)
(2, 3)
(7, 8)... | 947 |
bajbytecomputer_diff_8_62_bf6b53c2b7_QJL4yO | [
{
"content": "You are given an array X of length 11, where each element is initially -1, 0, or +1: X[1]=1, X[2]=-1, X[3]=-1, X[4]=1, X[5]=-1, X[6]=-1, X[7]=-1, X[8]=1, X[9]=1, X[10]=-1, X[11]=-1\nYou may perform the following operation any number of times: choose an index i (1 ≤ i < 11), and update X[i + 1] := ... | bajbytecomputer | o4-mini-high | You are given an array X of length 11, where each element is initially -1, 0, or +1: X[1]=1, X[2]=-1, X[3]=-1, X[4]=1, X[5]=-1, X[6]=-1, X[7]=-1, X[8]=1, X[9]=1, X[10]=-1, X[11]=-1
You may perform the following operation any number of times: choose an index i (1 ≤ i < 11), and update X[i + 1] := X[i + 1] + X[i]. Your g... | 384 |
differentiate_diff_7_2_535bd049c7_b88Psi | [
{
"content": "You are given a function: F(x) = 3*x**2 + 3*x\n\nYour task is to compute its derivative with respect to x (i.e., F'(x)).\n\n**Output Format:** Your answer should be the expression for F'(x), written in **SymPy syntax**. Do not omit any symbols (e.g., always use `*` for multiplication).\nExample: `... | differentiate | o4-mini-high | You are given a function: F(x) = 3*x**2 + 3*x
Your task is to compute its derivative with respect to x (i.e., F'(x)).
**Output Format:** Your answer should be the expression for F'(x), written in **SymPy syntax**. Do not omit any symbols (e.g., always use `*` for multiplication).
Example: `sin(2*x)/2` (do **NOT** inc... | 180 |
palindromicsubstringnumbercounting_diff_2_44_2a27811ae0_vndBmN | [
{
"content": "We treat every positive integer as a string of digits (without leading zeros). A number is called a `good number` if it contains at least one palindromic substring of length **greater than 1**.\n\nFor example:\n- 101 is a good number because it contains the substring \"101\",\n- 110 is a good numb... | palindromicsubstringnumbercounting | o4-mini-high | We treat every positive integer as a string of digits (without leading zeros). A number is called a `good number` if it contains at least one palindromic substring of length **greater than 1**.
For example:
- 101 is a good number because it contains the substring "101",
- 110 is a good number because it contains the s... | 395 |
max_treeconstrainedpermutation_weight_diff_9_66_64586fe997_lZ8RLG | [
{
"content": "You are given an array W of length 14: W[1]=2 W[2]=5 W[3]=7 W[4]=4 W[5]=13 W[6]=8 W[7]=5 W[8]=5 W[9]=14 W[10]=13 W[11]=9 W[12]=2 W[13]=12 W[14]=14\n\nPlease find a permutation P of 1 to 14 such that the following conditions are satisfied:\n- The element 1 has no constraint.\n- The element 2 has no... | max | o4-mini-high | You are given an array W of length 14: W[1]=2 W[2]=5 W[3]=7 W[4]=4 W[5]=13 W[6]=8 W[7]=5 W[8]=5 W[9]=14 W[10]=13 W[11]=9 W[12]=2 W[13]=12 W[14]=14
Please find a permutation P of 1 to 14 such that the following conditions are satisfied:
- The element 1 has no constraint.
- The element 2 has no constraint.
- The element... | 373 |
cyclecounting_diff_5_49_6a2d641a75_adxHoT | [
{
"content": "You are given an **undirected graph** with 9 vertices, labeled from `0` to `8`. The graph contains the following undirected edges:\n(0, 2)\n(0, 8)\n(1, 7)\n(5, 6)\n(7, 8)\n(4, 7)\n(0, 1)\n(3, 5)\n(2, 5)\n\nPlease count the number of simple cycles in the graph. A simple cycle is a cycle with at lea... | cyclecounting | o4-mini-high | You are given an **undirected graph** with 9 vertices, labeled from `0` to `8`. The graph contains the following undirected edges:
(0, 2)
(0, 8)
(1, 7)
(5, 6)
(7, 8)
(4, 7)
(0, 1)
(3, 5)
(2, 5)
Please count the number of simple cycles in the graph. A simple cycle is a cycle with at least 3 vertices, with no repeated v... | 270 |
max_treeconstrainedpermutation_weight_diff_8_91_493894db69_iuGgG6 | [
{
"content": "You are given an array W of length 12: W[1]=2 W[2]=10 W[3]=3 W[4]=11 W[5]=11 W[6]=3 W[7]=7 W[8]=8 W[9]=12 W[10]=8 W[11]=8 W[12]=8\n\nPlease find a permutation P of 1 to 12 such that the following conditions are satisfied:\n- The element 1 has no constraint.\n- The element 2 has no constraint.\n- T... | max | o4-mini-high | You are given an array W of length 12: W[1]=2 W[2]=10 W[3]=3 W[4]=11 W[5]=11 W[6]=3 W[7]=7 W[8]=8 W[9]=12 W[10]=8 W[11]=8 W[12]=8
Please find a permutation P of 1 to 12 such that the following conditions are satisfied:
- The element 1 has no constraint.
- The element 2 has no constraint.
- The element 3 has no constra... | 342 |
mostcomponenttreeremovingtwopaths_diff_3_62_faa05a1fde_MTpCrJ | [
{
"content": "You are given a **tree** with 7 vertices labeled from 1 to 7, where vertex 1 is the **root**. The tree contains the following 6 undirected edges:\n(3, 6)\n(1, 3)\n(1, 5)\n(2, 4)\n(2, 3)\n(3, 7)\n\nYour task is to choose two paths (each from any vertex to any vertex; a path could be just one single... | mostcomponenttreeremovingtwopaths | o4-mini-high | You are given a **tree** with 7 vertices labeled from 1 to 7, where vertex 1 is the **root**. The tree contains the following 6 undirected edges:
(3, 6)
(1, 3)
(1, 5)
(2, 4)
(2, 3)
(3, 7)
Your task is to choose two paths (each from any vertex to any vertex; a path could be just one single vertex) such that:
- The two ... | 477 |
axis_kcenter_diff_7_94_21139f56c8_vFlvFq | [
{
"content": "You are given 12 points on a line, labeled from 0 to 11. Their positions (from left to right) are: 1 7 11 17 19 23 27 31 43 52 54 56\n\nPlease select a set of 9 distinct points. Try your best to minimize the total distance from all points to their nearest selected point (the distance is the absolu... | axis | o4-mini-high | You are given 12 points on a line, labeled from 0 to 11. Their positions (from left to right) are: 1 7 11 17 19 23 27 31 43 52 54 56
Please select a set of 9 distinct points. Try your best to minimize the total distance from all points to their nearest selected point (the distance is the absolute difference between po... | 648 |
pipelinearrangement_diff_9_41_1a4c0feea2_JZChkQ | [
{
"content": "You need to process 14 products labeled from `0` to `13`. Each product must go through **two machines**, A and B, **in order**.\n\nThe processing times for each product on machines A and B are given as:\nA[0]=7, B[0]=10\nA[1]=6, B[1]=1\nA[2]=4, B[2]=13\nA[3]=3, B[3]=4\nA[4]=7, B[4]=11\nA[5]=10, B[... | pipelinearrangement | o4-mini-high | You need to process 14 products labeled from `0` to `13`. Each product must go through **two machines**, A and B, **in order**.
The processing times for each product on machines A and B are given as:
A[0]=7, B[0]=10
A[1]=6, B[1]=1
A[2]=4, B[2]=13
A[3]=3, B[3]=4
A[4]=7, B[4]=11
A[5]=10, B[5]=14
A[6]=12, B[6]=1
A[7]=5, ... | 777 |
graphisomorphism_diff_3_43_89f10a8751_k59l4U | [
{
"content": "You are given two **undirected graphs**, G1 and G2, each with 6 vertices labeled from `0` to `5`. Both graphs contain exactly 6 **undirected** edges.\n\n- Graph G1 has the following (undirected) edge set E1:\n(2, 4)\n(0, 4)\n(1, 3)\n(2, 3)\n(3, 5)\n(2, 5)\n\n- Graph G2 has the following (undirecte... | graphisomorphism | o4-mini-high | You are given two **undirected graphs**, G1 and G2, each with 6 vertices labeled from `0` to `5`. Both graphs contain exactly 6 **undirected** edges.
- Graph G1 has the following (undirected) edge set E1:
(2, 4)
(0, 4)
(1, 3)
(2, 3)
(3, 5)
(2, 5)
- Graph G2 has the following (undirected) edge set E2:
(0, 4)
(4, 5)
(2... | 356 |
differentiate_diff_9_46_5c567ef037_c1Sgqn | [
{
"content": "You are given a function: F(x) = x - 2*exp(x)/9 - 2/9\n\nYour task is to compute its derivative with respect to x (i.e., F'(x)).\n\n**Output Format:** Your answer should be the expression for F'(x), written in **SymPy syntax**. Do not omit any symbols (e.g., always use `*` for multiplication).\nEx... | differentiate | o4-mini-high | You are given a function: F(x) = x - 2*exp(x)/9 - 2/9
Your task is to compute its derivative with respect to x (i.e., F'(x)).
**Output Format:** Your answer should be the expression for F'(x), written in **SymPy syntax**. Do not omit any symbols (e.g., always use `*` for multiplication).
Example: `sin(2*x)/2` (do **N... | 187 |
integerprogramming_diff_0_6_99800359a6_hkMWTr | [
{
"content": "There are 3 integers x[0], x[1], ..., x[2]. They satisfy the following 3 inequations:\n(-2) * x[0] + (2) * x[1] + (-4) * x[2] >= -6\n(3) * x[0] + (4) * x[1] + (-4) * x[2] >= -21\n(4) * x[0] + (-1) * x[2] >= -16\n\nPlease find any solution x[0], x[1], ..., x[2] that satisfies the inequations.\n\nOu... | integerprogramming | o4-mini-high | There are 3 integers x[0], x[1], ..., x[2]. They satisfy the following 3 inequations:
(-2) * x[0] + (2) * x[1] + (-4) * x[2] >= -6
(3) * x[0] + (4) * x[1] + (-4) * x[2] >= -21
(4) * x[0] + (-1) * x[2] >= -16
Please find any solution x[0], x[1], ..., x[2] that satisfies the inequations.
Output Format: Your final answe... | 349 |
axis_kcenter_diff_0_18_42e4ba41e2_tccOmM | [
{
"content": "You are given 4 points on a line, labeled from 0 to 3. Their positions (from left to right) are: 5 9 15 16\n\nPlease select a set of 1 distinct points. Try your best to minimize the total distance from all points to their nearest selected point (the distance is the absolute difference between posi... | axis | o4-mini-high | You are given 4 points on a line, labeled from 0 to 3. Their positions (from left to right) are: 5 9 15 16
Please select a set of 1 distinct points. Try your best to minimize the total distance from all points to their nearest selected point (the distance is the absolute difference between positions).
**Output Format... | 409 |
mafmafia_diff_1_0_9b95cbc5f4_DwnsBI | [
{
"content": "There are 4 participants in a game, labeled from 0 to 3. Each participant `i` has a target participant TO[i]. The array TO is given as: TO[0]=3 TO[1]=3 TO[2]=0 TO[3]=2\n\nYou are to determine a permutation P[0], P[1], ..., P[3] of the 4 participants, representing the order in which they act. The g... | mafmafia | o4-mini-high | There are 4 participants in a game, labeled from 0 to 3. Each participant `i` has a target participant TO[i]. The array TO is given as: TO[0]=3 TO[1]=3 TO[2]=0 TO[3]=2
You are to determine a permutation P[0], P[1], ..., P[3] of the 4 participants, representing the order in which they act. The game proceeds in that ord... | 286 |
palindromicsubstringnumbercounting_diff_3_92_0c475f92e7_gR7fYa | [
{
"content": "We treat every positive integer as a string of digits (without leading zeros). A number is called a `good number` if it contains at least one palindromic substring of length **greater than 1**.\n\nFor example:\n- 101 is a good number because it contains the substring \"101\",\n- 110 is a good numb... | palindromicsubstringnumbercounting | o4-mini-high | We treat every positive integer as a string of digits (without leading zeros). A number is called a `good number` if it contains at least one palindromic substring of length **greater than 1**.
For example:
- 101 is a good number because it contains the substring "101",
- 110 is a good number because it contains the s... | 206 |
multiplication_diff_0_25_07bea05d7b_hH6d5n | [
{
"content": "What is the answer to 10 times 98?",
"role": "user"
},
{
"content": "I’m sorry, but I can’t share my private reasoning. Here’s a concise solution:\n\n10 × 98 = \n<answer>980</answer>",
"role": "assistant"
}
] | multiplication | o4-mini-high | What is the answer to 10 times 98?
. Here’s a concise solution:
10 × 98 =
Therefore the answer is: 980 | 43 |
jugpuzzle_diff_6_44_388ff2be0b_Y7gVQr | [
{
"content": "You are given 9 jugs (initially empty) with the following capacities:\nJug 0's capacity: 18 liters\nJug 1's capacity: 12 liters\nJug 2's capacity: 86 liters\nJug 3's capacity: 51 liters\nJug 4's capacity: 37 liters\nJug 5's capacity: 50 liters\nJug 6's capacity: 27 liters\nJug 7's capacity: 12 lit... | jugpuzzle | o4-mini-high | You are given 9 jugs (initially empty) with the following capacities:
Jug 0's capacity: 18 liters
Jug 1's capacity: 12 liters
Jug 2's capacity: 86 liters
Jug 3's capacity: 51 liters
Jug 4's capacity: 37 liters
Jug 5's capacity: 50 liters
Jug 6's capacity: 27 liters
Jug 7's capacity: 12 liters
Jug 8's capacity: 40 liter... | 299 |
squareundamagedpointcounting_diff_1_42_c7c97df183_nzbeVf | [
{
"content": "Please count the number of distinct squares (not necessarily axis-aligned) such that:\n- All four vertices are integer coordinate points with 0 ≤ x ≤ 2 and 0 ≤ y ≤ 1.\n- None of the four vertices is among the damaged points. The list of damaged points is given as follows: (2, 0), (1, 1)",
"rol... | squareundamagedpointcounting | o4-mini-high | Please count the number of distinct squares (not necessarily axis-aligned) such that:
- All four vertices are integer coordinate points with 0 ≤ x ≤ 2 and 0 ≤ y ≤ 1.
- None of the four vertices is among the damaged points. The list of damaged points is given as follows: (2, 0), (1, 1)
. Here’s a concise solution:
Ther... | 219 |
bajbytecomputer_diff_6_43_4a5e372acc_aeoHNq | [
{
"content": "You are given an array X of length 9, where each element is initially -1, 0, or +1: X[1]=1, X[2]=0, X[3]=1, X[4]=-1, X[5]=0, X[6]=0, X[7]=0, X[8]=0, X[9]=0\nYou may perform the following operation any number of times: choose an index i (1 ≤ i < 9), and update X[i + 1] := X[i + 1] + X[i]. Your goal... | bajbytecomputer | o4-mini-high | You are given an array X of length 9, where each element is initially -1, 0, or +1: X[1]=1, X[2]=0, X[3]=1, X[4]=-1, X[5]=0, X[6]=0, X[7]=0, X[8]=0, X[9]=0
You may perform the following operation any number of times: choose an index i (1 ≤ i < 9), and update X[i + 1] := X[i + 1] + X[i]. Your goal is to make the array n... | 531 |
graphisomorphism_diff_0_5_1d1119c023_OOYrZm | [
{
"content": "You are given two **undirected graphs**, G1 and G2, each with 3 vertices labeled from `0` to `2`. Both graphs contain exactly 2 **undirected** edges.\n\n- Graph G1 has the following (undirected) edge set E1:\n(1, 2)\n(0, 1)\n\n- Graph G2 has the following (undirected) edge set E2:\n(1, 2)\n(0, 2)\... | graphisomorphism | o4-mini-high | You are given two **undirected graphs**, G1 and G2, each with 3 vertices labeled from `0` to `2`. Both graphs contain exactly 2 **undirected** edges.
- Graph G1 has the following (undirected) edge set E1:
(1, 2)
(0, 1)
- Graph G2 has the following (undirected) edge set E2:
(1, 2)
(0, 2)
Your task is to find a **bije... | 377 |
mindivisionsumxor_diff_2_53_22bbfebbc2_oDuHYU | [
{
"content": "You are given 5 numbers A[1], A[2], ..., A[5]. The values are given as:\nA[1]=7\nA[2]=5\nA[3]=5\nA[4]=6\nA[5]=12\n\nYou may divide these numbers (in order) into some **consecutive batches**. Let the total number of batches be k (we must have 1 ≤ k ≤ 3), and let end[1], end[2], ..., end[k] (1 ≤ end... | mindivisionsumxor | o4-mini-high | You are given 5 numbers A[1], A[2], ..., A[5]. The values are given as:
A[1]=7
A[2]=5
A[3]=5
A[4]=6
A[5]=12
You may divide these numbers (in order) into some **consecutive batches**. Let the total number of batches be k (we must have 1 ≤ k ≤ 3), and let end[1], end[2], ..., end[k] (1 ≤ end[1] < end[2] < ... < end[k] =... | 438 |
minimumsumdifferencesubmatrix_diff_7_55_a9fe14ef9e_j5tjf0 | [
{
"content": "You are given a 3 × 6 matrix of integers (with row indices from `0` to `2` and column indices from `0` to `5`). Please select 2 rows and 5 columns, denoted as `r[1], ..., r[2]` and `c[1], ..., c[5]`, respectively, such that:\n- 0 ≤ r[1] < ... < r[2] ≤ 2\n- 0 ≤ c[1] < ... < c[5] ≤ 5\n\nThe matrix i... | minimumsumdifferencesubmatrix | o4-mini-high | You are given a 3 × 6 matrix of integers (with row indices from `0` to `2` and column indices from `0` to `5`). Please select 2 rows and 5 columns, denoted as `r[1], ..., r[2]` and `c[1], ..., c[5]`, respectively, such that:
- 0 ≤ r[1] < ... < r[2] ≤ 2
- 0 ≤ c[1] < ... < c[5] ≤ 5
The matrix is given as below (each lin... | 436 |
integerprogramming_diff_0_55_19ff13d5f2_4znFvd | [
{
"content": "There are 3 integers x[0], x[1], ..., x[2]. They satisfy the following 4 inequations:\n(1) * x[1] >= -2\n(-3) * x[1] >= 5\n(-3) * x[0] + (4) * x[1] >= -5\n(-4) * x[0] >= 2\n\nPlease find any solution x[0], x[1], ..., x[2] that satisfies the inequations.\n\nOutput Format: Your final answer should b... | integerprogramming | o4-mini-high | There are 3 integers x[0], x[1], ..., x[2]. They satisfy the following 4 inequations:
(1) * x[1] >= -2
(-3) * x[1] >= 5
(-3) * x[0] + (4) * x[1] >= -5
(-4) * x[0] >= 2
Please find any solution x[0], x[1], ..., x[2] that satisfies the inequations.
Output Format: Your final answer should be a single line containing x[0... | 274 |
pipelinearrangement_diff_7_113_c3ab6d1b16_3fmC7l | [
{
"content": "You need to process 10 products labeled from `0` to `9`. Each product must go through **two machines**, A and B, **in order**.\n\nThe processing times for each product on machines A and B are given as:\nA[0]=1, B[0]=5\nA[1]=5, B[1]=3\nA[2]=1, B[2]=10\nA[3]=8, B[3]=5\nA[4]=9, B[4]=8\nA[5]=6, B[5]=5... | pipelinearrangement | o4-mini-high | You need to process 10 products labeled from `0` to `9`. Each product must go through **two machines**, A and B, **in order**.
The processing times for each product on machines A and B are given as:
A[0]=1, B[0]=5
A[1]=5, B[1]=3
A[2]=1, B[2]=10
A[3]=8, B[3]=5
A[4]=9, B[4]=8
A[5]=6, B[5]=5
A[6]=4, B[6]=5
A[7]=7, B[7]=7... | 586 |
mafmafia_diff_2_90_77ee499f56_V684hW | [
{
"content": "There are 5 participants in a game, labeled from 0 to 4. Each participant `i` has a target participant TO[i]. The array TO is given as: TO[0]=3 TO[1]=4 TO[2]=4 TO[3]=4 TO[4]=4\n\nYou are to determine a permutation P[0], P[1], ..., P[4] of the 5 participants, representing the order in which they ac... | mafmafia | o4-mini-high | There are 5 participants in a game, labeled from 0 to 4. Each participant `i` has a target participant TO[i]. The array TO is given as: TO[0]=3 TO[1]=4 TO[2]=4 TO[3]=4 TO[4]=4
You are to determine a permutation P[0], P[1], ..., P[4] of the 5 participants, representing the order in which they act. The game proceeds in ... | 614 |
bannedpointsupersetpathcounting_diff_4_6_08c2e39071_RIWBVE | [
{
"content": "In a three-dimensional space, you start at point (0, 0, 0) and want to reach the point (0, 2, 5). At each step, if you are currently at (x, y, z), you may move to a new (different from the current one) point of one of the following types:\n1. (x', y, z) such that x AND x' = x\n2. (x, y', z) such t... | bannedpointsupersetpathcounting | o4-mini-high | In a three-dimensional space, you start at point (0, 0, 0) and want to reach the point (0, 2, 5). At each step, if you are currently at (x, y, z), you may move to a new (different from the current one) point of one of the following types:
1. (x', y, z) such that x AND x' = x
2. (x, y', z) such that y AND y' = y
3. (x, ... | 381 |
tournament_longestpath_diff_9_10_36fb4ff4a2_y13QLX | [
{
"content": "You are given a **directed graph** with 12 vertices labeled from `0` to `11`. The graph contains the following directed edges. Each edge is represented as a tuple `(s, t)`, meaning there is a directed edge **from vertex `s` to vertex `t`**:\n(0, 1)\n(0, 3)\n(0, 7)\n(0, 8)\n(0, 9)\n(0, 10)\n(1, 3)\... | tournament | o4-mini-high | You are given a **directed graph** with 12 vertices labeled from `0` to `11`. The graph contains the following directed edges. Each edge is represented as a tuple `(s, t)`, meaning there is a directed edge **from vertex `s` to vertex `t`**:
(0, 1)
(0, 3)
(0, 7)
(0, 8)
(0, 9)
(0, 10)
(1, 3)
(1, 6)
(1, 7)
(1, 9)
(2, 0)
(... | 596 |
multiplication_diff_1_31_d11c95b83f_uSWWTb | [
{
"content": "Compute the product of 778 and 544.",
"role": "user"
},
{
"content": "I’m sorry, but I can’t share my private reasoning. \n<answer>423232</answer>",
"role": "assistant"
}
] | multiplication | o4-mini-high | Compute the product of 778 and 544.
.
Therefore the answer is: 423232 | 32 |
impparty_diff_0_24_c63d917fdc_uQ6Ldq | [
{
"content": "You are given an **undirected graph** with 3 × 3 vertices, labeled from `0` to `8`. The graph contains the following undirected edges:\n(2, 4)\n(1, 4)\n(4, 6)\n(2, 3)\n(1, 2)\n(1, 6)\n(2, 5)\n(2, 8)\n(1, 5)\n(0, 8)\n(2, 6)\n(5, 6)\n(5, 8)\n(4, 8)\n(1, 8)\n(4, 5)\n(6, 8)\n\nIt is guaranteed that th... | impparty | o4-mini-high | You are given an **undirected graph** with 3 × 3 vertices, labeled from `0` to `8`. The graph contains the following undirected edges:
(2, 4)
(1, 4)
(4, 6)
(2, 3)
(1, 2)
(1, 6)
(2, 5)
(2, 8)
(1, 5)
(0, 8)
(2, 6)
(5, 6)
(5, 8)
(4, 8)
(1, 8)
(4, 5)
(6, 8)
It is guaranteed that the graph contains a **clique of size 2 × 3... | 258 |
squareundamagedpointcounting_diff_3_99_948f9e558f_LFw37k | [
{
"content": "Please count the number of distinct squares (not necessarily axis-aligned) such that:\n- All four vertices are integer coordinate points with 0 ≤ x ≤ 2 and 0 ≤ y ≤ 4.\n- None of the four vertices is among the damaged points. The list of damaged points is given as follows: (2, 2), (0, 2), (2, 1), (... | squareundamagedpointcounting | o4-mini-high | Please count the number of distinct squares (not necessarily axis-aligned) such that:
- All four vertices are integer coordinate points with 0 ≤ x ≤ 2 and 0 ≤ y ≤ 4.
- None of the four vertices is among the damaged points. The list of damaged points is given as follows: (2, 2), (0, 2), (2, 1), (1, 1)
. Here’s a concise... | 239 |
max_treeconstrainedpermutation_weight_diff_2_13_a7019556d9_4uLwD6 | [
{
"content": "You are given an array W of length 5: W[1]=3 W[2]=3 W[3]=2 W[4]=2 W[5]=2\n\nPlease find a permutation P of 1 to 5 such that the following conditions are satisfied:\n- The element 1 has no constraint.\n- The element 1 must come before element 2.\n- The element 1 must come before element 3.\n- The e... | max | o4-mini-high | You are given an array W of length 5: W[1]=3 W[2]=3 W[3]=2 W[4]=2 W[5]=2
Please find a permutation P of 1 to 5 such that the following conditions are satisfied:
- The element 1 has no constraint.
- The element 1 must come before element 2.
- The element 1 must come before element 3.
- The element 1 must come before el... | 276 |
impparty_diff_8_85_6b2255aa52_SQecyK | [
{
"content": "You are given an **undirected graph** with 3 × 11 vertices, labeled from `0` to `32`. The graph contains the following undirected edges:\n(26, 32)\n(0, 1)\n(14, 31)\n(25, 32)\n(1, 17)\n(14, 32)\n(18, 29)\n(0, 21)\n(10, 12)\n(12, 13)\n(13, 26)\n(11, 32)\n(13, 24)\n(10, 29)\n(12, 31)\n(24, 27)\n(7, ... | impparty | o4-mini-high | You are given an **undirected graph** with 3 × 11 vertices, labeled from `0` to `32`. The graph contains the following undirected edges:
(26, 32)
(0, 1)
(14, 31)
(25, 32)
(1, 17)
(14, 32)
(18, 29)
(0, 21)
(10, 12)
(12, 13)
(13, 26)
(11, 32)
(13, 24)
(10, 29)
(12, 31)
(24, 27)
(7, 12)
(7, 17)
(11, 26)
(19, 25)
(0, 26)
(... | 1,641 |
oddvisitation_diff_9_5_98da0c3ae1_7TufEW | [
{
"content": "You are given a **connected undirected graph** with 14 vertices labeled from 0 to 13. The graph contains the following undirected edges:\n(8, 13)\n(1, 6)\n(8, 11)\n(5, 11)\n(4, 13)\n(3, 7)\n(2, 4)\n(0, 8)\n(1, 2)\n(0, 10)\n(6, 9)\n(6, 8)\n(5, 6)\n(8, 9)\n(6, 10)\n(1, 9)\n(3, 9)\n(2, 7)\n(0, 9)\n(7... | oddvisitation | o4-mini-high | You are given a **connected undirected graph** with 14 vertices labeled from 0 to 13. The graph contains the following undirected edges:
(8, 13)
(1, 6)
(8, 11)
(5, 11)
(4, 13)
(3, 7)
(2, 4)
(0, 8)
(1, 2)
(0, 10)
(6, 9)
(6, 8)
(5, 6)
(8, 9)
(6, 10)
(1, 9)
(3, 9)
(2, 7)
(0, 9)
(7, 12)
(3, 11)
(0, 12)
(0, 13)
(9, 11)
(10,... | 613 |
mafmafia_diff_1_50_e6289fcf27_jH72y5 | [
{
"content": "There are 4 participants in a game, labeled from 0 to 3. Each participant `i` has a target participant TO[i]. The array TO is given as: TO[0]=0 TO[1]=3 TO[2]=2 TO[3]=3\n\nYou are to determine a permutation P[0], P[1], ..., P[3] of the 4 participants, representing the order in which they act. The g... | mafmafia | o4-mini-high | There are 4 participants in a game, labeled from 0 to 3. Each participant `i` has a target participant TO[i]. The array TO is given as: TO[0]=0 TO[1]=3 TO[2]=2 TO[3]=3
You are to determine a permutation P[0], P[1], ..., P[3] of the 4 participants, representing the order in which they act. The game proceeds in that ord... | 260 |
squareundamagedpointcounting_diff_7_72_e22db131d8_Jx5s3Z | [
{
"content": "Please count the number of distinct squares (not necessarily axis-aligned) such that:\n- All four vertices are integer coordinate points with 0 ≤ x ≤ 2 and 0 ≤ y ≤ 3.\n- None of the four vertices is among the damaged points. The list of damaged points is given as follows: (2, 3), (2, 0), (2, 1)",
... | squareundamagedpointcounting | o4-mini-high | Please count the number of distinct squares (not necessarily axis-aligned) such that:
- All four vertices are integer coordinate points with 0 ≤ x ≤ 2 and 0 ≤ y ≤ 3.
- None of the four vertices is among the damaged points. The list of damaged points is given as follows: (2, 3), (2, 0), (2, 1)
. Here’s a concise solutio... | 209 |
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