id string | text string | meta string |
|---|---|---|
00000129_cpt | ## Problem
Three friends — Alice, Bob, and Charlie — are about to receive hats. Each person receives a hat of a different color: Red, Blue, or Green. The order in which they receive their hats determines the color: the first person gets Red, the second gets Blue, and the third gets Green. Use the following clues to de... | {"format": "cpt", "domain": "reasoning", "subcategory": "temporal_reasoning", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Alice', 'Bob', 'Charlie']", "method": "unique_match"}, "taxonomy_key": "reasoning/temporal_reasoning/hat_color/transitive_inf... |
00000130_cpt | ## Problem
You are given an array of integers `nums` of length `n` and an integer `k` representing the maximum number of elements you can choose. You must select a contiguous subarray of length exactly `k` that maximizes the total sum. Using dynamic programming, find and return the maximum sum of any contiguous subarr... | {"format": "cpt", "domain": "code", "subcategory": "dynamic_programming", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/dynamic_programming/arrays_strings/o_n_time_required/easy"} |
00000131_cpt | ## Problem
A sustainable orchard plants exactly three heritage apple varieties: Pippin, Russet, and Blenheim. On planting day, the total number of trees satisfies these strict requirements: (1) The total is a positive integer between 800 and 1600. (2) Exactly 3/7 of the total are Pippin trees. (3) Exactly 5/13 of the ... | {"format": "cpt", "domain": "math", "subcategory": "number_theory", "difficulty": "hard", "has_code": false, "verified": true, "verification": {"derived_answer": "1547", "model_answer": "1547", "method": "equation_solved"}, "taxonomy_key": "math/number_theory/word_problem_real_world/exact_rational_answer/hard"} |
00000132_cpt | ## Problem
A bioengineering lab is fabricating a hemispherical tissue scaffold of inner radius R and outer radius 2R (a spherical shell). Two robotic depositors build the scaffold layer by layer, from the inner surface (radius R) outward to the outer surface (radius 2R). Depositor A works at a constant volumetric depo... | {"format": "cpt", "domain": "math", "subcategory": "rate_and_work", "difficulty": "hard", "has_code": false, "verified": true, "verification": {"derived_answer": "64", "model_answer": "64", "method": "equation_solved"}, "taxonomy_key": "math/rate_and_work/applied_science/geometric_intuition/hard"} |
00000133_cpt | ## Problem
You are given a queue of integers `nums` and an integer `k`. In one operation, you can dequeue the first two elements `a` and `b` from the front of the queue, compute the value `(a + b) % k`, and enqueue this result at the back of the queue. You stop when the queue is reduced to a single element.
Without s... | {"format": "cpt", "domain": "code", "subcategory": "math_formula", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/math_formula/stacks_queues/two_data_structures/medium"} |
00000134_cpt | ## Problem
Two players, Petra and Quinn, play a token game on a 5×5 grid. The game piece starts at the top-left cell (1,1) and must reach the bottom-right cell (5,5). On each turn, a player moves the piece to an adjacent cell: either one step Down (increasing the row by 1) or one step Right (increasing the column by 1... | {"format": "cpt", "domain": "math", "subcategory": "combinatorics", "difficulty": "hard", "has_code": false, "verified": true, "verification": {"derived_answer": "53", "model_answer": "53", "method": "equation_solved"}, "taxonomy_key": "math/combinatorics/combinatorial_game/requires_substitution/hard"} |
00000135_cpt | ## Problem
A number x satisfies the following: when 3 times the number is added to 5, the result equals 2 times the number added to 11. Find the number.
## Solution
**Step 1:** Start with the equation: 3x + 5 = 2x + 11.
**Step 2:** Subtract 2x from both sides to gather the x terms: x + 5 = 11.
**Step 3:** Subtract... | {"format": "cpt", "domain": "math", "subcategory": "algebraic_manipulation", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "6", "model_answer": "6", "method": "equation_solved"}, "taxonomy_key": "math/algebraic_manipulation/pure_arithmetic/exact_rational_answer/easy"} |
00000136_cpt | ## Problem
You are simulating a streaming data processor that monitors a sequence of signals. The processor maintains a state that starts at 0. For each signal `x` in the stream `nums`, the processor updates its state by XORing it with `x`. After processing exactly `k` signals from the stream (or all of them if the st... | {"format": "cpt", "domain": "code", "subcategory": "bit_manipulation", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/bit_manipulation/simulation_state/streaming_online/easy"} |
00000137_cpt | ## Problem
In a theoretical proof sketch regarding the prime factorization of integers, suppose a lemma states that if a positive integer N satisfies N = 2^a · 5^b · 7^c for nonnegative integers a, b, c, and if log₂(N) = log₂(N/4) + log₂(N/8) + 3, then the prime factorization of N has a unique structure. The proof pro... | {"format": "cpt", "domain": "math", "subcategory": "logarithms_exponents", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "2", "model_answer": "2", "method": "equation_solved"}, "taxonomy_key": "math/logarithms_exponents/theoretical_proof_sketch/requires_factoring/medium... |
00000138_cpt | ## Problem
On January 1st, Maya opens a savings account with an initial deposit of $2. Each week, she deposits $2 more than the previous week. How many weeks will it take for her total cumulative savings to reach exactly $72?
## Solution
**Step 1:** Maya's weekly deposits form an arithmetic sequence: 2, 4, 6, ...
*... | {"format": "cpt", "domain": "math", "subcategory": "sequences_and_series", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "8", "model_answer": "8", "method": "equation_solved"}, "taxonomy_key": "math/sequences_and_series/finance_economics/integer_answer_only/easy"} |
00000139_cpt | ## Problem
A sovereign wealth fund tracks a digital gold reserve using a hexagonal lattice of trading vaults. Exactly 2027 units of gold are distributed across the vaults, numbered 0 through 2026 around the hexagon's perimeter. The fund's smart contract executes 2027 redistribution rounds. In round $k$ (for $k = 0, 1,... | {"format": "cpt", "domain": "math", "subcategory": "modular_arithmetic", "difficulty": "hard", "has_code": false, "verified": true, "verification": {"derived_answer": "13328562621217331705881909690140288777455943436176739849590553475233664943713213488082349075150851246836928404828031503990914437788966634725915286828315... |
00000140_cpt | ## Problem
Three friends — Alice, Bob, and Charlie — are scheduling meetings. Each person meets at a different time: first, second, or third. Use the following clues to determine the exact order of their meetings:
1. Bob meets before Alice.
2. Alice is adjacent to Charlie (they meet in consecutive time slots).
3. Ali... | {"format": "cpt", "domain": "reasoning", "subcategory": "temporal_reasoning", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Bob', 'Charlie', 'Alice']", "method": "unique_match"}, "taxonomy_key": "reasoning/temporal_reasoning/scheduling/contradiction... |
00000141_cpt | ## Problem
Given an array of integers `nums` and an integer `k`, find the maximum sum of any contiguous subarray of length exactly `k`. If the array has fewer than `k` elements, return 0.
## Solution
**Step 1:** Check if the array length is less than `k` or if `k` is non-positive; if so, return 0.
**Step 2:** Compu... | {"format": "cpt", "domain": "code", "subcategory": "sliding_window", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/sliding_window/arrays_strings/no_extra_alloc/easy"} |
00000142_cpt | ## Problem
Three friends—Alice, Bob, and Charlie—finished a race, each taking a different place (1st, 2nd, or 3rd). Determine the finishing order from 1st to 3rd using these clues: Alice finished before Bob. Bob finished before Charlie. Charlie did not finish 2nd.
## Solution
**Step 1:** Clue 1 tells us Alice finish... | {"format": "cpt", "domain": "reasoning", "subcategory": "temporal_reasoning", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Alice', 'Bob', 'Charlie']", "method": "unique_match"}, "taxonomy_key": "reasoning/temporal_reasoning/logic_puzzle/small_domai... |
00000143_cpt | ## Problem
A chemistry lab has two pumps that can fill a reaction tank with solvent. Pump A fills the tank in 6 minutes. Pump B fills the tank in 3 minutes. If both pumps are turned on at the same time, how many minutes does it take to fill the tank?
## Solution
**Step 1:** Pump A fills 1/6 of the tank per minute.
... | {"format": "cpt", "domain": "math", "subcategory": "rate_and_work", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "2", "model_answer": "2", "method": "equation_solved"}, "taxonomy_key": "math/rate_and_work/applied_science/exact_rational_answer/easy"} |
00000144_cpt | ## Problem
You are given a string `s` and an integer `k`. The string contains exactly `k` distinct characters. A substring is valid if it contains all `k` distinct characters at least once, and no character appears more than half the length of the substring.
Find the maximum length of a valid substring. If no such su... | {"format": "cpt", "domain": "code", "subcategory": "two_pointers", "difficulty": "hard", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/two_pointers/string_parsing/no_extra_alloc/hard"} |
00000145_cpt | ## Problem
A materials science lab tests a batch of 12 graphene samples for structural defects. Each sample independently has a 20% chance of being defective. The lab's imaging scanner can only process 4 samples per day. If the lab randomly selects 4 samples from the batch, what is the probability that at least 2 of t... | {"format": "cpt", "domain": "math", "subcategory": "probability", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "94/165", "model_answer": "94/165", "method": "equation_solved"}, "taxonomy_key": "math/probability/applied_science/multiple_solutions_possible/medium"} |
00000146_cpt | ## Problem
An investor allocates a total of $48,000 across three assets: Asset A, Asset B, and Asset C. The amount invested in Asset B is $4,000 more than half the amount invested in Asset A. The amount invested in Asset C is $2,000 less than twice the amount invested in Asset B. How much money does the investor place... | {"format": "cpt", "domain": "math", "subcategory": "algebraic_manipulation", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "15200", "model_answer": "15200", "method": "equation_solved"}, "taxonomy_key": "math/algebraic_manipulation/finance_economics/multiple_solutions_p... |
00000147_cpt | ## Problem
You are given a linked list of non-negative integers and a target value `k`. The linked list is provided as a list of integers `nums` representing its values in sequential order. Each node in the linked list contains an integer value and a pointer to the next node.
Your task is to find the length of the lo... | {"format": "cpt", "domain": "code", "subcategory": "prefix_sum", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 19, "failed": 0, "total": 19, "failing_case": ""}, "taxonomy_key": "code/prefix_sum/linked_lists/two_data_structures/medium"} |
00000148_cpt | ## Problem
You are given an integer array `nums` and a non-negative integer `k`. In one operation, you can select an index `i` and update `nums[i]` to `nums[i] + 1` or `nums[i] - 1` (this represents the in-place modification constraint). The absolute difference between the updated `nums[i]` and original `nums[i]` can ... | {"format": "cpt", "domain": "code", "subcategory": "greedy", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 18, "failed": 0, "total": 18, "failing_case": ""}, "taxonomy_key": "code/greedy/hashing_maps/in_place_modification/medium"} |
00000149_cpt | ## Problem
A small business sells two types of gift cards: a $3 card and a $5 card. A customer buys a total of 7 gift cards and pays exactly $29. How many $5 gift cards did the customer buy?
## Solution
**Step 1:** Let x be the number of $5 gift cards. Since the total number of gift cards is 7, the number of $3 gift... | {"format": "cpt", "domain": "math", "subcategory": "diophantine", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "4", "model_answer": "4", "method": "equation_solved"}, "taxonomy_key": "math/diophantine/finance_economics/requires_substitution/easy"} |
00000150_cpt | ## Problem
You are given an $n \times n$ integer matrix `grid` and an integer `k`. Your task is to find the $k$-th smallest element in the matrix. The matrix has the special property that each row is sorted in strictly increasing order, and each column is also sorted in strictly increasing order. Since there may be du... | {"format": "cpt", "domain": "code", "subcategory": "binary_search", "difficulty": "hard", "has_code": true, "verified": true, "verification": {"passed": 2, "failed": 0, "total": 2, "failing_case": ""}, "taxonomy_key": "code/binary_search/matrix_grid/o_n_time_required/hard"} |
00000151_cpt | ## Problem
Elena opens a savings account. In the first month she deposits $3. Each month after that, she increases her deposit by $3, so she deposits $6 in month 2, $9 in month 3, and so on. After how many months will her total cumulative deposits equal $135?
## Solution
**Step 1:** The monthly deposits form an arit... | {"format": "cpt", "domain": "math", "subcategory": "sequences_and_series", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "9", "model_answer": "9", "method": "equation_solved"}, "taxonomy_key": "math/sequences_and_series/finance_economics/requires_factoring/easy"} |
00000152_cpt | ## Problem
You are given an array of integers `nums` representing the difficulty of challenges, and an integer `k` representing your initial skill level.
You want to complete as many challenges as possible. You can only complete a challenge if your skill level is greater than or equal to the challenge's difficulty. W... | {"format": "cpt", "domain": "code", "subcategory": "greedy", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/greedy/arrays_strings/two_data_structures/medium"} |
00000153_cpt | ## Problem
Two players take turns placing a token on a 3-by-3 grid. Alice goes first, then Bob, then Alice, then Bob. A player wins if their two tokens are in the same row, same column, or same diagonal. If no one achieves this, the game is a draw. How many distinct game sequences end in a draw? (A game sequence is th... | {"format": "cpt", "domain": "math", "subcategory": "combinatorics", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "72", "model_answer": "72", "method": "equation_solved"}, "taxonomy_key": "math/combinatorics/combinatorial_game/geometric_intuition/easy"} |
00000154_cpt | ## Problem
Let S be the set of all positive integers n satisfying the congruence n^{24} ≡ 1 (mod 144). Define f(n) as the product of all distinct prime factors of n. Determine the sum of all possible values of f(n) for n in S.
## Solution
**Step 1:** First, factor the modulus: 144 = 2^4 * 3^2. The congruence n^{24} ... | {"format": "cpt", "domain": "math", "subcategory": "modular_arithmetic", "difficulty": "hard", "has_code": false, "verified": true, "verification": {"derived_answer": "30", "model_answer": "30", "method": "equation_solved"}, "taxonomy_key": "math/modular_arithmetic/theoretical_proof_sketch/integer_answer_only/hard"} |
00000155_cpt | ## Problem
In the addition SEND + MORE = MONEY, each letter is a distinct digit 0-9. Consider the sets A = {S,E,N,D}, B = {M,O,R,E}, C = {M,O,N,E,Y}. Let U = A ∪ B ∪ C. Given these constraints: (1) |A ∩ B| = 1, (2) |A ∩ C| = 2, (3) |B ∩ C| = 3, (4) |U| = 6, (5) |A ∩ B ∩ C| = 1, (6) The sum of all digits in U equals 28... | {"format": "cpt", "domain": "reasoning", "subcategory": "set_logic", "difficulty": "hard", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "[0, 1, 2, 5, 6, 7, 8, 9]", "method": "set_match"}, "taxonomy_key": "reasoning/set_logic/cryptarithmetic/contradiction_needed/hard"} |
00000156_cpt | ## Problem
A venture capital firm is designing a new triangular rooftop terrace for its headquarters. The terrace will occupy a right triangle with two legs measuring 30 meters (the east side) and 40 meters (the north side), forming the right angle at the northeast corner. The firm's CFO proposes that the terrace can ... | {"format": "cpt", "domain": "math", "subcategory": "geometry", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "125/4", "model_answer": "125/4", "method": "equation_solved"}, "taxonomy_key": "math/geometry/finance_economics/multiple_solutions_possible/medium"} |
00000157_cpt | ## Problem
You are given an array of integers `nums` and an integer `k`. You process the elements of `nums` from left to right in an online fashion. At any point, you can choose a subarray of length exactly `k` ending at the current position, and remove its minimum element. Your task is to return an array `answer` of ... | {"format": "cpt", "domain": "code", "subcategory": "monotonic_stack", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/monotonic_stack/arrays_strings/streaming_online/medium"} |
00000158_cpt | ## Problem
Let $x$ be a positive real number satisfying $x^{(\log_2 x)^2 - \log_2 x} = 16$. Find the sum of all possible values of $x$.
## Solution
**Step 1:** Let $y = \log_2 x$, so $x = 2^y$. Substituting into the equation yields $(2^y)^{y^2 - y} = 2^4$, which simplifies to $2^{y(y^2 - y)} = 2^4$.
**Step 2:** Equ... | {"format": "cpt", "domain": "math", "subcategory": "logarithms_exponents", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "4", "model_answer": "4", "method": "equation_solved"}, "taxonomy_key": "math/logarithms_exponents/competition_style/multiple_solutions_possible/medi... |
00000159_cpt | ## Problem
You are given an integer array `nums` and an integer `k`. Find the length of the longest contiguous subarray that contains at most `k` distinct integers. If the array is empty or `k` is 0, return 0. Note: The frequency map size is bounded by `k+1`, maintaining O(1) auxiliary space.
## Solution
**Step 1:**... | {"format": "cpt", "domain": "code", "subcategory": "two_pointers", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 19, "failed": 0, "total": 19, "failing_case": ""}, "taxonomy_key": "code/two_pointers/hashing_maps/o_1_space_required/medium"} |
00000160_cpt | ## Problem
A positive integer n has exactly 18 positive divisors. The sum of these divisors equals 1820, and the sum of the reciprocals of these divisors equals 1820 divided by n. Find n.
## Solution
**Step 1:** The sum of the reciprocals of the divisors of n is (sum of divisors)/n. Since the sum of divisors is 1820... | {"format": "cpt", "domain": "math", "subcategory": "diophantine", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "684", "model_answer": "684", "method": "equation_solved"}, "taxonomy_key": "math/diophantine/pure_arithmetic/integer_answer_only/medium"} |
00000161_cpt | ## Problem
You are given an array of integers `nums` representing a circular queue of `n` people, where `nums[i]` is the `value` of the person at position `i`. You also have an integer `k` representing a jump step.
The process begins at the person at index `0`. At each step, the current person's value is added to a ... | {"format": "cpt", "domain": "code", "subcategory": "simulation", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 18, "failed": 0, "total": 18, "failing_case": ""}, "taxonomy_key": "code/simulation/stacks_queues/no_extra_alloc/medium"} |
00000162_cpt | ## Problem
Four friends—Alice, Bob, Charlie, and Dana—each put on a hat at a different time: 1 PM, 2 PM, 3 PM, or 4 PM. Each hat was a different color: Red, Blue, Green, or Yellow. Using the clues below, determine the exact time each person put on their hat and the color of each hat. (In the clues, 'before' means earl... | {"format": "cpt", "domain": "reasoning", "subcategory": "temporal_reasoning", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Alice', 'Bob', 'Dana', 'Charlie']", "method": "unique_match"}, "taxonomy_key": "reasoning/temporal_reasoning/hat_color/smal... |
00000163_cpt | ## Problem
You are given a 0-indexed m x n matrix `grid` of integers and a strictly positive integer `k`. A grid contains exactly m rows, where each row has n integers. The matrix is fully sorted: integers in every row are strictly increasing from left to right, and the first integer of each row is strictly greater th... | {"format": "cpt", "domain": "code", "subcategory": "two_pointers", "difficulty": "hard", "has_code": true, "verified": true, "verification": {"passed": 2, "failed": 0, "total": 2, "failing_case": ""}, "taxonomy_key": "code/two_pointers/matrix_grid/o_n_time_required/hard"} |
00000164_cpt | ## Problem
You are given an array of integers `nums` and an integer `k`. The array represents a sequence of nodes forming a singly linked list, where the value of each node is `nums[i]`. Two nodes are considered 'connected' if they are adjacent in the array and their absolute difference is less than or equal to `k`. C... | {"format": "cpt", "domain": "code", "subcategory": "union_find", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/union_find/linked_lists/no_extra_alloc/easy"} |
00000165_cpt | ## Problem
You are given an array of positive integers `nums` and a prime number `k`. We define the `k-magnitude` of a positive integer `x` as the exponent of the prime `k` in the prime factorization of `x` (i.e., the largest power `e` such that `k^e` divides `x`). If `x` is not divisible by `k`, its `k-magnitude` is ... | {"format": "cpt", "domain": "code", "subcategory": "monotonic_stack", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/monotonic_stack/number_theory/two_data_structures/medium"} |
00000166_cpt | ## Problem
You are given an array of integers `nums` and an integer `k`. The array is 0-indexed. You want to group the indices into connected components. Two indices `i` and `j` are connected if they contain the exact same value (i.e., `nums[i] == nums[j]`). However, if a value appears fewer than `k` times in the arra... | {"format": "cpt", "domain": "code", "subcategory": "union_find", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/union_find/hashing_maps/integer_overflow_safety/easy"} |
00000167_cpt | ## Problem
A positive integer x has the following property: when 3 is added to x, the result equals 5 times x minus 13. What is the value of x?
## Solution
**Step 1:** Start with the equation x + 3 = 5x - 13.
**Step 2:** Subtract x from both sides to get 3 = 4x - 13.
**Step 3:** Add 13 to both sides to get 16 = 4x... | {"format": "cpt", "domain": "math", "subcategory": "algebraic_manipulation", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "4", "model_answer": "4", "method": "equation_solved"}, "taxonomy_key": "math/algebraic_manipulation/pure_arithmetic/integer_answer_only/easy"} |
00000168_cpt | ## Problem
You are given an m x n grid of integers and an integer k. You need to find the maximum sum of a k x k submatrix within the grid. If the grid is smaller than k x k in either dimension, return 0. The solution must efficiently compute this using a sliding window approach on the matrix grid to avoid recalculati... | {"format": "cpt", "domain": "code", "subcategory": "sliding_window", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 4, "failed": 0, "total": 4, "failing_case": ""}, "taxonomy_key": "code/sliding_window/matrix_grid/handle_edge_cases/medium"} |
00000169_cpt | ## Problem
A token starts on step 0 of a staircase. On turn 1, Maya moves the token up 1 step. On turn 2, she moves it up 2 more steps. On turn 3, she moves it up 3 more steps. She continues this pattern, adding one more step each turn. However, if the token ever lands exactly on step 10, she loses the game. The targe... | {"format": "cpt", "domain": "math", "subcategory": "sequences_and_series", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "5", "model_answer": "5", "method": "equation_solved"}, "taxonomy_key": "math/sequences_and_series/combinatorial_game/requires_substitution/easy"} |
00000170_cpt | ## Problem
Five friends — Aria, Ben, Cleo, Dan, and Eve — each picked exactly one activity from the set {Hiking, Ice skating, Jogging, Kayaking, Reading} and each activity was picked by exactly one person. Determine who picked which activity using these clues:
1. The set of people who picked an activity starting with... | {"format": "cpt", "domain": "reasoning", "subcategory": "set_logic", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "[]", "method": "set_match"}, "taxonomy_key": "reasoning/set_logic/logic_puzzle/unique_solution_required/medium"} |
00000171_cpt | ## Problem
You are given a list of `n` strings `patterns`, where each string represents a chain of equivalences between lowercase English words separated by the token `==`. Additionally, you are given a list of `m` strings `queries`, where each string is a comparison between two words separated by either `==` or `!=`.... | {"format": "cpt", "domain": "code", "subcategory": "union_find", "difficulty": "hard", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/union_find/string_parsing/handle_edge_cases/hard"} |
00000172_cpt | ## Problem
In a theoretical proof sketch, a mathematician claims that for a certain rational number x, the expression 3(x + 4) is always equal to 5x + 8. To verify this claim, she sets up the equation 3(x + 4) = 5x + 8 and solves for x. What rational number x makes this equation true?
## Solution
**Step 1:** First, ... | {"format": "cpt", "domain": "math", "subcategory": "algebraic_manipulation", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "2", "model_answer": "2", "method": "equation_solved"}, "taxonomy_key": "math/algebraic_manipulation/theoretical_proof_sketch/exact_rational_answer/e... |
00000173_cpt | ## Problem
A vault is secured with a triangular lock. The lock has 3 different colored keys arranged in a circle (red, blue, green). Any two colors can be swapped, but you never swap the same pair twice. Each swap moves you along a different edge of the color triangle. In how many distinct ways can you perform exactly... | {"format": "cpt", "domain": "math", "subcategory": "combinatorics", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "2", "model_answer": "2", "method": "equation_solved"}, "taxonomy_key": "math/combinatorics/finance_economics/geometric_intuition/easy"} |
00000174_cpt | ## Problem
You are given an m x n binary matrix `grid` where `0` represents water and `1` represents land. The grid completely surrounds the land, meaning the entire outermost border of the grid is water. Two land cells are connected if they are adjacent horizontally or vertically. A connected component of land cells ... | {"format": "cpt", "domain": "code", "subcategory": "union_find", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 3, "failed": 0, "total": 3, "failing_case": ""}, "taxonomy_key": "code/union_find/matrix_grid/handle_edge_cases/medium"} |
00000175_cpt | ## Problem
Consider the equation a + b + c + d = 15 where a, b, c, and d are positive integers. Two solutions are considered equivalent if one can be obtained from the other by swapping the values of the variables. For example, (1, 2, 3, 9) and (3, 1, 9, 2) are equivalent, but (1, 1, 4, 9) and (1, 4, 4, 6) are not. Ho... | {"format": "cpt", "domain": "math", "subcategory": "combinatorics", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "27", "model_answer": "27", "method": "equation_solved"}, "taxonomy_key": "math/combinatorics/pure_arithmetic/multiple_solutions_possible/medium"} |
00000176_cpt | ## Problem
A rectangle is divided into exactly 12 smaller squares of integer side lengths. The large rectangle has a width of 7 and a height of 6. The squares can be of various sizes. Let $x$ be the number of $1 \times 1$ squares used in this tiling. Find the maximum possible value of $x$.
## Solution
**Step 1:** Th... | {"format": "cpt", "domain": "math", "subcategory": "diophantine", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "2", "model_answer": "2", "method": "equation_solved"}, "taxonomy_key": "math/diophantine/competition_style/geometric_intuition/easy"} |
00000177_cpt | ## Problem
You are given a 0-indexed array of integers `nums` and an integer `k`. For each element in `nums`, in place, replace its value with the bitwise XOR of the original element and `k`. Return the modified array. This problem demonstrates applying bit manipulation over a specified interval range (the entire arra... | {"format": "cpt", "domain": "code", "subcategory": "bit_manipulation", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/bit_manipulation/interval_range/in_place_modification/easy"} |
00000178_cpt | ## Problem
In triangle ABC, a point P is located inside the triangle. It is given that angle PAB = 10°, angle PBA = 20°, angle PCA = 30°, and angle PAC = 40°. Find the measure of angle BPC.
## Solution
**Step 1:** Determine the angles of triangle ABC. Since angle PAB = 10° and angle PAC = 40°, angle A = 50°. Since a... | {"format": "cpt", "domain": "math", "subcategory": "geometry", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "120", "model_answer": "120", "method": "equation_solved"}, "taxonomy_key": "math/geometry/competition_style/multiple_solutions_possible/medium"} |
00000179_cpt | ## Problem
You are monitoring a data stream of characters. Each character is either a letter (indicating a data packet) or a comma (indicating a pause). You need to process this stream character by character and keep track of the longest contiguous sequence of letters (packets) you have seen so far at any point in the... | {"format": "cpt", "domain": "code", "subcategory": "simulation", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/simulation/string_parsing/streaming_online/easy"} |
00000180_cpt | ## Problem
You are given a list of integers `nums` and an integer `k`. You want to select a subset of indices such that for any two selected indices `i` and `j` (where `i < j`), the absolute difference `|nums[i] - nums[j]| >= k`. Your task is to find the maximum number of elements you can select. This is equivalent to... | {"format": "cpt", "domain": "code", "subcategory": "greedy", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/greedy/interval_range/integer_overflow_safety/medium"} |
00000181_cpt | ## Problem
A drone is delivering a package and needs to maintain a signal connection with a receiver on the ground. The drone travels in a straight horizontal line at a constant altitude of 12 kilometers. At its closest point of approach, the drone is directly over a point on the ground that is 5 kilometers horizontal... | {"format": "cpt", "domain": "math", "subcategory": "geometry", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "0", "model_answer": "0", "method": "equation_solved"}, "taxonomy_key": "math/geometry/word_problem_real_world/geometric_intuition/medium"} |
00000182_cpt | ## Problem
A biologist is testing a new water filter that removes contaminants. The filter contains 3 activated carbon layers and 2 UV light stages, each equally likely to be the component that clogs first during testing. If the filter fails to work properly only when a UV light stage clogs first, what is the probabil... | {"format": "cpt", "domain": "math", "subcategory": "probability", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "2/5", "model_answer": "2/5", "method": "equation_solved"}, "taxonomy_key": "math/probability/applied_science/exact_rational_answer/easy"} |
00000183_cpt | ## Problem
Five messengers — Alice, Bob, Charlie, Diana, and Eve — departed from headquarters on a mapped route through five checkpoints (positions 1 through 5, where position 1 departed first and position 5 departed last). Each messenger visited exactly one checkpoint in sequence. Using the temporal clues below, dete... | {"format": "cpt", "domain": "reasoning", "subcategory": "temporal_reasoning", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Charlie', 'Bob', 'Alice', 'Diana', 'Eve']", "method": "unique_match"}, "taxonomy_key": "reasoning/temporal_reasoning/map_na... |
00000184_cpt | ## Problem
Three friends—Alice, Bob, and Charlie—are standing in a single-file line, each wearing a hat of a different color: Red, Green, and Blue. They are ranked from front (1st) to back (3rd) of the line. Determine the order of the three friends from front to back. Clue 1: The person wearing the Red hat is somewher... | {"format": "cpt", "domain": "reasoning", "subcategory": "ordering_ranking", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Bob', 'Alice', 'Charlie']", "method": "unique_match"}, "taxonomy_key": "reasoning/ordering_ranking/hat_color/transitive_inferen... |
00000185_cpt | ## Problem
A positive integer x satisfies the following: when 3 is added to x, the result equals twice the quantity of x minus 4. What is the value of x?
## Solution
**Step 1:** Start with the equation x + 3 = 2(x - 4).
**Step 2:** Distribute the 2 on the right side to get x + 3 = 2x - 8.
**Step 3:** Subtract x fr... | {"format": "cpt", "domain": "math", "subcategory": "algebraic_manipulation", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "11", "model_answer": "11", "method": "equation_solved"}, "taxonomy_key": "math/algebraic_manipulation/competition_style/exact_rational_answer/easy"} |
00000186_cpt | ## Problem
You are given an array of integers `nums` and an integer `k`. You want to form groups of numbers where the difference between the maximum and minimum number in each group is at most `k`. Each number must belong to exactly one group. Return the minimum number of groups required.
## Solution
**Step 1:** Sor... | {"format": "cpt", "domain": "code", "subcategory": "sorting_sweep", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/sorting_sweep/interval_range/integer_overflow_safety/easy"} |
00000969_cpt | ## Problem
A number x satisfies the following: when 2 is subtracted from x, the result equals 3 times x minus 14. Find the value of x.
## Solution
**Step 1:** Start with the equation x - 2 = 3x - 14.
**Step 2:** Subtract x from both sides to get -2 = 2x - 14.
**Step 3:** Add 14 to both sides to get 12 = 2x.
**Ste... | {"format": "cpt", "domain": "math", "subcategory": "algebraic_manipulation", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "6", "model_answer": "6", "method": "equation_solved"}, "taxonomy_key": "math/algebraic_manipulation/pure_arithmetic/requires_substitution/easy"} |
00000970_cpt | ## Problem
A biochemist needs to test 4 different enzymes (A, B, C, D). Due to equipment limits, she tests only 2 at a time. The reaction result depends on the order enzymes are added. How many different ordered test-pairs can she run?
## Solution
**Step 1:** There are 4 enzymes available for the first addition.
**... | {"format": "cpt", "domain": "math", "subcategory": "combinatorics", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "12", "model_answer": "12", "method": "equation_solved"}, "taxonomy_key": "math/combinatorics/applied_science/multiple_solutions_possible/easy"} |
00000971_cpt | ## Problem
I am thinking of a number. When I multiply my number by 4 and add 5, I get the same result as when I multiply my number by 2 and add 11. What is my number?
## Solution
**Step 1:** Write the equation based on the problem: 4x + 5 = 2x + 11
**Step 2:** Subtract 2x from both sides to gather the variable term... | {"format": "cpt", "domain": "math", "subcategory": "algebraic_manipulation", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "3", "model_answer": "3", "method": "equation_solved"}, "taxonomy_key": "math/algebraic_manipulation/pure_arithmetic/exact_rational_answer/easy"} |
00000972_cpt | ## Problem
Maria is planting flowers in a circular garden bed. She plants the first flower and then plants one flower every 4 feet along the circular edge. The distance all the way around the circular garden bed is 36 feet. Maria continues planting flowers until she reaches the spot where she planted her first flower.... | {"format": "cpt", "domain": "math", "subcategory": "modular_arithmetic", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "9", "model_answer": "9", "method": "equation_solved"}, "taxonomy_key": "math/modular_arithmetic/word_problem_real_world/multiple_solutions_possible/easy... |
00000973_cpt | ## Problem
Three friends—Alice, Bob, and Charlie—are lining up to try on hats. Each person will put on a hat of a different color: Red, Blue, or Green. Their positions in line determine the order they try on hats. The clues are: (1) Bob puts on his hat before Alice. (2) Charlie puts on his hat before Bob. (3) Bob puts... | {"format": "cpt", "domain": "reasoning", "subcategory": "temporal_reasoning", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Charlie', 'Bob', 'Alice']", "method": "unique_match"}, "taxonomy_key": "reasoning/temporal_reasoning/hat_color/transitive_inf... |
00000974_cpt | ## Problem
Lena saves money each week. In week 1 she saves $2, in week 2 she saves $4, in week 3 she saves $6, and so on, increasing by $2 each week. After x weeks, her total savings reach exactly $72. How many weeks did it take?
## Solution
**Step 1:** The weekly savings form the arithmetic sequence 2, 4, 6, ..., w... | {"format": "cpt", "domain": "math", "subcategory": "sequences_and_series", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "8", "model_answer": "8", "method": "equation_solved"}, "taxonomy_key": "math/sequences_and_series/finance_economics/requires_factoring/easy"} |
00000975_cpt | ## Problem
Mia's geometric-themed coin display holds exactly 36 coins arranged in a rectangle. Each row has the same number of coins, and each column has the same number of coins, with more than one row and more than one column. A single-row or single-column display is not allowed. The number of rows times the number ... | {"format": "cpt", "domain": "math", "subcategory": "diophantine", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "6", "model_answer": "6", "method": "equation_solved"}, "taxonomy_key": "math/diophantine/finance_economics/geometric_intuition/easy"} |
00000976_cpt | ## Problem
Three friends — Alice, Bob, and Charlie — are scheduling back-to-back meetings. Each person meets exactly once, and the meetings are scheduled in three consecutive time slots (1st, 2nd, and 3rd). Use the following clues to determine the order of their meetings:
1. Bob's meeting is before Charlie's meeting.... | {"format": "cpt", "domain": "reasoning", "subcategory": "temporal_reasoning", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Alice', 'Bob', 'Charlie']", "method": "unique_match"}, "taxonomy_key": "reasoning/temporal_reasoning/scheduling/contradiction... |
00000977_cpt | ## Problem
Three friends — Alice, Bob, and Charlie — finished a race. Each finished at a different time, occupying first, second, and third place. Determine the exact finishing order (first to last) using these clues: (1) Alice finished before Bob. (2) Charlie finished before Alice. (3) Bob finished after Charlie.
##... | {"format": "cpt", "domain": "reasoning", "subcategory": "temporal_reasoning", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Charlie', 'Alice', 'Bob']", "method": "unique_match"}, "taxonomy_key": "reasoning/temporal_reasoning/logic_puzzle/small_domai... |
00000978_cpt | ## Problem
A botanical research team is studying two competing plant species, Species A and Species B, on a restored prairie. Species A currently covers 40 square meters and expands at a continuous rate of 8% per year. Species B currently covers 90 square meters but is declining due to a soil pathogen, losing 4% of it... | {"format": "cpt", "domain": "math", "subcategory": "logarithms_exponents", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "43046721*2**(1/3)*3**(2/3)/131072", "model_answer": "43046721*2**(1/3)*3**(2/3)/131072", "method": "equation_solved"}, "taxonomy_key": "math/logarit... |
00000979_cpt | ## Problem
A cybersecurity firm's intrusion detection system (IDS) monitors 1,000 identical servers. Each server independently has a 3% chance of being compromised on any given day. The IDS runs a diagnostic scan on each server. If a server is compromised, the scan correctly flags it with probability 4/5. If a server ... | {"format": "cpt", "domain": "math", "subcategory": "probability", "difficulty": "hard", "has_code": false, "verified": true, "verification": {"derived_answer": "60/157", "model_answer": "60/157", "method": "equation_solved"}, "taxonomy_key": "math/probability/word_problem_real_world/multiple_solutions_possible/hard"} |
00000980_cpt | ## Problem
Four digits A, B, C, D (each a different single digit 0-9) are being ranked from largest (1st) to smallest (4th). You know the following: (1) A is before B in the ranking (A > B). (2) C and A are adjacent in the ranking. (3) D is after C in the ranking (D < C). (4) B is after D in the ranking (B < D). (5) T... | {"format": "cpt", "domain": "reasoning", "subcategory": "ordering_ranking", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['C', 'A', 'D', 'B']", "method": "unique_match"}, "taxonomy_key": "reasoning/ordering_ranking/cryptarithmetic/requires_casework... |
00000981_cpt | ## Problem
Given a sorted array of integers `nums` and an integer `k`, remove all occurrences of `k` in-place and return the new length of the array. The order of the elements may be changed. It does not matter what you leave beyond the returned length.
Example:
If nums = [1, 2, 2, 3, 4, 5] and k = 2, the array becom... | {"format": "cpt", "domain": "code", "subcategory": "two_pointers", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/two_pointers/arrays_strings/two_data_structures/easy"} |
00000982_cpt | ## Problem
Maya bought a total of 8 financial assets consisting of shares of stock and bonds. Each share of stock costs $5 and each bond costs $2. If she paid exactly $25 for these 8 assets, how many shares of stock did she buy?
## Solution
**Step 1:** Let x be the number of shares of stock Maya bought.
**Step 2:**... | {"format": "cpt", "domain": "math", "subcategory": "diophantine", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "3", "model_answer": "3", "method": "equation_solved"}, "taxonomy_key": "math/diophantine/finance_economics/requires_substitution/easy"} |
00000983_cpt | ## Problem
In a combinatorial game, two players take turns. On each turn, a player rolls a fair 6-sided die (faces numbered 1 through 6) and then moves their token forward on a circular track of length $\pi$ units. The total distance $d$ a player moves in a turn equals $\sin(\text{roll})$ units. At a special bonus spa... | {"format": "cpt", "domain": "math", "subcategory": "trigonometry_identity", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "6", "model_answer": "6", "method": "equation_solved"}, "taxonomy_key": "math/trigonometry_identity/combinatorial_game/casework/easy"} |
00000984_cpt | ## Problem
Alice and Bob play a game on 21 stones arranged in a single pile. On each turn, a player removes 1, 2, 3, or 4 stones. Alice moves first. Under standard play, the player who removes the last stone wins. Before the game begins, Alice secretly designates one specific number k in {1,2,3,4} as her 'power number... | {"format": "cpt", "domain": "math", "subcategory": "optimization", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "4", "model_answer": "4", "method": "equation_solved"}, "taxonomy_key": "math/optimization/combinatorial_game/bounding_argument/medium"} |
00000985_cpt | ## Problem
You are given an array `nums` of non-negative integers and an integer `k`. In one operation, you can choose any element of the array and reduce it by 1 (to a minimum of 0). You want to apply at most `k` operations in total such that the maximum frequency of any value in the modified array is maximized. Retu... | {"format": "cpt", "domain": "code", "subcategory": "binary_search", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/binary_search/simulation_state/in_place_modification/medium"} |
00000986_cpt | ## Problem
Two players, Ana and Ben, take turns placing L-shaped tiles on a 4-by-6 grid. An L-shaped tile covers exactly 3 unit squares. Ana goes first, and the player who cannot place a tile without overlapping loses. The game ends in a draw if no tiles can be placed and the grid is exactly full. Assuming both player... | {"format": "cpt", "domain": "math", "subcategory": "diophantine", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "8", "model_answer": "8", "method": "equation_solved"}, "taxonomy_key": "math/diophantine/combinatorial_game/geometric_intuition/easy"} |
00000987_cpt | ## Problem
You are given a list of integers `nums` representing the IDs of items collected in a game, in the order they were picked up. You are also given an integer `k`.
You want to find the maximum number of *unique* items you can collect in a contiguous sequence (subarray) of exactly length `k`. If the list has fe... | {"format": "cpt", "domain": "code", "subcategory": "sliding_window", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/sliding_window/hashing_maps/two_data_structures/easy"} |
00000988_cpt | ## Problem
Alice and Bob play a game with a pile of N stones. On each turn, a player must remove a positive number of stones that is a divisor of the current pile size and is less than the current pile size. The player unable to move (when the pile has 1 stone) loses. For N = 1200, Alice goes first. Bob employs a stra... | {"format": "cpt", "domain": "math", "subcategory": "number_theory", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "601", "model_answer": "601", "method": "equation_solved"}, "taxonomy_key": "math/number_theory/combinatorial_game/requires_substitution/medium"} |
00000989_cpt | ## Problem
You are given a list of integers `nums` and an integer `k`. You want to find the maximum sum of any contiguous subarray of `nums` that has a length of exactly `k`. If the list has fewer than `k` elements, return 0. To solve this, you must process the elements in order by adding them to a queue. Once the que... | {"format": "cpt", "domain": "code", "subcategory": "bfs_dfs", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/bfs_dfs/stacks_queues/two_data_structures/easy"} |
00000990_cpt | ## Problem
You are given a list of integers `nums` and an integer `k`. You need to select a subset of elements from `nums` such that the product of the selected elements is exactly divisible by `k`. The subset can be empty if `k == 1` (since the empty product is 1, which is divisible by 1).
You need to modify the lis... | {"format": "cpt", "domain": "code", "subcategory": "backtracking", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 18, "failed": 0, "total": 18, "failing_case": ""}, "taxonomy_key": "code/backtracking/number_theory/in_place_modification/easy"} |
00000991_cpt | ## Problem
Let $N$ be the smallest positive integer such that $\frac{N^2+3}{N+2}$ is an integer. Let $R$ be the remainder when $N^2+3$ is divided by $N+2$. Find the value of $R$.
## Solution
**Step 1:** Perform polynomial long division on $(N^2+3)/(N+2)$. We can rewrite the numerator by adding and subtracting $4N$: ... | {"format": "cpt", "domain": "math", "subcategory": "algebraic_manipulation", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "7", "model_answer": "7", "method": "equation_solved"}, "taxonomy_key": "math/algebraic_manipulation/pure_arithmetic/bounding_argument/medium"} |
00000992_cpt | ## Problem
Two players, Alice and Bob, take turns placing a single coin on a 3-by-3 grid. Alice places red coins and Bob places blue coins. Alice goes first. The first player to get three of their colored coins in a straight line (horizontally, vertically, or diagonally) wins the game. If the entire 3-by-3 grid is fil... | {"format": "cpt", "domain": "math", "subcategory": "combinatorics", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "16", "model_answer": "16", "method": "equation_solved"}, "taxonomy_key": "math/combinatorics/combinatorial_game/geometric_intuition/easy"} |
00000993_cpt | ## Problem
Four scholars — Alma, Burt, Cleo, and Dax — each submitted a unique single-digit positive integer (1 through 9, no repeats) as their answer to a cryptarithmetic riddle. They are ranked 1st through 4th (1st = highest value, 4th = lowest value). Use the following clues to determine the exact ranking from 1st ... | {"format": "cpt", "domain": "reasoning", "subcategory": "ordering_ranking", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"n_solutions": 1, "derived_solution": "['Dax', 'Cleo', 'Alma', 'Burt']", "method": "unique_match"}, "taxonomy_key": "reasoning/ordering_ranking/cryptarithmetic/requir... |
00000994_cpt | ## Problem
You are monitoring a streaming sequence of sensor readings. You maintain a single integer `state` (initially 0) that tracks which of the `k` sensor channels have ever reported a value greater than 0. The channels are numbered from 0 to k-1. For each reading in the stream `nums`, you receive the channel inde... | {"format": "cpt", "domain": "code", "subcategory": "bit_manipulation", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/bit_manipulation/simulation_state/streaming_online/easy"} |
00000995_cpt | ## Problem
You are given an array of integers `nums` and an integer `k`. The array represents `n` isolated nodes where `nums[i]` is the value of node `i`. You must link these nodes together into `k` separate circular linked lists using Union-Find. For each integer `i` from `0` to `n-1`, you must union node `i` with no... | {"format": "cpt", "domain": "code", "subcategory": "union_find", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/union_find/linked_lists/no_extra_alloc/easy"} |
00000996_cpt | ## Problem
You are given an array of integers `nums` representing the start times of events, and a positive integer `k` representing the duration of each event. This means an event that starts at time `t` will occupy the interval `[t, t + k]` (inclusive of `t`, but it is considered active until `t + k`, at which point... | {"format": "cpt", "domain": "code", "subcategory": "sorting_sweep", "difficulty": "medium", "has_code": true, "verified": true, "verification": {"passed": 17, "failed": 0, "total": 17, "failing_case": ""}, "taxonomy_key": "code/sorting_sweep/simulation_state/o_1_space_required/medium"} |
00000997_cpt | ## Problem
The Republic of Numeria issues only three denominations of geometric banknotes, which are perfect squares with side lengths of distinct positive integers $a < b < c$. The face values of these notes are $a^2$, $b^2$, and $c^2$ Numerian dollars. The National Treasury mandates that any integer face value from ... | {"format": "cpt", "domain": "math", "subcategory": "modular_arithmetic", "difficulty": "hard", "has_code": false, "verified": true, "verification": {"derived_answer": "6", "model_answer": "6", "method": "equation_solved"}, "taxonomy_key": "math/modular_arithmetic/finance_economics/geometric_intuition/hard"} |
00000998_cpt | ## Problem
A triangular plot of land is priced at $3 per square foot. Two sides of the triangle meet at a right angle, with lengths of 4 feet and 6 feet. An investor wants to spend exactly $36 on a triangular plot with the same two side lengths. What is the maximum scale factor by which the two perpendicular sides can... | {"format": "cpt", "domain": "math", "subcategory": "geometry", "difficulty": "easy", "has_code": false, "verified": true, "verification": {"derived_answer": "1", "model_answer": "1", "method": "equation_solved"}, "taxonomy_key": "math/geometry/finance_economics/bounding_argument/easy"} |
00000999_cpt | ## Problem
You are given an array of integers `nums` and an integer `k`. You need to find the maximum sum of a contiguous subarray of `nums` that has a length of exactly `k`. If the array has fewer than `k` elements, return 0.
## Solution
**Step 1:** Check if the array length is less than `k`; if so, return 0.
**St... | {"format": "cpt", "domain": "code", "subcategory": "dynamic_programming", "difficulty": "easy", "has_code": true, "verified": true, "verification": {"passed": 18, "failed": 0, "total": 18, "failing_case": ""}, "taxonomy_key": "code/dynamic_programming/arrays_strings/o_n_time_required/easy"} |
00001000_cpt | ## Problem
A laboratory uses three independent diagnostic sensors, A, B, and C, to detect a specific pathogen in a test sample. Each sensor independently returns a positive result with probabilities 0.80, 0.70, and 0.60, respectively. To improve reliability, the laboratory's protocol declares a sample as 'positive' if... | {"format": "cpt", "domain": "math", "subcategory": "probability", "difficulty": "medium", "has_code": false, "verified": true, "verification": {"derived_answer": "0.957200000000000", "model_answer": "2393/2500", "method": "equation_solved"}, "taxonomy_key": "math/probability/applied_science/multiple_solutions_possible/... |
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GLM 5.2 Synthetic Dataset (Mega)
Generated by GLM 5.2 (glm-5.2-fp8-pp3, 3-node H20 cluster) with deterministic verification. Every record's answer is independently verified:
- Math: sympy re-derives the answer from the equation
- Code: sandboxed execution against oracle + property tests (17 cases each)
- Reasoning: brute-force enumeration confirms unique solution
Formats
| Format | Split | Records |
|---|---|---|
| CPT (continued pre-training) | data/cpt/ |
129 |
| SFT (supervised fine-tuning) | data/sft/ |
129 |
| Instruction (chat) | data/instruction/ |
129 |
| DPO (preference pairs) | data/dpo/ |
129 |
Total: 516 format-records from 129 verified generation units.
Domains
- Math: 58 (algebra, number theory, geometry, combinatorics, sequences, rate/work)
- Code: 53 (two pointers, binary search, DP, greedy, etc. — all executed & verified)
- Reasoning: 18 (ordering, temporal, set logic — all uniqueness-checked)
Provenance
- Model: GLM 5.2 (FP8, pipeline-parallel ×3 on H20 GPUs)
- Generation: model-in-the-loop with taxonomy-driven diversity (7,056 taxonomy points)
- Verification: 100% of answers independently re-derived
- Dedup: MinHash near-duplicate filtering (0 duplicates in this sample)
- Yield: ~32% of generation attempts passed verification
- Downloads last month
- 28