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Question: The outskirts of the capital are being actively built up in Berland. The company "Kernel Panic" manages the construction of a residential complex of skyscrapers in New Berlskva. All skyscrapers are built along the highway. It is known that the company has already bought n plots along the highway and is prepar...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
fb5599ca-245e-4f6b-8c53-364516a7aceb
Question: In a chemical laboratory, you are working on a project to analyze a solution containing lead and silver ions using redox titration. The solution is initially treated with oxalic acid to form a precipitate of lead oxalate and silver oxalate. This precipitate is then partially dissolved using a saturated soluti...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
3cf5af1e-90e0-48a1-8d9a-7ad788579c07
Question: A chemist is analyzing a solution containing various sulfur compounds in lower oxidation states ($\text{S}^{2-}$, $\text{SO}_3^{2-}$, and $\text{S}_2\text{O}_3^{2-}$). To determine the concentration of these ions, the chemist performs a series of redox titrations. First, a 20.00 cm$^3$ sample of the solution ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
51f8a8db-60f0-46f3-bfc9-79a599d78f1e
Question: You are given a string a, consisting of n characters, where n is even. Each character in a represents a different chemical element involved in a complex electrochemical reaction. Specifically, each character is one of 'A', 'B', or 'C'. A bracket sequence is a string containing only characters '(' and ')'. A r...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
def20f3e-f8fe-47e9-af12-ac3842dc2913
Question: During the silver smelting process, various chemical reactions occur at specific temperatures. Given two sequences $A = \{a_0, a_1, ..., a_{n-1}\}$ and $B = \{b_0, b_1, ..., b_{m-1}\}$, where each element represents a distinct temperature (in Kelvin) at which reactions take place. Sequence $A$ includes the te...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
0b31915d-6e64-4e1e-b49d-d7a28c52c110
Question: SmallR is conducting an advanced biological experiment to change the sex of dogs using supercritical carbon dioxide (scCO2). The effectiveness of the process depends critically on the state of scCO2, particularly its density and pressure. SmallR can control the density of scCO2 by adjusting both the temperatu...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
dc1994ce-bf13-4f12-9620-1baa5bfe664f
Question: Squid Eiko is working on a project involving both mathematical sequences and chemical buffers. She has a sequence \( a = \{a_0, a_1, \ldots, a_n\} \) where \( a_0 \) is an even integer and all other \( a_i \) for \( i > 0 \) are odd integers. She generates a new sequence \( b = \{a_i \cdot a_j \mid i < j\} \)...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
9487f210-b831-46ac-a481-21a5f7a6857e
Question: Let's define a split of n as a nonincreasing sequence of positive integers, the sum of which is n. For example, the following sequences are splits of 8: [4, 4], [3, 3, 2], [2, 2, 1, 1, 1, 1], [5, 2, 1]. The following sequences aren't splits of 8: [1, 7], [5, 4], [11, -3], [1, 1, 4, 1, 1]. The weight of a spli...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
ab42ab31-c6de-4425-a209-adc3b8553e5a
Question: In a chemical experiment, you have a series of test tubes numbered from 1 to $n$. Each test tube can either contain a molecule of iodine or remain empty. The iodine molecules can undergo reactions if they are placed in adjacent test tubes separated by exactly $x$ or $y$ positions. These reactions form stable ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
4968af08-897a-4ccf-af8a-1151942d27d5
Question: AquaMoon is working on a project involving the determination of fluoride ion concentrations using complex formation reactions. She has n friends standing in a row, each holding a test tube containing a different sample. The i-th friend from the left has a test tube with a concentration of fluoride ions denote...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
7ca15d10-35c0-421a-bcbf-01e6afe92556
Question: In Treeland, a country with n towns connected by n - 1 two-way roads forming a tree structure, there are 2k universities located in different towns. The Ministry of Education wants to connect each university with another one using high-speed cables to maximize the total length of the required cables. The leng...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
c1902288-f921-4fea-8fe6-6a991994d9f3
Question: At the request of a friend who started learning abacus, you decided to create a program to display the abacus beads. Create a program that takes a certain number as input and outputs a row of abacus beads. However, the number of digits of the abacus to be displayed is 5 digits, and the arrangement of beads fr...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
450f2bc3-4da7-48c7-b957-9630449dd88b
Question: Neko is playing with his toys on the backyard of Aki's house. Aki decided to play a prank on him, by secretly putting catnip into Neko's toys. Unfortunately, he went overboard and put an entire bag of catnip into the toys... It took Neko an entire day to turn back to normal. Neko reported to Aki that he saw ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
6586c822-cac9-4d23-b701-c1c4a21a7cf7
Question: A series of experiments are conducted to study the reaction kinetics of a substance Y forming from Z under varying conditions. Each participant in the experiment starts a reaction at x-minute intervals, with the first participant starting at time 0, the second at time x, and so on. The initial duration of eac...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
20ce47b1-a898-4372-a564-c4d445dd0e55
Question: Rohit loves to play poker in a quantum world where piles of poker chips represent quantum states. He has N piles of poker chips in a line, with the number of chips in pile i represented by the wave function coefficient ( c_i ). Rohit wants to rearrange the chips such that the number of chips in pile i+1 is ex...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
d8c1054b-ddd2-4987-9eaf-7456428534c1
Question: In the year of 2048, the Virtual Reality Massively Multiplayer Online Role-Playing Game (VRMMORPG), Code Art Online (CAO), is released. With the Chef Gear, a virtual reality helmet that stimulates the user's five senses via their brain, players can experience and control their in-game characters with their mi...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
b2973f71-5d27-443e-b573-1cf00e773ab0
Question: Two participants, Jamie and Casey, are competing in a high-speed text entry contest on the platform "Key Races". The challenge requires them to type a text of s characters. Jamie types each character in v1 milliseconds and has a network latency of t1 milliseconds. Casey types each character in v2 milliseconds...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
db8b4db5-6e26-4aa0-bdff-e5f07145e475
Question: The Little Elephant from the Zoo of Lviv likes lucky strings, i.e., the strings that consist only of the lucky digits 4 and 7. The Little Elephant calls some string T of the length M balanced if there exists at least one integer X (1 ≤ X ≤ M) such that the number of digits 4 in the substring T[1, X - 1] is eq...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
e86a8425-474f-461c-9ed3-351f6287c9ee
Question: You are working in a laboratory where you need to analyze a series of chemical samples, each containing lead and silver ions. You are given an array $a_1, a_2, \ldots, a_n$ representing $n$ distinct samples, where each sample $a_i$ is a pair of positive integers $(p_i, s_i)$ indicating the initial concentrati...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
ad70acf4-babf-4c7d-9c3f-624917e43ed7
Question: In a unique experimental setup, Chef has 'n' set of planes arranged in a manner that simulates the light absorption and energy conversion process akin to photosynthesis. When two planes intersect, they form a line. Chef is interested in determining the maximum number of such line intersections that can be obs...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
3836ec49-c751-4ae4-a696-0b231b097781
Question: In a complex biochemical network, you have n different types of molecules, each represented by a unique integer number a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^{18}). Molecules i and j (i ≠ j) can interact if and only if a_i AND a_j ≠ 0, where AND denotes the bitwise AND operation. Each molecule type has a known init...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
126f2825-622e-4f44-9a30-c9e184323a25
Question: Valya and Tolya are an ideal pair, but they quarrel sometimes. Recently, Valya took offense at her boyfriend because he came to her in a t-shirt with lettering that differs from the lettering on her pullover. Now she doesn't want to see him and Tolya is sitting in his room and crying at her photos all day lon...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
5ecf4c76-c502-4114-93be-414d0b0de2af
Question: Taro is conducting an experiment involving N unique flower species arranged in a row. Each species i (1 ≤ i ≤ N) has a distinct height h_i and a beauty value a_i. Furthermore, each species has an associated free energy change ΔG_i when it grows under standard conditions at a fixed temperature T. Taro wants to...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
5de9fa35-7cdb-48b1-aa6e-a88547f1aa5c
Question: In a laboratory experiment, scientists are studying the distribution of different types of molecules in a solution. There are $n$ molecules in the solution, and each molecule belongs to one of $n$ types, denoted by $a_i$ ($1 \le a_i \le n$). The goal is to prepare a sample containing molecules such that no tw...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
b2815405-8cb9-4604-b109-cee32745fb5f
Question: Inna and Dima decided to surprise Sereja with a really huge candy matrix, it's big even for Sereja! Let's number the rows of the giant matrix from 1 to n from top to bottom and the columns — from 1 to m, from left to right. We'll represent the cell on the intersection of the i-th row and j-th column as (i, j)...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
a4a2008e-e439-4b48-a6cc-4c2266515ad7
Question: Consider a game played on a field of size 1 x N cells. The cells are numbered from 1 to N. In the i-th cell, there are 2 positive integers - Ai and Bi. Moreover, imagine a fluorescent lamp filled with low-pressure noble gas, such as argon, and mercury vapor at even lower pressure. Electrical discharge in the ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
6182764a-071e-4192-b6a5-858682776d71
Question: A new median filter has been developed to enhance image processing by simulating the principles of chemical equilibrium and reaction reversibility. This filter aims to not only reduce noise but also ensure that the resulting image can be adjusted to favor either black or white pixels based on external conditi...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
22faf421-c7e0-4f6b-a4ac-ab303b1ec276
Question: In a recent study, researchers analyzed the kinetics of a free radical reaction involving a model compound analogous to coal, where the structure can be visualized as a network of polycyclic aromatic building blocks connected by short aliphatic bridges. During the thermal decomposition, various radicals are g...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
a8103c7d-29b8-4c9a-88e6-9d6e6de28e48
Question: In the game 'Divisor is the Conquerer', you draw N cards (1 ≤ N ≤ 52) from a deck of playing cards, each with a rank between 1 and 13. You play the cards according to specific rules to win the game. However, to add complexity, let's introduce a dynamic factor based on the steady state approximation from chemi...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
052757d8-6a1a-4c8d-a5bf-b961277b2abc
Question: In a simulated nuclear reactor model, the state of a reactor core is represented by a sequence of 64 flags, each representing whether a specific nuclear reaction is active (ON) or inactive (OFF). The reactor core is composed of various isotopes, each requiring a specific configuration of active reactions to m...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
60c57cfd-ce72-4431-b48f-c6392e988b98
Question: In a high-tech laboratory, you are developing a program for a robot navigating through a sophisticated labyrinth that simulates the inner workings of a fluorescent lamp. The labyrinth is structured as an N × M grid of cells, with some cells containing walls, doors, keys, and exits. Adjacent cells may be separ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
0eefece5-6857-4204-af2c-b7e46d6f067d
Question: You are given an unrooted tree with $n$ vertices representing a network of chemical reactors. Each reactor can perform a reversible water-gas-shift (WGS) reaction, $CO + H_2O \rightleftharpoons CO_2 + H_2$, under specific initial conditions. There is a hidden reactor $x$ in this network that you are trying to...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
6110bc3c-c74c-4093-8e6e-7a45f1de3bb0
Question: Mishka is trying to avoid being kicked out of the university and needs to pass his final exam in thermodynamics and chemistry. The professor has given him a peculiar task related to the behavior of carbon dioxide under various pressures and temperatures. There are n classes of the subject during the semester,...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
a8aafcbf-9c65-4698-96ab-5549108599b0
Question: AtCoDeer the deer has N cards with positive integers written on them. Each card represents a different chemical element, and the number on the i-th card (1 ≤ i ≤ N) is a_i, representing the atomic mass of the element. AtCoDeer wants to create a compound with a total mass of at least K. He defines a subset of ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
a742e37c-6269-488e-9b85-f6d505d1fe5e
Question: There was an epidemic in Monstropolis and all monsters became sick. To recover, all monsters lined up in queue for an appointment to the only doctor in the city. Soon, monsters became hungry and began to eat each other. One monster can eat another monster if its weight is strictly greater than the weight of t...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
29b2ca81-536e-4861-a9dc-7f48ef4801eb
Question: In a laboratory setup, there are five sealed containers labeled A, B, C, D, and E, each containing various ideal gases at a constant temperature of 298 K and different pressures. Each container holds a set of unique molecules represented by integers. The operations u (union), i (intersection), d (difference),...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
a619fa7f-7ab6-4393-a220-a1c1dc2421c7
Question: You have an array a with length n, you can perform operations. Each operation is like this: choose two adjacent elements from a, say x and y, and replace one of them with gcd(x, y), where gcd denotes the greatest common divisor. Consider the scenario where you mix equal volumes of the acid solution with a bas...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
00d19208-a3fb-42d9-9e26-612358e6c80d
Question: In a cutting-edge bioinformatics study, researchers are analyzing the structural integrity of molecular chains represented by strings of curly brackets. These chains are essential for understanding the stability and functionality of certain biological molecules. The task is to determine the balance of these c...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
aa44dcbc-811e-4dc9-aa6b-20216c5113e6
Question: A championship is held in Berland, where n players participate. Each player i has a_i (a_i ≥ 1) tokens and a unique electrochemical compound with a specific Gibbs free energy change ΔG_i associated with its formation. The championship consists of n-1 games, which are played according to the following rules: ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
d6ba294f-5e8e-4b6a-b082-b5fed0eb9a52
Question: In a biochemical synthesis process, a complex molecular network is formed through a series of reactions involving substrates X and Y, producing a product P. The biochemical reactor maintains uniform conditions throughout, ensuring that the concentration of any substance is consistent across the reactor. The r...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
b6d0c223-e4fc-4403-8c6d-93f9213f25c4
Question: The Fair Nut has recently conducted an experiment where he wrote $k$ strings of length $n$, consisting of letters "a" and "b", under varying humidity conditions. Each string was generated such that it was lexicographically not smaller than string $s$ and not bigger than string $t$. He noticed that the humidit...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
10793e93-859e-4170-8082-9922e9071c69
Question: Alperen is exploring a grid-based environment starting from the point $(0,0)$. He is given a series of commands encoded in a string $s$ of length $n$, where each command corresponds to a specific move. The commands are as follows: - If $s_i = L$, then move one unit left; - If $s_i = R$, then move one unit ri...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
2ac8f49a-0586-4736-8b84-7a580dc64bf2
Question: Gildong is working on a project involving radioactive isotopes and permutations. He has a series of nuclear reactions and wants to simulate their decay patterns using sequences of integers. Each integer in the sequence represents the concentration of a different radioactive isotope after a certain number of d...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
d5d663c3-1f85-48e6-a8d5-9a7ca2bf3dbc
Question: Bear Limak studies a network of ancient scrolls. Each scroll is considered a 'member' of the network, and two scrolls can be 'friends' if they were found in the same location during an archaeological dig. The network is considered 'reasonable' if it satisfies the following condition: For every three distinct ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
ad2b6c5d-a6b8-45f5-a56f-1bcaed7465c8
Question: Twin adventurers Rin and Len are searching for treasure in the Mirror Cave. The cave has two pairs of rooms, the Hall of Mirrors, and an expensive treasure lies behind the door of the room. For convenience, each of the two rooms is considered to have W × H cells arranged in a grid pattern. The outside of the ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
5bfc67e2-1468-45c2-b596-e1c8ec04c0c0
Question: The town consists of $n$ districts, each belonging to a distinct bandit gang denoted by $a_i$. No roads exist between districts initially. As the mayor, you must construct $n-1$ two-way roads connecting all districts such that no two directly connected districts belong to the same gang. However, the construct...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
ecbf8b27-8d8b-4b6d-8aaa-cdcece03f761
Question: Takahashi wants to be a member of a web service that requires a unique ID. He attempted to register with the ID S, which is already taken. To generate a new ID, he appends one character to the end of S, resulting in the ID T. Takahashi is interested in understanding the stability of certain chemical species i...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
b51c0aa7-e7e2-4478-961f-d96a27fd7eb6
Question: Xenia likes puzzles very much. She is especially fond of the puzzles that consist of domino pieces. Look at the picture that shows one of such puzzles. A puzzle is a 3 × n table with forbidden cells (black squares) containing dominoes (colored rectangles on the picture). A puzzle is called correct if it meet...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
29713e19-8956-4d74-a844-beea52e1031b
Question: ICPC is developing a new mobile phone model equipped with advanced communication tools. To meet user demands, the phone must have efficient text input software. The phone's keypad includes buttons 2-9, each mapped to multiple letters. Given a dictionary and a sequence of button presses, your task is to determ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
9b401220-05d0-4425-a1f6-f6ea29ee164a
Question: In the study of superacids, scientists often analyze the behavior of solutions containing these extremely powerful acids. Consider a scenario where a researcher is working with a mixture of hydrogen fluoride (HF) and antimony pentafluoride (SbF₅), known to form solvated protons. To ensure accurate measurement...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
84dc8c64-306e-496c-91c9-76010a7db5b2
Question: A long time ago in some far country lived king Copa. After the recent king's reform, he got so large powers that started to keep the books by himself. The total income A of his kingdom during 0-th year is known, as well as the total income B during n-th year (these numbers can be negative — it means that ther...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
1505f17a-2c50-4eac-95d9-756fdb718205
Question: In a scientific research facility, a team of linguists and chemists are collaborating on a project involving oxide-ion conductors. The chemists are conducting experiments with an oxygen pump, while the linguists are documenting the languages spoken by the researchers. To ensure effective communication, they n...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
3e28d03f-7abf-4031-84d4-b9f191f13469
Question: Researchers studying ancient biological samples use logical expressions to model the presence or absence of specific isotopes. Implication is a function of two logical arguments, its value is false if and only if the value of the first argument is true and the value of the second argument is false. Implicatio...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
b36ad017-5759-4aec-9ade-eb52fe8aa1cd
Question: Consider a sequence of N positive integers A_1, A_2, \ldots, A_N, where each integer represents the energy level of a photon absorbed by a photosynthetic protein. You are also given a positive integer K, which denotes a specific quantum state transition threshold. Your goal is to determine the number of non-e...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
ff6a1f94-2da5-40a1-8d8d-b7d90c012229
Question: Let's solve the puzzle by programming. The numbers n x n are arranged in a grid pattern. Some of the numbers are circled and we will call them the starting point. The rules of the puzzle are as follows: * Draw one line that goes vertically and horizontally from each starting point (cannot be drawn diagonall...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
baca999f-2aaf-4e5a-ae26-b74081c235e1
Question: A boy PCK has N straight iron bars, which are serially indexed. Unfortunately, the first M bars (0 ≤ M ≤ N) among them were bent during transportation. They all suffered a perpendicular bend at one point. He plans to make a set of rectangular parallelepipeds (RPs) using a subset of these bars. Specifically, h...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Mr. KM, the mayor of KM city, is planning to construct a new elementary school on a polygonal plot of land. The boundary of the site has a simple polygonal shape without self-intersection, and the track can touch the boundary. Note that the boundary might not be convex. To reinforce the racetrack, a special a...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Memory match is a single-player game which employs a set of 2M cards. Each card is labeled with a number between 1 and M on its face. For each number i (1 ≤ i ≤ M), there are exactly two cards which have the number i. At the start of the game, all cards are shuffled and laid face down on a table. In each turn...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: There is a line with 1000 cells numbered from 1 to 1000 from left to right and N coins placed on it. Coin i is placed at cell Xi, and no two coins are placed at the same cell. Each coin represents a molecule of trans-cinnamic acid that can isomerize under ultraviolet irradiation into either cis-cinnamic acid ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: The lunar rover has landed on planet X and faces an obstacle represented by a permutation $p$ of length $n$. To clear the obstacle, the robot must transform $p$ into the identity permutation (where $p_i = i$ for all $i$). The robot can perform the following operation multiple times: select two indices $i$ and...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Consider a system where permutations of size n represent possible molecular arrangements of a gas mixture. Each position i in the permutation represents a molecule, and pi represents its energy level. We define a position i as 'stable' if the absolute difference between the molecule's energy level and its pos...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Little penguin Polo has an n × m matrix representing concentrations of a substrate in different compartments of a biochemical reactor. Each compartment can be indexed by (i, j), where the concentration at position (i, j) is denoted as aij. Polo wishes to understand the behavior of an enzyme in this reactor un...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: King Arthur has arranged n knights around a circular table, each in either a good or bad mood, represented by 1 and 0 respectively. Merlin predicts that a fortunate month will follow if a regular polygon can be formed with knights in good mood at all vertices. However, the formation of such a polygon is affec...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Quan_Lank is fascinated by both awesome numbers and chemical kinetics. He defines a nearly awesome number as a number where the count of awesome digits, denoted as $N$, evolves according to a simplified chemical reaction model. In this model, the awesome digits can either persist or transform into non-awesome...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: You are given a set of n vectors on a plane representing the velocity vectors of gas molecules in a volcanic gas sample. For each vector you are allowed to multiply any of its coordinates by -1. Thus, each vector vi = (xi, yi) can be transformed into one of the following four vectors: * vi1 = (xi, yi), * vi...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: There are N sightseeing spots on the x-axis, numbered 1, 2, ..., N. Spot i is at the point with coordinate A_i. It costs |a - b| yen (the currency of Japan) to travel from a point with coordinate a to another point with coordinate b along the axis. The travel paths are affected by the presence of laumontite, ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: A chemist is conducting experiments to synthesize a specific compound and records various parameters for each trial. The mass of the synthesized product $m$ is noted, along with the theoretical yield $T$ based on stoichiometry. The melting point $P$ of the product is also measured to verify its purity. A posi...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: This is the hard version of Problem F. The only difference between the easy version and the hard version is the constraints. We will call a non-empty string balanced if it contains the same number of plus and minus signs. For example: strings '+--+' and '++-+--' are balanced, and strings '+--', '--' and '' a...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: In the North Pole, Santa Claus and his assistant Elf are tasked with clearing the roads connecting huts to ensure efficient travel for delivering future presents. The North Pole consists of n huts connected by m roads, forming a network where one can travel between any two huts using exactly one simple path. ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: You have $n$ distinct microscopic steel balls $(x_1, y_1),\ldots,(x_n,y_n)$ on a plane, each representing a molecule of a Blue Copper Protein (PC). Each molecule can exist in one of two states: oxidized (Cu(II)) or reduced (Cu(I)). Initially, some molecules are in the oxidized state and others in the reduced ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Consider a diatomic molecule with vibrational energy levels described by the harmonic oscillator model. You are given an array a of 2n distinct integers representing these energy levels. Your task is to arrange these energy levels in a circular sequence such that no energy level is equal to the arithmetic mea...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Petya, now deeply interested in both physics and biochemistry, has been given a unique puzzle by his teacher Anna V. The puzzle involves a half-decay tree intertwined with protein sequencing experiments. A half-decay tree is a complete binary tree with height h. The height of a tree is defined as the length...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Chef is organizing a science fair where participants need to solve a complex puzzle involving both mathematics and chemistry. Each participant is given a positive integer N and must find the maximum sum of distinct numbers such that the Least Common Multiple (LCM) of all these numbers is N. However, there's a...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: A team of geologists has uncovered a rare zircon mineral specimen that holds clues about the Earth's early history. To understand the mineral's composition, they need to reconstruct the sequence of atomic configurations within it, represented by a permutation $p$ of length $n$. Each element in the permutation...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Vasya, a quantum physicist, is shopping at a futuristic store where goods are priced based on their ionization energy levels. Each good corresponds to a hypothetical atom, and its price is determined by the ionization energy required to remove the electron from the atom's ground state. Today, the store offers...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: A journey through the cosmic dungeon When I woke up, Mr. A was in a pitch-black room within a cosmic dungeon. This dungeon represents various stages of the universe's cooling process, from the hot and dense early universe to the present day. You couldn't know which room A got lost in, but fortunately he got ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: A chemist has prepared strontium peroxide ($\text{SrO}_2$) and wishes to determine its purity and peroxide content through a series of titrations. The preparation involves reacting strontium chloride hexahydrate ($\text{SrCl}_2 \cdot 6\text{H}_2\text{O}$) with hydrogen peroxide ($\text{H}_2\text{O}_2$) and am...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: In a haunted laboratory, $ N $ ghosts are arranged in a line, each holding a vial of a unique essential oil. Initially, the $ i $th ghost is facing left if $ U_i $ is 'L' and facing right if it is 'R'. You can command each ghost to turn around, incurring a fear cost of $ A_i $. When a ghost turns around, it c...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: You are organizing a special edition of the AtCoder Janken competition, where players engage in a series of rock-paper-scissors matches across multiple playing fields. The competition takes place in a laboratory setting where bromine formation from bromate and bromide ions is being studied. Specifically, the ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Farmer John has just given the cows a program to play with! The program contains two integer variables, x and y, and performs the following operations on a sequence a_1, a_2, ..., a_{n} of positive integers representing the concentrations of a certain substrate in a biochemical reaction. Initially, x = 1 and ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Polycarp has been working tirelessly on coding problems and now needs to rest and recharge his energy. To do this, he uses a special device that absorbs light energy and converts it into usable energy for his body. Polycarp needs to absorb a total of $a$ units of usable energy to feel refreshed. The device st...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Big P is fairly good in mathematics and chemistry. His teacher has asked him to add two numbers during a laboratory experiment. However, Big P sometimes writes a '6' as a '5' and vice versa while recording his observations. Given two numbers, A and B, representing the initial concentrations of two substances ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Arseny is hosting a chemistry-themed party where guests are categorized based on their knowledge of specific chemical reactions and solubility properties of salts. Each guest has expertise in either the solubility of calcium salts or specific chemical reactions involving these salts. Arseny wants to ensure th...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Carousel Boutique is busy again! Rarity has decided to visit the pony ball and she surely needs a new dress, because going out in the same dress several times is a sign of bad manners. First of all, she needs a dress pattern, which she is going to cut out from the rectangular piece of the multicolored fabric....
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: In a special school canteen, there are n students lined up in front of a magical bun stall. The buns aren't ready yet, and the line is undergoing some changes influenced by magical energies. Each student has a unique magical potential, and the line rearranges based on these potentials. Additionally, each stud...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem? You have a perfect binary tree of $2^k - 1$ nodes — a binary tree where all vertices $i$ from $1$ to $2^{k - 1} - 1$ have exactly two children: vertices $...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
39d08645-c252-427a-8f51-77e0ce34a4ea
Question: A chemist is preparing a series of experiments to study the iodination of acetone. For each experiment, the chemist needs to create N solutions of acetone with non-negative integer concentrations (in millimoles per liter), denoted as A_1, A_2, ..., A_N. These concentrations must meet the following criteria: ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: In a mystical forest, Mr. Hagiwara, a witch, has cast spells that create N magical barriers represented by line segments on the ground. These barriers enclose various areas, forming distinct holes. Two holes are considered the same if they overlap or touch at any point other than their vertices. Mr. Hagiwara'...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: The campus has m rooms numbered from 0 to m - 1. Each room contains a different compound, labeled C_i, where i ranges from 0 to m - 1. The x-mouse lives in the campus and each second moves from room i to the room i ⋅ x mod{m}. The starting position of the x-mouse is unknown. The x-mouse reacts with the compou...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: You are given a string s consisting of n characters, where each character represents a type of bioorganic substance involved in a series of redox reactions during photosynthesis. These characters are among the first k lowercase letters of the Latin alphabet. Each substance can either be transformed through an...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Nauuo is a girl who loves traveling. One day she went to a tree, Old Driver Tree, literally, a tree with an old driver on it. The tree is a connected graph consisting of n nodes and n-1 edges. Each node has a color, and Nauuo will visit the ODT through a simple path on the tree in the old driver's car. Nauuo ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Calendars in widespread use today include the Gregorian calendar, which is the de facto international standard, and is used almost everywhere in the world for civil purposes. The Gregorian reform modified the Julian calendar's scheme of leap years as follows: Every year that is exactly divisible by four is a...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Kostya likes Codeforces contests very much. However, he is very disappointed that his solutions are frequently hacked. That's why he decided to obfuscate (intentionally make less readable) his code before upcoming contest. To obfuscate the code, Kostya first looks at the first variable name used in his progr...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
656fe974-ecde-4460-ad35-ec97b5e1732a
Question: The robot is situated on a checkered rectangular board of size $n \times m$ ($n$ rows, $m$ columns). The rows are numbered from $1$ to $n$ from top to bottom, and the columns from $1$ to $m$ from left to right. The robot can move from its current cell to one of the four adjacent cells. The sequence of command...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Takahashi is preparing to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper. To ensure high-quality printing, Takahashi uses a constant-flow reactor to synthesize a specialized ink. The reactor's volume and reaction rate constants are crucial for maintain...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: Little Shino is conducting experiments with an oxygen sensor using a solid electrolyte. She is interested in how the electromotive force (EMF) generated by the sensor changes with different oxygen partial pressures at the cathode and anode. She hypothesizes that the EMF is related to the sum of the last four ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
18765f14-a476-48c9-b3f6-7bb745265d11
Question: Mr. B, an enthusiastic chemist and competitive programmer, has decided to combine his passions by creating a Brainf*ck program that simulates a chemical experiment. In this experiment, a mixture of calcium salts (40.0% CaCO₃, 5.0% CaCl₂, and 55.0% CaSO₄) reacts with hydrochloric acid (HCl) to produce carbon d...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
1e677c60-05af-458b-aa34-021692fb768c
Question: You are going to work in Codeforces as an intern in a team of n engineers, numbered 1 through n. You want to give each engineer a souvenir: a T-shirt from your country (T-shirts are highly desirable in Codeforces). Unfortunately, you don't know the size of the T-shirt each engineer fits in. There are m differ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: A metal rod initially free of any impurities is represented as a straight line colored in white. Over time, segments of black paint, representing brass deposits, are added on it one by one. Each brass deposit can be dissolved in nitric acid, releasing copper and zinc ions into a solution. These ions can then ...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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Question: In a botany class, students are studying the cultivation techniques of peaches and apples. They mistakenly wrote descriptions of peaches and apples in reverse in their notes. Each student has written a paragraph describing either the cultivation techniques of peaches or apples. Your task is to write a program...
cc-by-4.0
{ "category": "Nemotron-Pretraining-InfiniByte-Reasoning", "models_used": "QwQ-32B" }
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