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Question: In a chemistry lab, Jury is tasked with determining the concentrations of Fe³⁺, Zn²⁺, Cr³⁺, and Cu²⁺ ions in four separate solutions. Each second, a titration step is required for one of the solutions, indicated by a black square appearing on the corresponding strip of a touchscreen device. The amount of calo... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | f1b9cb40-2830-46d8-9bfe-b169b1e152ed |
Question: The wizard of Berland is preparing for a grand tour in his Blue Helicopter, visiting cities connected by bidirectional roads. The wizard is also deeply interested in radioactive decay chains and the transformation of nuclides. For his tour, he wants to plan as many episodes as possible, adhering to certain co... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 13019c9f-dff3-4700-8639-b634efdacea9 |
Question: A cosmic fighting tournament takes place on a distant planet with a unique gravitational field. $n$ athletes, each with a unique strength level $a_i$ where $1 \leq a_i \leq n$, compete in a series of fights. The athletes line up in ascending order of their IDs and fight in rounds where the first two athletes ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 3e1ea146-b398-4399-a138-fbbd16812005 |
Question: Duff, the queen of her country, Andarz Gu, continues to challenge her minister, Malek, with programming tasks. She has provided him with a sequence representing the methylation levels of side chains in a protein, consisting of n non-negative integers, a1, a2, ..., an. Each integer ai represents the level of m... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | d1394efc-2512-4a6c-ab45-757e193ad44f |
Question: To celebrate the innovative spirit in IT City, a special award ceremony is organized where local IT companies are honored with stars covered in gold. The gold plating process involves a series of chemical reactions akin to the bromination of methane, where intermediate species and rate constants play a crucia... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ec408cc9-22a7-49f5-a400-6f01a1896326 |
Question: Ayan's favourite musical instrument is the keyboard. He practices regularly as well, you can hear him playing even at 3 or 4 in the night.
Unfortunately, he got into a fight in his room and his keyboard was damaged beyond repair. However, being a rich fellow he quickly ordered another one.
But this time he fe... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 190ff234-7332-4b03-ae4d-c34bb9c150a1 |
Question: Given two circles A and B in a two-dimensional plane, where circle A has center (x_A, y_A) and radius r_A, and circle B has center (x_B, y_B) and radius r_B, these two circles do not intersect internally. Consider a set of circles S such that each circle in S touches both A and B externally and does not inter... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 82848db7-776d-4e19-9e21-090a45894a02 |
Question: Himu is planning a long drive with his girlfriend across N cities, where each city is directly connected to every other city by bidirectional roads. The length of the road connecting any two cities i and j is determined by the XOR operation on their city numbers, i.e., i XOR j. Himu aims to select the longest... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 7ba1bde1-0bcc-41b7-80a2-84122d080600 |
Question: William is experimenting with chemical reactions involving lead and silver compounds to determine their concentrations in various solutions. He records his experimental steps in a nested list format, where each step is an integer corresponding to a specific reaction or measurement. A valid nested list is any ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | f4486b65-8c39-48f9-9b94-a13d5a77f7f2 |
Question: In a galaxy far, far away, Lesha the student has just got to know that he has an exam in two days. As always, he hasn't attended any single class during the previous year, so he decided to spend the remaining time wisely. Lesha knows that today he can study for at most a hours, and he will have b hours to stu... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 1d406742-5281-494a-81b9-69b9aa8e8879 |
Question: Bessie is planning a vacation! In Cow-lifornia, there are n cities, with n-1 bidirectional roads connecting them. It is guaranteed that one can reach any city from any other city. Bessie is considering v possible vacation plans, with the i-th one consisting of a start city a_i and destination city b_i. It is ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 211b32b9-b1e4-4363-8a78-5caf536e331f |
Question: A scientist is conducting experiments with N different chemical solutions arranged in test tubes labeled from 1 to N. The scientist has made M observations about the reactivity distances between pairs of solutions. Each observation is given in the form (L_i, R_i, D_i), meaning the reactivity distance between ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 47037d4a-4aaa-40b5-a284-1c4feaae81d3 |
Question: Miroslav is preparing a special dish called shashlik using a novel cooking technique involving boron-oxygen compounds. He arranges n skewers parallel to each other, numbered from 1 to n in order from left to right. To enhance the taste, he uses a special method where applying the cooking tool to skewer number... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 20b19cbd-5181-4eb1-9728-8b3ad5546f46 |
Question: Consider a chemical reaction involving the decomposition of a complex organic molecule X into simpler molecules Y and Z through the formation of radicals R1 and R2. The reaction mechanism is given as follows:
$X \xrightarrow{k_1} R1 + R2$ (slow)
$R2 + X \xrightarrow{k_2} Y + W$ (fast)
$R1 + X \xrightarrow{k_... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | fb4dfe2b-1101-45a8-b4d6-88b069b543ae |
Question: You are working with a large array of 2^{30} molecules, indexed from 0 to 2^{30}-1, each represented by an integer a_i (0 ≤ a_i < 2^{30}). These molecules are involved in a series of chemical reactions catalyzed by a zeolite similar to laumontite, which affects the stoichiometry and introduces impurities. You... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 426a7640-de12-4f2b-9580-e428d599f370 |
Question: Rick is stranded in a post-apocalyptic world surrounded by walkers. He has an advanced butane-oxygen fuel cell that can generate electricity to power his high-tech rifle. Each shot from the rifle consumes 0.5 volts of electricity. Rick needs to kill walkers before they reach him; each walker requires one shot... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 95dbfdca-dea3-4a24-b5c0-4998c7deabe5 |
Question: Mr. John is conducting a chemical experiment where he measures the concentration changes of a reactant over time. The reactant decomposes following second-order kinetics. He records a series of concentrations at different time intervals. For each pair of adjacent concentrations, he wants to determine the leas... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 145e1ba9-6a91-47c9-841a-bcc3df63ee83 |
Question: Jack is a great mathematician and chemist. He loves to solve both series and chemical problems. Stuart gave Jack a series and a chemistry experiment to solve using a computer program. However, Jack doesn't know how to code.
The series is:
1 + (a1).(x)^1 + (a2).(x)^2 + (a3).(x)^3 +........+(an).(x)^n
And th... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 03605e21-63b4-42e2-9338-1db10c7be682 |
Question: Snuke is conducting an experiment involving the assembly of a two-row rectangular structure using tetromino-based components. He possesses various quantities of I-, O-, T-, J-, L-, S-, and Z-tetrominos, each with different production schedules. The structure must be constructed such that each row is 2K units ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 6eefb081-e4ec-4aaa-b191-7f738dd3abb8 |
Question: Squirrel Liss is studying sequences and decay chains in her lab. She thinks n integers a1, a2, ..., an are good. Each good integer represents a unique nuclide in a decay chain, where the atomic number increases by 1 in each subsequent step starting from a base nuclide.
Now she is interested in good sequences... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 9a05fb7d-4901-43b7-a5a3-7d2993ee56ae |
Question: In an advanced experimental setup, a square board, consisting of n rows and n columns, is used for a unique coloring process. Each tile in it should be colored either white or black. Simultaneously, an electrochemical reaction takes place where copper is lost from the anode as copper atoms are converted to co... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | e34688de-0c43-4de1-a290-57b2c7287c44 |
Question: SmallY has devised a sophisticated variant of the classic Tower of Hanoi puzzle. The puzzle involves three rods and n disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical sh... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 28ba50fe-156f-4c61-9221-0d086ab0a058 |
Question: You've recently stumbled upon the remains of a ruined ancient city. Luckily, you've studied enough ancient architecture to know how the buildings were laid out. The city had n buildings in a row. Unfortunately, all but the first two buildings have deteriorated. All you can see in the city are the heights of t... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 964ad38f-1ae3-48ea-913d-6181dc97448e |
Question: Arcady's apple-tree again fruits once per year, with n inflorescences numbered from 1 to n. Inflorescence 1 is at the base, and inflorescence i (i > 1) is connected to inflorescence p_i (p_i < i). Each apple starts rolling down to the base every second, with apples in the same inflorescence annihilating each ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 2833a648-796f-4b55-ac31-6a8370e4c94a |
Question: Two rival cities near a river decide to reclaim land from the river to expand their territories. The river can be represented as a grid with r rows and two columns, where each cell represents a rectangular area. Rows are numbered 1 through r from top to bottom, and columns are numbered 1 and 2. Initially, all... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | b15b90ab-0d26-4bac-b27a-ed7901440f44 |
Question: A geologist is analyzing a grid-like landscape of n rows and n columns, where each cell can either be barren (represented by 'B') or part of a mud volcano (represented by 'M'). The geologist aims to create exactly k distinct regions of mud volcanoes, where each region forms a contiguous cluster of 'M' cells c... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | be180623-d5db-43de-84de-c9529b7ffdef |
Question: You might have heard about our new goodie distribution program aka the "Laddu Accrual System". This problem is designed to give you a glimpse of its rules. You can read the page once before attempting the problem if you wish, nonetheless we will be providing all the information needed here itself.
Laddu Accr... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 9a8dc106-d8b2-4e39-a80f-188dc255c9e3 |
Question: The kingdom of Lazyland is the home to n idlers. These idlers are incredibly lazy and create many problems for their ruler, the mighty King of Lazyland. Today, k important jobs for the kingdom (k ≤ n) should be performed. Every job should be done by one person and every person can do at most one job. The King... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 37a41999-a146-4b36-acdc-c2df5a7ae7b7 |
Question: Eugene, the coach of a hockey team, is selecting a starting lineup for an important match, consisting of one goaltender, two defenders, and three forwards. Eugene places significant importance on the visual appeal of the team on the ice, requiring that the jersey numbers of any two players in the starting lin... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 6d127340-5a19-4e3d-8b89-f3d450ed5a09 |
Question: The programming competition season has already started and it's time to train for ICPC. Sereja coaches his teams for a number of years and he knows that to get ready for the training session it's not enough to prepare only problems and editorial. As the training sessions last for several hours, teams become h... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 79e88936-62ba-4a14-bf9e-d6a7bc8f4558 |
Question: Polycarp is conducting an experiment involving a large number $s$ representing the concentration of a cyanide solution in milligrams per decimeter cubed (mg/dm³). He wants to cut this number into parts such that each part represents a concentration of a solution that can form a stable complex with iron(II) io... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | b63c67fa-0427-4e0e-a61f-a98803a5571a |
Question: In the realm of quantum chemistry, the behavior of electrons in atoms can be described using wavefunctions. Consider a scenario where the electrons in an atom can exist in a superposition of different states, each characterized by a wavefunction. The probability of finding the electron in a particular state i... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | c7c46d22-faab-43a9-8a40-fd740480f0bf |
Question: In the design of a new electrochemical power generation system for electric vehicles, the system's efficiency is represented by a binary string of length $n$, where '0' indicates a low-energy state and '1' indicates a high-energy state. To optimize the system's performance, you need to rearrange the string in... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 610726c0-77ba-459d-bd8f-5fe7f663aab0 |
Question: Vasya has decided to build a zip-line on trees of a nearby forest. He wants the line to be as long as possible but he doesn't remember exactly the heights of all trees in the forest. He is sure that he remembers correct heights of all trees except, possibly, one of them. The forest consists of n trees staying... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 2da01a64-7a4f-4446-b80d-95e148cd703d |
Question: A company of $n$ friends wants to order exactly two pizzas for their annual space-themed party. It is known that in total there are $9$ pizza ingredients in nature, which are denoted by integers from $1$ to $9$. These ingredients symbolize different elements found in the solar system, with each ingredient rep... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | e8559068-a337-497f-8d8c-444b98608442 |
Question: Natsume loves big cats. I haven't kept cats at Natsume's house for a long time, and Natsume, who loves cats, was always playing with stray cats. However, this time Natsume decided to keep a cat at her own house. Natsume welcomed the cat to her house and named her Lennon and began to pet her. Lennon loves summ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | e5ceb0c8-354c-41e0-8bab-e1ce355d717c |
Question: During Diwali, little Roy is experimenting with water chemistry and creating a unique Rangoli design based on water hardness. He has an N x N grid where each cell represents a sample of water with varying levels of calcium and magnesium ions. Each cell at position (i, j) has a hardness level determined by the... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 19553e69-727e-480a-a216-5467a5ce636e |
Question: In a biochemical experiment, you are observing the formation of the enzyme-substrate complex $[ES]$ under varying substrate concentrations modeled by the sequence $1, 2, \dots, n$. The complex formation is described by $[ES] = \frac{s [E]_0}{K_m + s}$, where $[E]_0$ is the initial enzyme concentration and $K_... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 7a386f3f-eb19-47fe-9b9a-cd80b14a304d |
Question: Boboniu, an innovative scientist and economist, has created a new currency system based on the purity of chemical substances. Each BBY denomination corresponds to a specific purity level of a chemical substance. Boboniu has a collection of these substances arranged in a sequence, denoted as ( a ), where each ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 46afbb3c-fcf8-4238-b576-280c7a9ea330 |
Question: A chemist is analyzing a gas sample contained in a flask to determine its molecular composition. The gas is represented by a string of lowercase Latin letters, where each unique letter represents a different type of molecule. The chemist can remove up to k molecules (characters) from the gas to simplify the a... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 2a82c6c4-463c-43c9-9e93-c039a1e8426f |
Question: During a series of experiments to study atmospheric chemistry, researchers are examining the formation of ozone in a laboratory setting. They initiate the process by introducing a small amount of nitrogen dioxide (NO₂) into a reaction chamber. The NO₂ undergoes photolysis under simulated sunlight, leading to ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 53d54cf4-7288-4bbc-8495-bfe9c1574b7b |
Question: Little Elephant from the Zoo of Lviv enjoys both card games and thermodynamics. He has a collection of N cards, each colored with one of 1000 distinct colors numbered from 1 to 1000. Little Elephant and Big Hippo are engaged in a strategic card game. Little Elephant selects a subset of the cards, and Big Hipp... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 4e251059-8471-4d79-b8d8-86e4a84ade5c |
Question: Ilya is working for the company that constructs robots. Ilya writes programs for entertainment robots, and his current project is "Bob", a new-generation game robot. Ilya's boss wants to know his progress so far. Especially he is interested if Bob is better at playing different games than the previous model, ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 8b907e35-c82c-4d11-8e59-289d3a34688a |
Question: Did you hear about the Nibiru collision? It is a supposed disastrous encounter between the earth and a large planetary object. Astronomers reject this idea. But why listen to other people's beliefs and opinions. We are coders above all, so what better way than to verify it by a small code. The earth and N ast... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | d53d4c22-7e1d-4bbb-ad9c-da62c26e3848 |
Question: In a futuristic rendition of "Mafia," n participants engage in a series of virtual rounds using advanced electrochemical devices. Each participant requires the device to operate for a specific number of rounds, and during each round, one player acts as the supervisor while the remaining n - 1 players particip... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | a3968168-b57a-46c7-9be2-912a5daa6c73 |
Question: In a laboratory experiment, you are tasked with determining the empirical formula of a complex formed between a metal ion M^3+ and a ligand L in an aqueous solution. The complex ML_n absorbs light at a specific wavelength, and its concentration can be measured using optical absorbance A, which is related to t... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | b27b5480-b9bb-4763-a8ad-baa335cd51fe |
Question: In a secure system, passwords must adhere to specific criteria to ensure robust security. A string representing the password is given. Check if the character string meets all of the following conditions, and if it meets all of the conditions, output "VALID", and if there is an item that does not meet even one... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 7df55acd-9836-40fc-ba7b-1bc3176e19c5 |
Question: Ksusha the Squirrel is standing at the beginning of a straight road, divided into n sectors. The sectors are numbered 1 to n, from left to right. Initially, Ksusha stands in sector 1. Ksusha wants to walk to the end of the road, that is, get to sector n. Unfortunately, there are some rocks on the road. We kno... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 4c0e7372-4d0b-4e6e-9726-0336d62b7e2b |
Question: Mr. Bill is shopping at the store. There are some coins in his wallet (10-yen coins, 50-yen coins, 100-yen coins, 500-yen coins), but he is now trying to consume as much of this coin as possible. In other words, by paying for the goods with an appropriate number of coins, we are trying to minimize the total n... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 739a2af3-bac3-407b-af21-be40809036dc |
Question: Consider a network of thermal conductors modeled as a connected undirected graph with n vertices and m edges, representing junctions and pipes, respectively. The network is in thermal equilibrium at 298 K, and there are no self-loops or multiple edges in the graph. Each edge represents a pipe through which id... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 058ea2b8-4962-4998-9c1e-4bbfec858dba |
Question: Sasha, fascinated by the principles of chemical thermodynamics, painted a canvas with two overlapping rings on an infinite Cartesian plane. Each ring is characterized by its center coordinates (xi, yi) and internal (ri) and external (Ri) radii (1 ≤ ri < Ri ≤ 100), with the centers of the rings not coinciding ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ec753e63-744c-46fc-81d0-bb882318736f |
Question: A scientist is investigating a chemical reaction in a closed system where a substance X decays at a rate proportional to its current amount, following a first-order rate law with decay constant \(\lambda\) per minute. The substance X is continuously replenished by another substance Y, which decays at a differ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 81b644d4-d9e3-4243-8826-dc6f8136e2f8 |
Question: Consider a network of interconnected laboratories where each laboratory is represented as a vertex in a connected undirected graph with N vertices and M edges. Each vertex i has a weight X_i representing the initial concentration of a solution in laboratory i. Each edge i connecting vertices A_i and B_i has a... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 60502457-01ae-4efd-baac-f3b9b49c8f17 |
Question: Joseph is deeply fascinated by the intersection of art and science. While exploring the Japanese game Nonogram, he decides to incorporate principles from chemical equilibrium to create a dynamic puzzle. In this version of the game, each cell in a row of n cells can be in one of three states: filled (#), empty... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | c5cfd0e0-e183-4d43-86ba-0c974416bfcb |
Question: You are participating in a science fair and have been tasked with creating an interactive game for visitors. The game involves a series of chemical reactions where visitors must choose the correct reagent to add to a solution based on the color change observed. Each round corresponds to a specific chemical re... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 70eab75b-92fe-4040-8cea-40c464f9a0ed |
Question: Recently, the Fair Nut has written $k$ strings of length $n$, consisting of letters "a" and "b". He calculated $c$ — the number of strings that are prefixes of at least one of the written strings. Every string was counted only one time.
Then, he lost his sheet with strings. He remembers that all written stri... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 4dd44f37-4bc6-4881-87b8-933f367019b5 |
Question: In a similar molecular structure as described in the original problem, you are given a sequence of integers representing the types of bonds between carbon atoms in a chain. Each carbon atom contributes one (pi)-electron to the system. Using the given parameters (alpha) and (eta), calculate the net charges on ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 90ca4651-6c6c-4da2-b6af-db2e5f5fcda7 |
Question: Chef is conducting an advanced experiment involving the synthesis of special molecules in a controlled environment. The molecules are formed by combining '0' and '1' atoms in a specific pattern, similar to how gases combine in a sealed container. An Asmany molecule is defined as a sequence of '0's and '1's wh... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | d4946806-aa1c-49d2-a46e-527b641e7b14 |
Question: Om Nom has discovered a magical forest where the paths are illuminated by glowing lights, representing aldehydes undergoing base-catalyzed aldol condensation reactions. The forest is organized as a full binary tree of depth n, with the entrance at the root node (node 1) and exits at the leaf nodes (nodes 2^n,... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ad5d2f73-4a74-4063-8a36-49eeb767863b |
Question: You have a solution containing three types of sulfur compounds: ( ext{S}^{2-}), ( ext{SO}_3^{2-}), and ( ext{S}_2 ext{O}_3^{2-}). The concentrations of these compounds are represented by an array of n positive integers. You need to divide the solution into the smallest number of m-divisible arrays where each ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 81da7020-0be0-4ac5-98de-f1e1d1326e3e |
Question: Mr. Infinity has a string S consisting of digits from `1` to `9`. Each time the date changes, this string changes as follows:
* Each occurrence of `2` in S is replaced with `22`. Similarly, each `3` becomes `333`, `4` becomes `4444`, `5` becomes `55555`, `6` becomes `666666`, `7` becomes `7777777`, `8` becom... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | dc69badf-b5fd-4ec8-9c27-94a954ca9045 |
Question: Last summer, Peter was at his granny's house in the country when a wolf attacked sheep in the nearby forest. Now he fears to walk through the forest, to walk round the forest, even to get out of the house. He explains this not by the fear of the wolf, but by a strange, in his opinion, pattern of the forest th... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 7563b89f-af82-419c-8818-96db67be98e7 |
Question: In an electrical circuit, there are N switches, each capable of being either "on" or "off", and M bulbs. Each bulb i is connected to k_i specific switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. Bulb i will light up if the count of "on" switches among its connected switches is congruent to p_i modulo 2. De... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 31022109-7072-4a21-b04e-93002783aa84 |
Question: Square1001 has seen an electric bulletin board displaying the integer 1. He can perform the following operations A and B to change this value:
* Operation A: The displayed value is doubled.
* Operation B: The displayed value increases by K.
Square1001 needs to perform these operations N times in total. Find... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 38af1351-42ab-4d66-ae9a-bfae6531cd40 |
Question: Within a molecular structure, consider two circular regions representing localized probability distributions of two electrons. Circle $A$ with radius $r_a$ and central coordinate $(x_a, y_a)$ represents the distribution of one electron, and circle $B$ with radius $r_b$ and central coordinate $(x_b, y_b)$ repr... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ca7f7534-43b9-4101-ae54-662b57efda98 |
Question: Pak Chanek manages a hydrogen production facility utilizing the water-gas-shift (WGS) reaction. The facility includes three reactors, each equipped with a distinct catalyst. The efficiency of these catalysts in converting CO and steam into CO₂ and H₂ is crucial for the plant's performance. Each reactor has a ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | f3d39ee0-bb40-4558-a670-aa413b0d7f0b |
Question: The Red Kingdom is under threat from the White King and the Black King! The Kingdom is protected by $n$ castles, each defended by $a_i$ soldiers. The Kings alternate their attacks, starting with the White King. Each attack reduces the number of defenders in a targeted castle by $x$, $y$, or $z$ soldiers, depe... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 12821353-8900-4c28-a0fb-6aadc8ea03d3 |
Question: The police department of your city has just started its journey. Initially, they don’t have any manpower. So, they started hiring new recruits in groups. The efficiency of the police officers in solving crimes decreases with increasing temperatures. Specifically, the number of crimes an officer can solve in a... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | bf92bb4b-358c-4e2f-8240-a00255680d06 |
Question: Hexadecimal is working on a project involving cyclic compounds in graph theory. She has a partially constructed graph where vertices represent atoms and edges represent chemical bonds. Each atom has a specific atomic weight. Hexadecimal aims to complete this graph into a single cycle (ring) where each atom is... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | e4326ba9-908f-40b0-a91c-038d1f51077c |
Question: Dima the hamster has discovered a peculiar binary search tree made from nodes representing different compounds in a laboratory. Each node contains a unique compound represented by an integer value indicating its molecular weight. Dima nibbled the edges of the tree, disrupting its structure. To avoid upsetting... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 6262ddb1-97d7-4943-af05-759b5cbe6d0c |
Question: Seyyed and MoJaK are friends of Sajjad. Sajjad likes a permutation. Seyyed wants to change the permutation in a way that Sajjad won't like it. Seyyed thinks more swaps yield more probability to do that, so he makes MoJaK to perform a swap between every pair of positions (i, j), where i < j, exactly once. MoJa... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | fd12aad8-42b1-42d5-ad69-acd6df0e1122 |
Question: Heidi found out that the Daleks have created a network of bidirectional Time Corridors connecting different destinations (at different times!). She suspects that they are planning another invasion on the entire Space and Time. In order to counter the invasion, she plans to deploy a trap in the Time Vortex, al... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 033703e3-5c08-461e-8a68-4d92da61b39c |
Question: George is a cat who enjoys both playing with cards and conducting chemical experiments. Vitaly put n cards in a row in front of George. Each card has one integer written on it, representing the concentration of a specific polyprotic acid in moles per decimeter cubed. All cards have distinct concentrations. Le... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 803c75bd-fccb-4e9b-872c-c556eae44241 |
Question: In the magical land of Zephyria, the King has issued an order to simplify calculations involving high precision numbers due to the interference of the ACMers. The rounding rules are as follows:
- If a number's integer part does not end with digit 9 and its fractional part is strictly less than 0.5, the round... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | d5f72764-dd16-4e74-8abf-ed9d3be81b24 |
Question: Drazil and Varda are now studying radioactive minerals. They have discovered a unique mineral that decays over time, releasing different isotopes. The mineral contains a mixture of two isotopes, X and Y, with initial concentrations $C_X$ and $C_Y$ in moles per cubic decimeter. The distribution coefficient $D$... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 8ee4d63c-e5fd-48d5-98a1-a7315b6e67fe |
Question: In a specialized iron processing facility, there are N furnaces arranged in a two-dimensional plane. Each furnace is at coordinates (x_i, y_i). The furnaces need to be activated in a specific sequence to optimize the reduction process of iron ore into pure iron. To activate a furnace, a chemical reaction must... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 8a7df755-a235-4bd6-a971-739293ca1984 |
Question: Innokenty is a president of a new football league in Byteland. The first task he should do is to assign short names to all clubs to be shown on TV next to the score. Of course, the short names should be distinct, and Innokenty wants that all short names consist of three letters. Each club's full name consists... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 5b9646f8-4f4b-428e-a032-db69ae7a6071 |
Question: It is given a positive integer $n$. In $1$ move, one can select any single digit and remove it (i.e. one selects some position in the number and removes the digit located at this position). The operation cannot be performed if only one digit remains. If the resulting number contains leading zeroes, they are a... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | f802f4e3-f6a0-441a-a2b4-fe2499a9fb60 |
Question: You are analyzing a batch of chemical samples where each sample has a specific mass and a theoretical yield. You need to determine the smallest mass larger than a given threshold within a specific range of samples, but only consider samples whose mass falls within a predefined acceptable range. Given an array... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 1e95bfd7-8ed1-4705-a40d-8f41c45bf610 |
Question: Vika has n jars with paints of distinct colors. All the jars are numbered from 1 to n and the i-th jar contains ai liters of paint of color i. Vika also has an infinitely long rectangular piece of paper of width 1, consisting of squares of size 1 × 1. Squares are numbered 1, 2, 3 and so on. Vika decides to st... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | e57e8b13-71f6-4dd7-981c-e107b750dc65 |
Question: In the study of molecular stability, consider a hypothetical molecule Y2+, where two Y⁺ ions form a bond through the coupling of their unpaired d electrons, similar to the formation of O2+. The molecule Y2+ is observed to be thermodynamically stable due to the strong covalent bonding between the Y⁺ ions. This... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 3db371ad-c595-4149-8fe6-669b76668ef3 |
Question: In the two-dimensional kingdom, the police are tracking the movements of an outlaw from the notorious 'Pihters' gang using a GPS transmitter. The transmitter logs the car's possible movements, but due to inaccuracies, each log entry represents a set of possible directions: 'U', 'D', 'L', or 'R'. The car start... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 3786ea18-8417-43d5-ae74-7f9175115854 |
Question: The Kingdom of Kremland is a tree (a connected undirected graph without cycles) consisting of $n$ vertices. Each vertex $i$ has its own value $a_i$. All vertices are connected in series by edges. Formally, for every $1 \leq i < n$ there is an edge between the vertices of $i$ and $i+1$.
Denote the function $f... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | f3aab108-2e39-46d2-803f-4bb04f320853 |
Question: Captain Flint has uncovered a secret formula that can amplify the energy output of a series of chemical reactions, potentially making them exothermic and thus releasing more energy. To activate this formula, Flint needs to perform a series of operations based on two arrays a and b of length n. Initially, an a... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | bf4641b0-a1e2-491f-9d58-a9649aca421b |
Question: Little Lalit is an extremely good competitive coder. But recently, he was challenged by another fellow competitive programmer called Little Kundu. Lalit decides to challenge Kundu to prove that he's better than him. After a tough grueling competitive fight, Lalit manages to beat Kundu. Let us give you some st... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ecb4cca1-6612-4a70-8695-b5a93c90d198 |
Question: You are given a sequence of N integers: A_1, A_2, ..., A_N, representing the initial concentrations of a polyprotic acid (e.g., sulfuric acid) in different containers. Each container can undergo a series of operations where the concentration of the acid can change according to specific rules. The goal is to d... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 663d8090-463a-48dd-a00f-0179ecac2999 |
Question: In an advanced version of their computer game, Rubik and Furik face a dynamic environment where the efficiency of completing game parts is influenced by the current state of the game, akin to a chemical system in equilibrium. The game consists of n parts, each of which can only be completed on one of three co... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | b7e6a96e-f63c-488e-a452-84aed8216fcf |
Question: This is the hard version of the problem. The only difference from the easy version is that in this version the coordinates can be both odd and even. Additionally, the fence posts are coated with a special material that affects their electrical potential, and the ground beneath the plane has varying solubility... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 39ee0559-918b-4d31-8e08-cb908f6bd72b |
Question: William has a certain sequence of integers a_1, a_2, ..., a_n in his mind, but due to security concerns, he does not want to reveal it to you completely. William is ready to respond to no more than 2 ⋅ n of the following questions:
* What is the result of a [bitwise AND](https://en.wikipedia.org/wiki/Bitwi... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 09ad0e4e-ad2c-435f-8d05-908d67cecf74 |
Question: Little Vaishnavi is now deeply fascinated by chemistry experiments. She has set up a series of chemical reactions using ascorbic acid (vitamin C) and potassium iodate (KIO3). She wants to integrate her jumping game with these reactions to create a more complex and educational experience.
Vaishnavi has 5 diff... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 3212dfde-fb92-41fb-9d6b-e4bb56d5d585 |
Question: In all schools in Buryatia, in the 1st class, everyone is told the theory of Fibonacci strings.
"A block is a subsegment of a string where all the letters are the same and are bounded on the left and right by the ends of the string or by letters other than the letters in the block. A string is called a Fibon... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 6acf1763-35e5-4a3c-9f6c-27b8f6561770 |
Question: A university is organizing a series of experiments involving high-pressure gases. There are n student groups, each requiring a chamber for their experiment, and these chambers need to be scheduled across seven time slots throughout the day. Each group's experiment duration is indicated by a sequence of 7 bina... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 31171d65-5d4b-4c11-a69b-bcf04d4d5f27 |
Question: The Galactik Football Association (GFA) is organizing a tournament across N planets, each potentially having unique conditions that affect the performance of the players. To enhance player performance, the GFA plans to use a special green solvent, similar to carbon dioxide, which requires compression from 1 b... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 40bfe9e9-b0bc-4b9f-8584-8644d0bc66cd |
Question: In a laboratory setting, Laharl, Etna, and Flonne are conducting an experiment involving a brass alloy containing $Cu^{2+}$ and $Zn^{2+}$ ions. They need to analyze the alloy using complexometric titration. The brass alloy sample is dissolved in concentrated nitric acid, and the resulting solution is titrated... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | f53056b3-648d-4405-8741-52463d5b4edd |
Question: You are designing a specialized mirror-based communication system for a futuristic fuel cell laboratory. The system consists of a grid of size n × m where each cell contains a mirror oriented either as '\' or '/'. Some cells have been damaged and require new mirrors to be installed. The system must satisfy th... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | e4722ab2-333d-4e2e-b43a-4e8801971a65 |
Question: You are given an array a, consisting of n integers representing electrical charges. Each position i (1 ≤ i ≤ n) of the array is either locked or unlocked. You can take the values on the unlocked positions, rearrange them in any order and place them back into the unlocked positions. You are not allowed to remo... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 36da4035-1309-4395-84b8-331a3c461d3e |
Question: User ainta is experimenting with a new type of card game influenced by thermodynamics. He has `a` cards containing letter 'o' and `b` cards containing letter 'x'. He arranges these cards in a row to create blocks of 'o's and 'x's. The score of the deck is determined by the formula: for each block of contiguou... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 5041f145-76d7-47c2-af9e-d6321347c9b6 |
Question: In a long corridor divided into n square cells of size 1 × 1, numbered from 1 to n from left to right, two entities are present: a hooligan and a security guard. Initially, the hooligan is positioned in the a-th cell, and the guard is in the b-th cell (a ≠ b). The hooligan has m firecrackers, each with a spec... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | bcffdd56-413d-4235-bb6b-8fb4359ae700 |
Question: In a certain universe, there are n stars on a two-dimensional lattice point, and aliens use the Reflection Warp Machine to move between the stars. This device can draw a straight line at any position and angle. With this straight line as the axis of symmetry, it is possible to move from the current coordinate... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 5543dfcb-2f03-4c7c-97d3-13154ee1fcd5 |
Question: The judges have selected N problems for a prestigious coding competition and need to assign scores to them. Each problem i must be assigned an integer score A_i such that 1 \le A_i \le N, and the sequence of scores must be non-decreasing: A_1 \le A_2 \le \ldots \le A_N. To ensure fair ranking, for any k (1 \l... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 6c259de5-8331-4be9-9ffa-cda629224437 |
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