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Question: Homu-chan's recent boom is making sweets. It seems that he makes a lot of sweets and shares them with his friends. Homu-chan seems to be trying to make donuts this time. By the way, it doesn't matter if you stick to it, but is it possible to prepare a sufficient number of donuts that Homu-chan is particular a... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | b682bd92-48a8-40e9-ae13-dd851ceee675 |
Question: Rachel, an advanced android programmer, has created an app that allows users to draw triangles by selecting three points on a touch-plane. To enhance the app, she wants to incorporate the effect of light absorption by molecules in the environment where the app is used. Specifically, the app needs to determine... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | d5a1e415-b08a-403b-8dc1-89bad2f92c3c |
Question: Pari is developing a novel oxygen sensor based on a solid electrolyte with a $CaF_2$ crystal structure. The sensor uses porous Pt electrodes on both the cathode and anode sides. When the oxygen partial pressures differ between the two electrodes, an electromotive force (EMF) is generated, which can be measure... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 04f94056-0820-483e-8df7-d4228027ae6f |
Question: You have a garland consisting of $n$ lamps. Each lamp is colored red, green, or blue. The color of the $i$-th lamp is $s_i$ ('R', 'G' and 'B' — colors of lamps in the garland). The garland is made of a special material that can undergo molecular rearrangements at different temperatures, affecting the visibili... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 749a667d-373d-4ac5-ade0-b81164162845 |
Question: Badawy is tasked with designing a new rocket engine that uses a mixture of n different hydrazine derivatives as fuel. Each derivative i has a unique integer representation a_i (0 ≤ a_i ≤ 2^{30}-1). To ensure optimal performance, Badawy needs to choose an integer X such that the maximum enthalpy of combustion ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | eee5037e-71e1-48d5-8248-77d42a290f62 |
Question: Phoenix is picking berries in his backyard, situated in a region of space where the cosmic background radiation provides a constant temperature of 2.7 K. There are $n$ shrubs, and each shrub has $a_i$ red berries and $b_i$ blue berries. Each basket can contain $k$ berries. However, Phoenix has decided that ea... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 6fdb5e9f-08c0-40a8-882b-11eca3d16a07 |
Question: Consider a sequence of n integers a1, a2, ..., an and a positive integer k (1 ≤ k ≤ n). You need to find the maximum value of the sum of k consecutive integers Si = ai + ai+1 + ... + ai+k-1 (1 ≤ i ≤ n --k + 1). Two rigid containers at thermal equilibrium at 298 K are connected by a valve and isolated from the... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 0ea4e73b-faa2-460e-ba14-a8ef2377b5da |
Question: In Takahashi Kingdom, there is a railroad consisting of N sections, numbered 1, 2, ..., N, and N+1 stations, numbered 0, 1, ..., N. Section i directly connects the stations i-1 and i. A train takes exactly A_i minutes to run through section i, regardless of direction. Each of the N sections is either single-t... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | c7c57253-8c0a-4cff-895f-cff8d04442a5 |
Question: In the year 2023, scientists have developed a novel device $ M $ inspired by the principles of chemical oscillators. This device takes two animals, Tanuki ($ T $) and Fox ($ F $), and outputs one animal based on a complex internal mechanism. The device operates similarly to the Belousov-Zhabotinsky reaction, ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | cd336ca8-f376-4c8b-9d56-0526ed044d10 |
Question: In your latest research, you are investigating the crystalline forms of cinnamic acid derivatives under ultraviolet irradiation. You have observed that these derivatives can crystallize into different forms, α-form and β-form, depending on the conditions. Each form exhibits unique properties and transformatio... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | e3c67a14-bea2-4526-92b9-7686129255ae |
Question: Levko is analyzing a protein sequence using a combination of chemical cleavage and automated sequencing techniques. The protein sequence is represented as an array a1, a2, ..., an, where each element ai represents the type of amino acid at position i in the protein. Levko performs a series of operations on th... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | efe6e135-7044-4aaf-b492-6701503adf52 |
Question: Polycarp's phone has n phone numbers stored in its contacts, each represented as a 9-digit integer starting with a digit different from 0. All numbers are distinct. The phone employs a sophisticated filtering mechanism inspired by the chemical equilibria involving lead species in aqueous solutions. When a seq... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 2f0341ac-72d4-4d2c-9cee-b8c112995993 |
Question: For an upcoming chemistry experiment, Takahashi requires a water bottle shaped like a rectangular prism with a square base of side length (a) cm and height (b) cm. He intends to pour (x) cm³ of water into the bottle and then tilt it around one of the sides of the base. Before and after tilting the bottle, Tak... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 055c0070-8af2-421b-bf86-3c151aa62441 |
Question: Chandu is struggling with his combined maths and chemistry homework. His teacher has assigned a problem that involves both mathematics and chemical kinetics. The mathematical part requires finding the maximum possible pair XOR in a matrix of size N x M with specific conditions. The condition imposed is that t... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 93da1520-8439-4a80-bebc-15ca55285d3f |
Question: An elementary school student Takahashi has come to a variety store. He has two coins, A-yen and B-yen coins (yen is the currency of Japan), and wants to buy a toy that costs C yen. Can he buy it? Note that he lives in Takahashi Kingdom, and may have coins that do not exist in Japan.
To add complexity to his ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ed368df8-35d7-4b1d-bd2c-71ae38f0c169 |
Question: In the country of Numberia, there is a city called Primeland. Sherry is one of the rich inhabitants of the city, who likes to collect coins of various denominations. Coins in Primeland are little strange; they are only available in prime denominations (i.e., as coins of value 2, 3, 5, etc.). Sherry is taking ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 67045725-332d-48d4-abda-927272687efa |
Question: Malek lives in an apartment block with 100 floors numbered from 0 to 99. The apartment has an elevator with a digital counter showing the floor that the elevator is currently on. The elevator shows each digit of a number with 7 light sticks by turning them on or off. The picture below shows how the elevator s... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | aad9becb-2b84-497a-bc49-124aaa96dda7 |
Question: A map of some object is a rectangular field consisting of n rows and n columns. Each cell is initially occupied by the sea but you can cover some cells of the map with sand so that exactly k islands appear on the map. We will call a set of sand cells to be island if it is possible to get from each of them to ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | b7a494ff-931a-42ab-a8a5-d7682e502a2b |
Question: You are given two integers n and m. You have to construct the array a of length n consisting of non-negative integers (i.e., integers greater than or equal to zero) such that the sum of elements of this array is exactly m and the value ∑_{i=1}^{n-1} |a_i - a_{i+1}| is the maximum possible. Recall that |x| is ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 75e9c716-2bbf-4df4-a855-943a06d12002 |
Question: The core of the sun, a region of intense nuclear reactions, is composed primarily of plasma. This plasma consists of a mixture of free protons, helium nuclei, and electrons, existing under extremely high temperatures and pressures. Given the density of the plasma as 158 g cm⁻³ and the pressure as 2.5×10¹¹ atm... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 65c898d8-0c90-492b-ac56-cc48a99a54a0 |
Question: A chemistry student is tasked with determining the concentrations of Fe³⁺, Al³⁺, and Mg²⁺ in a sample solution using EDTA titration. The formation constants for the complexes formed are K_f(FeY) = 10^25.1, K_f(AlY) = 10^16.13, and K_f(MgY) = 10^8.69. The student conducts the titration under different pH condi... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | e280ef81-d79d-4bed-bf99-9a381bc0beae |
Question: In the vicinity of Takahashi Airport, environmental scientists monitor the ozone levels to ensure public safety. They measure ozone concentration by bubbling air through an acidic solution containing iodide. The reaction involved is unbalanced and needs to be considered in your calculations. Additionally, the... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 3152d8fe-52eb-4391-8a35-076c252b91d7 |
Question: Vasya has decided to paint his fence using a special Chrome Green pigment, which is known for its vibrant color but also for its unique chemical properties. The fence consists of n wooden boards arranged in a single row, numbered 1 through n from left to right, with each board having a height of h_i centimete... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 801de84f-1b4f-4c1e-ac6b-ef813580b301 |
Question: Recently, Polycarp has invented a new mobile game with falling blocks. In the game, n blocks are falling down, one at a time, towards a flat surface with length d units. Each block can be represented as a rectangle with coordinates from l_i to r_i and unit height, dropped downwards from very high up. A block ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 1cabec37-dcfb-4c28-a45c-9b4cd2eac9b2 |
Question: Vasya's mom decided to give him an array of positive integers a of length n to celebrate his birthday. Vasya thinks that an array's beauty is the greatest common divisor (GCD) of all its elements. His mom wants to give him as beautiful an array as possible (with the largest possible GCD). However, the shop ha... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | a858f8b7-aa9a-4d20-8288-b161ec1305fa |
Question: The busses in Berland are equipped with a video surveillance system. The system records information about changes in the number of passengers in a bus after stops. If x is the number of passengers in a bus just before the current bus stop and y is the number of passengers in the bus just after the current bus... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 84a6d321-f7ab-40a7-8b46-7ac9cf4480e4 |
Question: In the Republic of AtCoder, Snuke Chameleons (Family: Chamaeleonidae, Genus: Bartaberia) are very popular pets. Ringo keeps N Snuke Chameleons in a sophisticated terrarium designed to study the interaction between chameleons and various chemical compounds. The terrarium contains a mixture of solutions, includ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | e5af6a70-143f-4abe-9013-97c418a52d7f |
Question: Let's define the cost of a string s as the number of index pairs i and j (1 ≤ i < j < |s|) such that s_i = s_j and s_{i+1} = s_{j+1}.
You are given two positive integers n and k. Among all strings with length n that contain only the first k characters of the Latin alphabet, find a string with minimum possibl... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 078d0bc3-83d6-4127-b87a-349910d5f843 |
Question: In a laboratory experiment, a researcher is analyzing the impact of beta radiation from $^{32}P$ on a sample of DNA. The researcher has two DNA sequences of equal length, one representing the original sequence and the other representing the sequence after exposure to radiation. The researcher needs to calcula... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 5c693666-12f7-49ff-9424-b3d8c215ba93 |
Question: In a futuristic racing competition, you are tasked with optimizing your vehicle's performance using advanced materials derived from zinc oxide powder. After defeating a Blacklist Rival, you get a chance to draw $1$ reward slip out of $x$ hidden valid slips. Initially, $x=3$ and these hidden valid slips are Ca... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 4b7b6d43-a98d-411c-b6eb-d366f39e46fb |
Question: In an effort to understand someone's online habits, a person has installed spyware on their computer. This spyware meticulously logs every mouse operation performed while browsing different web pages. Each page is of uniform dimensions H × W, with the upper-left corner located at (0, 0) and the lower-right co... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ac8982ca-aaf2-4c36-bdac-ac57bb75fd01 |
Question: Vasya has a golden ticket represented by a sequence of $n$ digits $a_1a_2\dots a_n$. He considers the ticket lucky if it can be divided into two or more non-intersecting segments with equal sums. Vasya also needs to manage the iron content in his laboratory. He has a solution of iron(II) chloride, FeCl₂, with... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | a283dcc0-1ba7-4aa3-a7c8-551386529f0a |
Question: Chotu is fascinated by the universe and decides to combine his hobby of collecting coins with his interest in astrophysics. He has N coins, each having distinct values from 1 to N. Chotu plans to visit a shop to buy a teddy bear priced at K. However, the shopkeeper Motu informs him that he can only make the p... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | cbe89e25-92ea-48e3-9676-22cfbb40b263 |
Question: Christie, a renowned chemist and socialite, has recently earned her PhD and is now a celebrity at her university, with her Facebook profile inundated with friend requests. Despite her newfound fame, Christie remains humble and accepts all friend requests.
Kuldeep, feeling envious of Christie's popularity, pe... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 72cfdcca-dfaf-46a0-b5f9-76cf1befb1a2 |
Question: In a nanotechnology lab, you are tasked with manipulating the vapor pressures of a series of nanodroplets using controlled chemical reactions. You are given an array of integers $a$ of length $n$, where each element represents the initial vapor pressure of a nanodroplet. The elements of the array can be eithe... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | a003e946-22af-4438-8e1d-58f9ebb101a1 |
Question: Alice and Bob engage in a strategic game on a dynamic chessboard of dimensions n × m, where n and m are even. The chessboard is divided into cells, each possessing unique thermodynamic properties defined by enthalpy change (ΔH) and entropy change (ΔS). Two knights, a white one starting at (x_1, y_1) and a bla... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | c501c19b-97e2-4e3a-8f6c-b2385c9d6c65 |
Question: In an experimental setup, Limak the polar bear is analyzing strings of lowercase English letters. Each string represents a sequence of chemical reactions involving silver nanoclusters. To determine the feasibility of these reactions, Limak needs to classify each string as either hard or easy to pronounce base... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 282d39b6-b8ae-4e5e-840f-a508ac169b0a |
Question: For his latest experiment in cryptcowgraphy and cowculus, Kevin Sun is studying the behavior of a unique gas under various conditions for his research at the Bovinia State University (BGU). He defines a function $f : \{0,1,2, \cdots, p - 1 \} \rightarrow \{0,1,2, \cdots, p - 1 \}$ that satisfies the functiona... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | c3973744-0dd7-4f3b-a789-5c7c8396ab5e |
Question: A sealed type Ni-Cd battery consists of two half-cells, one involving cadmium and the other involving nickel hydroxide. During the discharge process, the battery maintains a regular bracket sequence of chemical reactions represented by '(' and ')'. A regular bracket sequence of reactions is a sequence that ca... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 80e1dc67-aafa-4f0e-ab23-96fdc0f1bc9b |
Question: A geologist has collected a sample of a new mineral that contains an impurity E, which partially substitutes one of the main elements in the mineral. The mineral formula is given as $(\text{E}_i\text{A}_{(1-i)}\text{B}_y\text{C}_z\cdot y \text{H}_2\text{O})$. The crystallographic parameters of the mineral are... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | b3435aaa-1563-4fe9-b4ef-707ec79cf88a |
Question: An apple orchard grows apples in N distinct colors, each color corresponding to a unique chemical compound. There are a_i apples of color i available. You and Lunlun the dachshund take turns performing the following operation (starting from you):
- Select one or more apples of different colors and consume th... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 61fd4860-74b4-4ea8-ad0e-e4a87d277835 |
Question: Squirrel Liss lives in a forest peacefully, but unexpected trouble happens. Stones of varying masses fall from a mountain. Initially, Squirrel Liss occupies an interval [0, 1]. Next, n stones will fall, and Liss will escape from the stones. The stones are numbered from 1 to n in order. Each stone has a specif... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 75dd3079-9b2b-4583-a16b-c3c0eb539c53 |
Question: A square pyramid of balls consists of square layers of balls stacked on top of each other. The i th (1-based indexing) layer from the top consists of exactly i^2 balls. Each layer has a unique color. During a mishap, you knocked over the pyramid and lost some (maybe all) balls from some (maybe all) layers. Yo... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 88ac0126-a70d-41cc-ad2e-c416a5fe917f |
Question: In a simulated environment mimicking the core of the sun, particles are emitted from a central source in intervals of x milliseconds. Each particle travels at a constant speed and takes t milliseconds to reach a detector. The core of the sun has a density of ρ grams per cubic centimeter and a pressure P atmos... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | f861b808-d1c7-4ede-bcc8-fb6d354b5f4b |
Question: Draude's latest robot model operates in a field where the stability of each cell affects its movement. The robot records its path, but sometimes it deviates from the shortest route due to a programming error. The stability of each cell is determined by the free energy change, which is influenced by the entrop... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 440c617c-0561-4a7a-a13c-de38002173d8 |
Question: Nanochemists are studying the behavior of nanodroplets of a substance with a known bulk boiling point ( T_b ) and enthalpy of vaporization ( \Delta H_{vap} ). They aim to synthesize nano-sized droplets of this substance using p-binary numbers to control the synthesis process. Given a positive integer n repres... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 80634e8f-23f5-4118-98c8-49bb3191ab62 |
Question: Jeff is painting a regular bracket sequence of length nm under the influence of cosmic evolution. The sequence consists of nm brackets, numbered from 0 to nm - 1 from left to right. Jeff knows that he is going to spend ai mod n liters of ink on the i-th bracket of the sequence if he paints it opened and bi mo... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 36ebb637-32bf-4a8b-abff-4747f9cccea2 |
Question: Aizuwakamatsu City is conducting a comprehensive study on the visitor demographics of Tsuruga Castle to enhance public relations and educational initiatives. As part of this study, they are analyzing the age distribution of visitors while also investigating the concentration of fluoride ions in the air around... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | f9da9659-aae6-4809-8303-fe1840715706 |
Question: In his latest scientific endeavor, Little penguin Polo is tasked with determining the amount of crystal water in a hydrate of nickel(II) sulfate. He prepares a solution of the hydrate and uses EDTA (ethylenediamine tetraacetate) for complexation. The concentration of the EDTA solution is 0.01 mol/dm³, and he ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 7f7cf4c8-605f-4264-8108-31babfbb3535 |
Question: Suppose you have two polynomials <image> and <image>. Then polynomial <image> can be uniquely represented in the following way:
<image>
This can be done using [long division](https://en.wikipedia.org/wiki/Polynomial_long_division). Here, <image> denotes the degree of polynomial P(x). <image> is called the r... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 4b89ac29-8db1-4fcd-a5e4-9b74c0547445 |
Question: Consider a scenario where you have two arrays $a$ and $b$, each containing $n$ positive integers representing the molar concentrations of different solutions in units of $\text{mol dm}^{-3}$. In one operation, you can choose an index $i$ from $1$ to $n$ and replace $a_i$ with its digital logarithm $f(a_i)$ or... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 8acdd9fa-00bc-4e15-a759-22f1e8d11cca |
Question: A chemist is studying a series of reactions involving gases in a sealed container. The reactions are modeled by the equations $A + B \rightleftharpoons C$ and $C + D \rightleftharpoons E$. The equilibrium constants for these reactions are $K_1 = 2.5$ and $K_2 = 3.0$, respectively. The chemist starts with a mi... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | b425d425-0b52-458c-9950-b7a9de33fa41 |
Question: Tavas, fascinated by both his love for coffee mix and the underwater world, decided to combine his interests. He imagined a scenario where a diver uses a snorkel to breathe underwater, and the pressure inside the lungs affects the diver's ability to breathe. Inspired by this, SaDDas formulated a problem that ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 81ccef5b-8596-4b8a-a309-d68c8f5baa18 |
Question: A research facility is conducting experiments to optimize the use of hydrazine derivatives for spacecraft propulsion. They have a calorimeter with a known heat capacity of 2.04 kJ/K and need to activate a series of scientific instruments using the energy released from the combustion of hydrazine derivatives. ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 82008a13-0d64-40c6-9517-012078894bd2 |
Question: In a laboratory setting, a chemist is working with xenon fluoride compounds in a solution. The solution's stability is represented by an array $v_1, v_2, \ldots, v_n$, where each element represents the concentration of a xenon fluoride compound. The score of this array is defined as the number of indices $i$ ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | dd18449f-dc0d-49c6-a218-7d20e291bac9 |
Question: Bob is playing a game called "Dungeon Chemistry" where he explores a dungeon consisting of $N$ rooms connected by $N-1$ roads, forming a tree structure. Each room contains a mixture of calcium salts, specifically a combination of calcium carbonate ($CaCO_3$), calcium chloride ($CaCl_2$), and calcium sulfate (... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 44bb74ab-b4d0-41a9-a70d-85b432162568 |
Question: Drazil and Varda are the earthworm couple. They want to find a good place to bring up their children. They found a good ground containing nature hole. The hole contains many rooms, some pairs of rooms are connected by small tunnels such that earthworm can move between them. Let's consider rooms and small tunn... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | d525ba0e-661d-4906-bcad-4cf0c1c103bb |
Question: Scientists have developed a new material Z, synthesized by reacting metallic tin with a concentrated acid solution. Upon heating, compound Z decomposes, releasing volatile products and leaving behind a residue. The residue is determined to be tin dioxide ($SnO_2$). When 1.5 grams of compound Z are heated, the... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 7cdb34c1-582d-459b-aec2-ecd69fbcf67e |
Question: In a chemistry lab experiment, a group of N students each holds a unique sample numbered 1 through N. They were initially arranged in a row for a demonstration, but now they have forgotten the exact order. Each student remembers the absolute difference between the number of samples to their left and the numbe... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 901f623e-d3c1-4b72-bc43-f21ab18bbf56 |
Question: Draude, a leading programmer from Berland, has developed an advanced robot designed to navigate through an infinite grid field while optimizing its path based on thermodynamic principles. The robot records its movements, which consist of steps in four cardinal directions: left (L), right (R), up (U), and down... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ef7c8a78-4afc-4c29-8a1f-a08a08e032e1 |
Question: Scientists are studying a triangular area on the moon defined by points $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$. They have identified two types of minerals, A and B, within this area. Mineral A has an initial $^{87}Rb / ^{86}Sr$ ratio of 0.004 and a final $^{87}Sr / ^{86}Sr$ ratio of 0.699, while Mineral... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 385a43fc-62a1-4f8b-9ba8-f4072fff6dce |
Question: To ensure safety during the night, the mayor of Gluharniki plans to illuminate a rectangular park divided into a grid of n rows and m columns. Each cell in the grid is a square, and the boundaries between cells are streets where lanterns can be placed. Each lantern illuminates two adjacent squares unless it i... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 894b8df0-5e0c-4b7e-a475-1741df6dec06 |
Question: A society can be represented by a connected, undirected graph of n vertices and m edges. The vertices represent people, and an edge (i,j) represents a friendship between people i and j. In society, the i-th person has an income a_i. A person i is envious of person j if a_j=a_i+1, meaning person j has exactly ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 094bf104-4f47-4093-b9b5-4080986be6db |
Question: Hanuman and Ram are tasked with navigating a mystical path filled with numbered rocks. Each rock number indicates the maximum jump length that can be made from that rock. However, the path is enchanted, and jumping over certain rocks triggers chemical oscillations involving bromine species. These oscillations... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 19dbab2a-737c-4bb9-bae8-55666b0fda3e |
Question: Little Chef, while exploring a mystical land, found himself stranded due to a series of unfortunate events. The local authorities, after verifying his innocence, decided to assist him by providing him with some currency. The monetary system in this land consists of coins valued at K^0, K^1, K^2, K^3, K^4, and... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 570b483a-7155-4b72-965a-df623256aaa3 |
Question: In your laboratory, you are analyzing a series of solutions containing tin(II) ions (Sn²⁺) and iron(III) ions (Fe³⁺). You have recorded the concentrations of Sn²⁺ ions in an array $a_1, a_2, \dots, a_n$. All $a_i$ are pairwise distinct.
Define function $f(l, r)$ as follows: define array $b_1, b_2, \dots, b_{... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 346b6993-118c-40d0-9971-d75d3ff6c3e0 |
Question: Polycarp is preparing for a challenging day at the university where he has to attend $a$ lectures and $b$ practical classes. He requires a pen to write down notes during lectures; one pen allows him to write $c$ lectures before running out of ink. For practical classes, he needs a pencil to draw blueprints; o... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 3444cdf8-4850-41c2-b6bd-8aaa624811f3 |
Question: A railroad running from west to east in Atcoder Kingdom is now complete. To ensure the longevity of the railroad, regular maintenance checks are performed based on the pH levels and absorbance readings of the tracks. These checks can sometimes delay train departures and arrivals.
There are N stations on the ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | beba5449-dacc-49e5-905b-ee245c2e1273 |
Question: In a chemical plant, you need to produce a specific amount of a compound through a series of reactions. Each reaction has a cost associated with it and produces certain outputs based on its inputs. Additionally, each reaction has thermodynamic properties that determine whether it is exothermic or endothermic.... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | a616b410-ff81-4b9e-9be0-9a8ee441643b |
Question: The fight between Batman and Superman just got dirtier. Superman tried to trick Batman and locked him inside an N x N grid. This grid is really special. It has values at each of its cell which is some positive integer. Superman also introduced a series of laser cooling cycles that affect the ions in the grid,... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ed550054-5c55-45fb-a353-a3ec6d5e9347 |
Question: Consider a compound with $n$ molecular bonds represented by an array of positive integers $a_1, a_2, \ldots, a_n$, denoting their initial energies. The compound can transition between two states at different temperatures: a rigid state at low temperatures and a flexible state at high temperatures. In the rigi... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 75e16a55-494d-48ae-b3e4-b4ac4f63c56a |
Question: In a magical forest, each tree is a boron halide molecule represented as a vertex in an acyclic undirected graph with n vertices and m edges. The forest is divided into several connected components. Each vertex is initially $sp^2$ hybridized and represents a boron atom bonded to a halide (either F, Cl, or Br)... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | a2c8c24b-7aef-4d3b-a8dc-b4da9cff2de4 |
Question: As part of a special event at Tsuruga Castle, visitors are invited to participate in a hands-on chemistry challenge. In this challenge, visitors must analyze a beverage sample to determine the concentration of ascorbic acid (C6H8O6) and citric acid (C6H8O7). The analysis involves simulating two types of titra... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 6e41c038-e15e-4582-91ea-1799b06717b2 |
Question: Let's define S(x) to be the sum of digits of number x written in decimal system. For example, S(5) = 5, S(10) = 1, S(322) = 7. We will call an integer x interesting if S(x + 1) < S(x). In each test you will be given one integer n. Your task is to calculate the number of integers x such that 1 ≤ x ≤ n and x is... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 90ed9b6f-ffe9-4dd5-8ee9-1de9e2ddfd56 |
Question: In the fest of Paradigm, every organizer is given a special kind of pager. The pager consists of a screen and a single big red button. To type a message in it, one has to push the red button that many times as the alphabet occurs in the alphabetical order. For example, for typing D, one needs to push the butt... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 03025e07-cda3-4340-81b4-862d9d62ea79 |
Question: Vanya is conducting experiments on a unique type of tree structure in a high-temperature laboratory where chemical reactions occur. The tree consists of n vertices connected by n-1 edges, each representing a chemical bond between molecules. Vanya can perform the following operation multiple times: choose a ve... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 77dab334-5f43-4f2d-b2ef-f4baaea6555e |
Question: William has an array of n integers a_1, a_2, ..., a_n. In one move he can swap two neighboring items. Two items a_i and a_j are considered neighboring if the condition |i - j| = 1 is satisfied.
William wants you to calculate the minimal number of swaps he would need to perform to make it so that the array do... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 4aa4ac21-7ed5-4a99-a8e1-189cb802ecdf |
Question: Na2a has a collection of N magical artifacts, each represented by a number Ai in his bag. He possesses a magic stone that allows him to multiply any artifact's number by lucky numbers (4 and 7) any number of times. Each artifact also undergoes a mystical transformation process governed by chemical reactions s... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 22a070b5-0468-43f7-9b58-504d8adc7628 |
Question: The princess must escape from the dragon's cave to reach the king's castle, situated c miles away. Running at vp miles per hour, she is pursued by the dragon flying at vd miles per hour after t hours. To impede the dragon, the princess can drop bijous, causing the dragon to pause, collect the item, and return... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 60259b40-80bd-4ef7-b530-e9b9a5b86e71 |
Question: Consider an interval from a to b (a ≤ b), where each integer represents the concentration (in ppm) of a cyanide solution buffered at pH 7.5. For each concentration, determine the number of prime numbers that can be formed by the sum of the concentrations of free cyanide ions ($CN^-$) and hydrogen cyanide (HCN... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 4ff88881-dccb-49ca-99c4-b196febc008d |
Question: You are standing near a very strange machine. If you put C cents in the machine, the remaining money in your purse will transform in an unusual way. If you have A dollars and B cents remaining in your purse after depositing the C cents, then after the transformation you will have B dollars and A cents. You ca... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | bf1c7437-824b-4a03-afdb-56a0af0d8636 |
Question: A mining company extracts chromite ore from four different locations, each yielding N samples of ore. The masses of chromite in each sample from locations A, B, C, and D are represented by $a_i$, $b_i$, $c_i$, and $d_i$ respectively. Each sample also contains impurities, with the chromite making up a specific... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 3eb3a950-bcda-4483-91b2-e75d808bc61e |
Question: Lunar New Year is approaching, and Bob is planning to go for a famous restaurant — "Alice's". The restaurant "Alice's" serves n kinds of food. The cost for the i-th kind is always c_i. Initially, the restaurant has enough ingredients for serving exactly a_i dishes of the i-th kind. In the New Year's Eve, m cu... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 5b21bf88-8e5e-41bc-b4ac-46dfd8dae160 |
Question: While exploring the old caves, researchers found a book, or more precisely, a stash of mixed pages from a book. Luckily, all of the original pages are present and each page contains its number. Therefore, the researchers can reconstruct the book. After taking a deeper look into the contents of these pages, li... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | afbebcb9-1265-46da-af19-fae3d42e9aac |
Question: The Turtle Academy of Sciences has developed a supercomputer consisting of n·m·k CPUs arranged in a parallelepiped of dimensions n × m × k, with each CPU located at a unique coordinate (x, y, z) where x ranges from 1 to n, y from 1 to m, and z from 1 to k. Communication between CPUs follows a specific rule: C... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | fba03437-473f-4e6f-b5cf-4d1ae850557e |
Question: In his latest experiment, Yash is investigating the relationship between the mass of a substance and its Fibonacci-ish potential. Given an array ai of length n representing the mass of individual particles in a sample, Yash needs to compute the theoretical yield for q different ranges of interest from lj to r... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | f97c87ee-0733-4374-b314-99673cb8fd71 |
Question: The winner of the card game popular in Berland 'Berlogging' is determined according to the following rules. If at the end of the game there is only one player with the maximum number of points, he is the winner. The situation becomes more difficult if the number of such players is more than one. During each r... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | d49ba3c8-481d-4ae2-aaa0-23d2019d7a6b |
Question: A tree is a connected undirected graph consisting of n vertices and n - 1 edges. Vertices are numbered 1 through n. Limak is a little polar bear and Radewoosh is his evil enemy. Limak once had a tree but Radewoosh stole it. Bear is very sad now because he doesn't remember much about the tree — he can tell you... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ad258d5a-a2a7-487d-88b8-0df87419b140 |
Question: Polycarp is very fond of playing the game Minesweeper. Recently he found a similar game and there are such rules. The game is played on a grid representing a crystalline structure of a natural zeolite called Laumontite. Each mine on the field represents an impurity atom in the crystal lattice, for each the co... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 8645f5ce-9e8c-4286-acc6-4b8f19f24cba |
Question: Exploring the intricate balance of nuclear forces and the composition of the early universe, Limak has encountered a series of strings. Limak can repeatedly remove one of the first two characters of a string, for example abcxyx → acxyx → cxyx → cyx. Given N different strings S_1, S_2, ..., S_N, determine how ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 59ef6451-c98c-40b0-9a95-3fd515f939d6 |
Question: Consider a series of chemical reactions involving metal ions and halide ions in solution. Let $ A $ represent the initial concentrations of a metal ion in different solutions, and $ B $ represent the initial concentrations of a halide ion in different solutions. Define the matrix $ C $ consisting of $ H $ row... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ee93268f-11e8-4633-a9bf-e3b92390ffc3 |
Question: A team of chemists is exploring the dynamics of nitrogen-based molecules in a computational model. The model consists of n cells, each representing a nitrogen atom in a simulated environment. Initially, each cell contains a number equal to its ordinal position (starting from 1). Each cell has a favorite numbe... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 638e8a77-4ec8-4a1a-b4e0-aaa5286579fa |
Question: Xsquare has recently opened a water treatment plant and needs to ensure the water quality meets certain standards. To do this, he measures the hardness of water samples, which includes both permanent and non-permanent hardness. Xsquare has a string S consisting of N lowercase alphabets, where each character r... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | ed7e6400-5aec-4669-9da0-a6dfc0578354 |
Question: Barney has finally found the one, a beautiful young lady named Lyanna. The problem is, Lyanna and Barney are trapped in Lord Loss' castle. This castle has the shape of a convex polygon with n points. Like most castles in the Demonata worlds, this castle has no ceiling. The castle was constructed using materia... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | a0fb6f99-ec1b-4f85-bba6-6d108a723aad |
Question: PolandBall has an undirected simple graph consisting of n vertices. Unfortunately, it has no edges. The graph is very sad because of that. PolandBall wanted to make it happier, adding some red edges. Then, he will add white edges in every remaining place. Therefore, the final graph will be a clique in two col... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 94eaa86e-c9ce-42bc-9cdf-b8dbc7e7d8ea |
Question: You have a large rectangular board which is divided into n × m cells (the board has n rows and m columns). Each cell is either white or black. You paint each white cell either red or blue. Obviously, the number of different ways to paint them is 2^w, where w is the number of white cells. After painting the wh... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 0f5407b2-2c3e-4b06-9844-73a1c58100ff |
Question: Chef wants to hire a new assistant. He published an advertisement regarding that in a newspaper. After seeing the advertisement, many candidates have applied for the job. Now chef wants to shortlist people for the interviews, so he gave all of them one problem which they must solve in order to get shortlisted... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 7557b66a-36b3-444f-9c0c-d190668e454f |
Question: Ivan plays a computer game where he needs to collect rare materials through microtransactions to enhance his character's abilities. Each day, Ivan earns exactly one burle. There are $n$ types of microtransactions in the game, each costing $2$ burles under normal conditions and $1$ burle if it is on sale. Ivan... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | cd017760-1472-47f3-a98f-5b2c1666f360 |
Question: A physicist is analyzing the electronic transitions in a one-dimensional box containing π electrons. The box has a length of L meters and the energy levels of the electrons are given by the formula $E_n = n^2 \frac{h^2}{8mL^2}$, where h is Planck's constant, m is the mass of the electron, and n is the quantum... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 011c0280-b551-43e4-9e9e-755e8213ea97 |
Question: A chemical engineer is studying the kinetics of a complex reaction involving multiple intermediates. The concentration of one specific intermediate at various stages of the reaction is represented by an array of n positive integers. To maintain the efficiency of the reaction, the concentration of this interme... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-InfiniByte-Reasoning",
"models_used": "QwQ-32B"
} | 68c63b4a-f018-4a81-8423-b996ae30d442 |
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