problem stringlengths 1 7.91k | generated_solution stringlengths 824 78.8k | expected_answer stringlengths 0 1.2k | problem_type stringclasses 1
value | problem_source stringclasses 16
values | domain stringclasses 3
values | difficulty stringclasses 30
values |
|---|---|---|---|---|---|---|
Let \(a, b, c\) be reals satisfying \(a^2 + b^2 + c^2 = 6\). Calculate the maximum value of the expression \((a-b)^3 + (b-c)(c-a)\). | <think>
Okay, so I have this problem where I need to find the maximum value of the expression (a - b)^3 + (b - c)(c - a) given that a² + b² + c² = 6. Hmm, let's see how to approach this.
First, I remember that optimization problems with constraints often use methods like Lagrange multipliers, but since this is a symm... | 24\sqrt{3} + 3 | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Which of the following scheduling algorithms could potentially lead to starvation in a computer system?
A: First-Come, First-Served (FCFS)
B: Shortest Job First (SJF)
C: Round Robin (RR)
D: Priority Scheduling with aging
E: Pri... | <think>
I need to determine which scheduling algorithms could lead to starvation. Starvation happens when a process is prevented from getting the CPU time it needs because other processes are always chosen over it.
First, recall what each algorithm does:
- A: First-Come, First-Served (FCFS): Processes are executed in... | \text{B, E, F, G, H, J} | nvidia/OpenScienceReasoning-2 | science | null | |
Let \( G \) be a simple graph on \( n \) vertices (\( n > 3 \)) with no vertex of degree \( n-1 \). Suppose that for any two vertices of \( G \), there is a unique vertex joined to both of them. Calculate the common degree of each vertex in \( G \). | <think>
Okay, so I have this problem here: Let G be a simple graph on n vertices (n > 3) with no vertex of degree n-1. Suppose that for any two vertices of G, there is a unique vertex joined to both of them. I need to find the common degree of each vertex in G. Hmm, interesting. Let me try to break this down step by st... | \frac{1 + \sqrt{4n - 3}}{2} | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
Find all integers $(x, y, z)$ satisfying the equation $12^x + y^4 = 56^z$. | <think>
Okay, so I need to find all integer solutions (x, y, z) to the equation 12^x + y^4 = 56^z. Hmm, let's start by understanding the problem. All variables are integers, so x, y, z must be non-negative integers, right? Because if they were negative, we'd have fractions or non-integers on either side. Wait, unless y... | (0, 0, 0) | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
You survived several months of exam wars and were able to enter ICPC University on a sunny day. On the day of admission, there was an enthusiastic recruitment of circles on the campus of the university, and you received a large number of pamphlets and returned. When you return to your room, you find one of the pamphlet... | <think>
Okay, let's see. I need to find the number of combinations of two or more consecutive positive integers that sum up to a given N. The example given is 9, which has two such combinations: 2+3+4 and 4+5. So the output is 2. Hmm.
First, I need to understand how these consecutive numbers form a sum equal to N. Let... | nvidia/OpenCodeReasoning|aizu | code | UNKNOWN_DIFFICULTY | ||
In a convex quadrilateral \(ABCD\) with diagonals intersecting at point \(S\), given that \(\angle SAB = \angle SBC = 30^\circ\) and \(\angle SCD = \angle SDA = 45^\circ\), find the angle between the diagonals of the quadrilateral. | <think>
Okay, so I have this geometry problem here. Let me read it again: In a convex quadrilateral ABCD with diagonals intersecting at point S. Given that angle SAB and angle SBC are both 30 degrees, and angles SCD and SDA are both 45 degrees. We need to find the angle between the diagonals of the quadrilateral. Hmm.
... | 60^\circ | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Let \( A = \{1, 2, 3\} \) and \( B = \{a, b, c, d\} \). Consider the Cartesian product \( A \times B \). How many subsets of \( A \times B \) contain exactly one element from each row and each column?
A: 0
B: 1
C: 2
D: 3
E: 4
F... | <think>
The problem states: Let \( A = \{1, 2, 3\} \) and \( B = \{a, b, c, d\} \). I need to consider the Cartesian product \( A \times B \), which should give me all possible ordered pairs: (1,a), (1,b), (1,c), (1,d), (2,a), (2,b), (2,c), (2,d), (3,a), (3,b), (3,c), (3,d). So, that's 3 elements in A and 4 in B, so 12... | 0 | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A nurse is preparing to administer a medication that requires a precise dosing based on the patient's weight. The patient weighs 75 kg, and the medication dosage is 2 mg/kg per hour. The medication is available in a vial contai... | <think>
I need to calculate how many milliliters of medication the nurse should administer per hour. The patient weighs 75 kg, and the dosage is 2 mg/kg per hour. The medication is available in a vial that has 50 mg per 10 mL. The options range from 3 mL to 25 mL.
First, I need to find out the total dosage required pe... | 15 | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In a linear eukaryotic chromosome, two replication origins, OriA and OriB, are separated by a distance D. OriA initiates replication at time t=0, while OriB initiates at time t = Δt (Δt > 0). Replication forks from both origins... | <think>
The problem involves two replication origins, OriA and OriB, on a linear eukaryotic chromosome. They're separated by a distance D. OriA starts replicating at time t=0, and OriB starts at time t=Δt, which is positive. Both forks move bidirectionally at speed V. I need to find what fraction of the region between ... | B | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
An angel investor is evaluating multiple startups for potential investment. Each startup has a unique combination of risk, growth potential, market size, and traction. The investor is looking to maximize returns while managing ... | <think>
I need to solve this problem about an angel investor choosing a strategy for a balanced portfolio with high growth potential and acceptable risk. There are ten options from A to J, each describing a different investment mix in startups with varying risk and growth levels.
First, I should define what "balanced ... | \text{F} | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In a computational model of traffic flow in a city, which of the following factors most significantly affects the accuracy of long-term traffic predictions?
A: The precision of initial traffic conditions at the start of the sim... | <think>
I need to determine which factor most significantly affects the accuracy of long-term traffic predictions in a computational model. There are ten options from A to J. I should reason step by step and then box my final answer.
First, I need to understand what "long-term traffic predictions" means. Long-term cou... | \text{F} | nvidia/OpenScienceReasoning-2 | science | null | |
Problem description.
An arithmetic progression(AP) is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
For example:- 1, 4, 7, 10,
13, 16, 19, ...
A geometric progression(GP) is a sequence of numbers where each term after the first is found by multiplying the p... | <think>
Okay, so I need to solve this problem where given three numbers, I have to determine if they form an arithmetic progression (AP) or geometric progression (GP), then find the next term. Hmm. Let's think about how AP and GP work.
First, AP: the difference between consecutive terms is constant. So for a1, a2, a3,... | nvidia/OpenCodeReasoning|codechef | code | UNKNOWN_DIFFICULTY | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In the context of workplace productivity, which of the following statements best describes the relationship between employee engagement, task complexity, and the effectiveness of management strategies in a high-stress environme... | <think>
I need to solve this problem about workplace productivity. The question asks which statement best describes the relationship between employee engagement, task complexity, and the effectiveness of management strategies in a high-stress environment. There are ten options from A to J.
First, I should recall what ... | \text{C} | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
During plant development, the process of organogenesis leads to the formation of various plant organs from meristematic tissues. Which of the following statements accurately describes the role of these meristematic tissues in t... | <think>
I need to solve this multiple-choice problem about plant meristematic tissues and their roles in organ development. The question is: "Which of the following statements accurately describes the role of these meristematic tissues in the development of specific plant organs?" There are options from A to J.
First,... | \text{H} | nvidia/OpenScienceReasoning-2 | science | null | |
- | <think>
Okay, I need to write a Python function called display that takes the head of a linked list and prints all the elements separated by a space, ending with a single space. The examples show that for the inputs like 1 2, the output is "1 2 " but the note says that the driver code handles the end of line, so maybe ... | nvidia/OpenCodeReasoning|geeksforgeeks | code | EASY | ||
- | <think>
Okay, let's see. The problem is about minimizing the total noise from parties in a dorm when students move in. The noise each day is equal to the number of students in the building they move into that day. We can empty a building up to K times to reset its count. The goal is to find the minimal possible total n... | nvidia/OpenCodeReasoning|kattis | code | interview | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Which of the following archaeological discoveries significantly contributed to our understanding of ancient Mesopotamian law and society?
A: The discovery of Tutankhamun's tomb in Egypt
B: The unearthing of the Dead Sea Scrolls... | <think>
I need to solve this problem: Which archaeological discovery significantly contributed to our understanding of ancient Mesopotamian law and society? Here are the options:
A: Tutankhamun's tomb in Egypt
B: Dead Sea Scrolls in Israel
C: Terracotta Army in China
D: Rosetta Stone in Egypt
E: Behistun Inscripti... | \text{I} | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
According to ICH-GCP E6(R3) guidelines and their application to orbital and deep-space clinical trials, which fundamental ethical principle faces an *irreconcilable conflict* when conducting randomized controlled trials (RCTs) ... | <think>
First, the question is about ICH-GCP E6(R3) guidelines applied to orbital and deep-space clinical trials. I need to find which fundamental ethical principle faces an irreconcilable conflict when conducting randomized controlled trials (RCTs) for novel countermeasures during long-duration missions to the Moon or... | H | nvidia/OpenScienceReasoning-2 | science | null | |
What is the largest five-digit integer whose digits have a product equal to the product $(7)(6)(5)(4)(3)(2)(1)$? | <think>
Okay, let's see. The problem is asking for the largest five-digit integer where the product of its digits equals the product of 7×6×5×4×3×2×1. First, I need to figure out what that product is. Let me calculate that real quick.
7×6 is 42, then 42×5 is 210, 210×4 is 840, 840×3 is 2520, 2520×2 is 5040, and 5040×... | 98752 | nvidia/OpenMathReasoning|MATH_training_set | math | null | |
Sherlock has a new girlfriend (so unlike him!). Valentine's day is coming and he wants to gift her some jewelry.
He bought n pieces of jewelry. The i-th piece has price equal to i + 1, that is, the prices of the jewelry are 2, 3, 4, ... n + 1.
Watson gave Sherlock a challenge to color these jewelry pieces such that t... | <think>
Okay, let's see. The problem is to color a sequence of jewelry pieces such that if one's price is a prime divisor of another, they must have different colors. And we need to find the minimal number of colors required, along with a valid coloring.
Hmm. So the prices start from 2 up to n+1. For example, when n i... | nvidia/OpenCodeReasoning|codeforces | code | competition | ||
AtCoDeer the deer has N cards with positive integers written on them. The number on the i-th card (1≤i≤N) is a_i. Because he loves big numbers, he calls a subset of the cards good when the sum of the numbers written on the cards in the subset, is K or greater.
Then, for each card i, he judges whether it is unnecessary... | <think>
Okay, I need to solve this programming problem. Let's read the problem statement carefully.
The problem is about finding the number of unnecessary cards in a set. Let's break down the definitions.
A subset is called good if the sum of the numbers in it is at least K. For a card to be unnecessary, any good sub... | nvidia/OpenCodeReasoning|atcoder | code | 0 | ||
All possible sequences of four consecutive positive integers less than 200 are created. A sequence is called orderly if the smallest member is divisible by 2, the next smallest member is divisible by 3, the next smallest is divisible by 4, and the largest is divisible by 5. What is the probability that a randomly-selec... | <think>
Okay, so I have this problem here where I need to find the probability that a randomly-selected sequence of four consecutive positive integers less than 200 is "orderly." An orderly sequence has the properties that the smallest number is divisible by 2, the next by 3, then by 4, and the largest by 5. Hmm, let m... | \frac{1}{49} | nvidia/OpenMathReasoning|aops_c5_contests_amp_programs | math | null | |
Let T be arbitrary binary tree — tree, every vertex of which has no more than two children. Given tree is rooted, so there exists only one vertex which doesn't have a parent — it's the root of a tree. Every vertex has an integer number written on it. Following algorithm is run on every value from the tree T:
1. Set ... | <think>
Okay, I need to solve this problem where I have to determine how many nodes in a given binary tree will fail the search algorithm when applied to their own values. The catch is that the tree isn't a binary search tree, so even though the algorithm is designed for BSTs, using it here might lead to incorrect resu... | nvidia/OpenCodeReasoning|codeforces | code | 10 | ||
What is the largest 3-digit palindrome that, when multiplied by 111, remains a palindrome? | <think>
Okay, so I need to find the largest 3-digit palindrome that, when multiplied by 111, the result is still a palindrome. Hmm, let's break this down step by step.
First, a 3-digit palindrome is a number that reads the same forwards and backwards. So, numbers like 121, 131, 141, etc. The largest 3-digit palindrome... | 414 | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In a 2D topological quantum field theory, anyons can exhibit statistics that are neither bosonic nor fermionic. Suppose a system contains two identical anyons with a statistical phase factor of $ e^{i\theta} $ when they are exc... | <think>
I'm dealing with a problem about anyons in a 2D topological quantum field theory. Anyons can have statistical phase factors that are neither bosonic nor fermionic. The problem states that when two identical anyons are exchanged, the wavefunction picks up a phase of \( e^{i\theta} \). But in this specific system... | \dfrac{\pi}{3} | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A company operates in a region with multiple regulatory bodies. The local environmental agency has imposed a restriction that limits the company's emissions to 100 units per day. However, the company holds a grandfather clause ... | <think>
I need to figure out the company's allowable emission limit based on the regulations. Let me read the problem carefully.
The local environmental agency has a limit of 100 units per day. But there's a grandfather clause that allows for a 20% higher emission limit based on historical operations. So, that would b... | 85 | nvidia/OpenScienceReasoning-2 | science | null | |
Along a road running in an east-west direction, there are A shrines and B temples. The i-th shrine from the west is located at a distance of s_i meters from the west end of the road, and the i-th temple from the west is located at a distance of t_i meters from the west end of the road.
Answer the following Q queries:
... | <think>
Okay, let's see. I need to solve this programming problem. The problem is about shrines and temples along a road, and for each query point, I have to find the minimal distance needed to visit at least one shrine and one temple. The key here is that the person can start moving from their initial position and nee... | nvidia/OpenCodeReasoning|atcoder | code | 0 | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
During surgery on a neonate, which active warming technique is most essential to prevent rapid heat loss?
A: Administering warmed intravenous fluids
B: Placing a warming blanket underneath the infant
C: Covering the infant's h... | <think>
First, the question is: "During surgery on a neonate, which active warming technique is most essential to prevent rapid heat loss?" I need to choose from options A through J.
The options are:
A: Administering warmed intravenous fluids
B: Placing a warming blanket underneath the infant
C: Covering the infant... | D | nvidia/OpenScienceReasoning-2 | science | null | |
Find the sum of the digits of the result of multiplying two numbers, each consisting of 2014 digits, where the first number is all 8s and the second number is all 9s. | <think>
Okay, let me try to figure this out. So the problem is to find the sum of the digits of the product of two numbers. Both numbers have 2014 digits each. The first number is all 8s, like 888...8 (2014 times), and the second is all 9s, 999...9 (2014 times). Then, after multiplying them, I need to sum all the digit... | 18126 | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A rectangular tank with a length of 20 cm, a width of 10 cm, and a height of 15 cm is filled with water. A solid plastic block with a volume of 600 cm³ is submerged into the water. By how much does the water level rise in the t... | <think>
I have a rectangular tank that's 20 cm long, 10 cm wide, and 15 cm high. It's filled with water, and I'm submerging a solid plastic block with a volume of 600 cm³ into it. I need to find out by how much the water level rises. The options range from 0.5 cm to 5 cm in 0.5 cm increments.
First, I recall that when... | 3 | nvidia/OpenScienceReasoning-2 | science | null | |
An \( n \)-gon (which is not self-intersecting) is triangulated using \( m \) interior vertices. The triangulation consists of \( N \) triangles such that: (1) their union is the original \( n \)-gon; (2) the union of their vertices is the set consisting of the \( n \) vertices of the \( n \)-gon and the \( m \) interi... | <think>
Okay, so I need to find the number of triangles, N, in a triangulated n-gon with m interior vertices. Let me start by recalling some basics about triangulation.
First, a polygon triangulation is when you divide the polygon into triangles such that no two triangles overlap except at their edges or vertices. Fo... | n + 2m - 2 | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
You have k pieces of laundry, each of which you want to wash, dry and fold. You are at a laundromat that has n1 washing machines, n2 drying machines and n3 folding machines. Each machine can process only one piece of laundry at a time. You can't dry a piece of laundry before it is washed, and you can't fold it before i... | <think>
Okay, let's see. The problem is about calculating the minimum time needed to process all the laundry through washing, drying, and folding, considering that each step's machines can only handle a certain number of items at once.
Hmm. So each piece of laundry has to go through all three stages in order, and eac... | nvidia/OpenCodeReasoning|codeforces | code | interview | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In the context of effective team management, which of the following strategies is most effective for a manager to enhance productivity and morale in a diverse workplace?
A: Implementing strict hierarchical structures to maintai... | <think>
I need to solve this problem about effective team management in a diverse workplace. The question is: which strategy is most effective for enhancing productivity and morale? There are ten options from A to J.
First, I should recall what makes a team effective in a diverse setting. Diversity can bring different... | \text{H} | nvidia/OpenScienceReasoning-2 | science | null | |
- | <think>
Okay, I need to solve this problem where given an array of positive integers and multiple queries, each asking how many elements in the array are divisible by a certain K. Let's think about how to approach this efficiently.
The brute force approach would be, for each query K, iterate through the array and coun... | nvidia/OpenCodeReasoning|geeksforgeeks | code | MEDIUM | ||
Evaluate the integral $\int_{0}^{1}\frac{2x-(1+x^2)^2\cot^{-1} x}{(1+x^2)\left(1-(1+x^2)\cot^{-1} x\right)}dx$. | <think>
Okay, let me try to tackle this integral. So, the problem is to evaluate the integral from 0 to 1 of [2x - (1 + x²)² arccot(x)] divided by [(1 + x²)(1 - (1 + x²)arccot(x))] dx. Hmm, that looks a bit complicated, but maybe there's a substitution that can simplify it.
First, let me write down the integral again ... | 1 + \ln 2 | nvidia/OpenMathReasoning|aops_c7_college_math | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In a Bose-Einstein condensate (BEC) of cold atoms, the Gross-Pitaevskii equation describes the macroscopic wave function of the condensate. Which of the following statements about the Gross-Pitaevskii equation is true?
A: The ... | <think>
I need to solve this problem about the Gross-Pitaevskii equation in the context of a Bose-Einstein condensate. The question is multiple-choice, and I have to choose which statement is true. Here are the options:
A: The equation is a linear Schrödinger equation with no interaction terms.
B: The equation incorp... | \text{C} | nvidia/OpenScienceReasoning-2 | science | null | |
We all know that GukiZ often plays with arrays.
Now he is thinking about this problem: how many arrays a, of length n, with non-negative elements strictly less then 2l meet the following condition: <image>? Here operation <image> means bitwise AND (in Pascal it is equivalent to and, in C/C++/Java/Python it is equival... | <think>
Okay, let's see. So the problem is to find the number of arrays of length n where each element is a non-negative integer less than 2^l. The condition is that the bitwise OR of all elements ANDed with k must equal exactly k. Wait, no, the condition is that the bitwise OR of all elements, when ANDed with k, equal... | nvidia/OpenCodeReasoning|codeforces | code | HARD | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In the context of mentoring new teachers, which of the following strategies is most effective for enhancing a mentee's confidence and teaching skills?
A: Providing direct solutions to all teaching challenges
B: Encouraging the ... | <think>
First, I need to solve this problem about mentoring new teachers. The question is: which strategy is most effective for enhancing a mentee's confidence and teaching skills? There are ten options from A to J.
Let me list them out:
A: Providing direct solutions to all teaching challenges
B: Encouraging the men... | \text{H} | nvidia/OpenScienceReasoning-2 | science | null | |
For a set of four distinct lines in a plane, there are exactly $N$ distinct points that lie on two or more of the lines. What is the sum of all possible values of $N$? | <think>
Okay, let me try to figure out this problem. The question is about four distinct lines in a plane and the number of distinct intersection points they can have. We need to find the sum of all possible values of N, where N is the number of such points.
First, I remember that when you have multiple lines in a pl... | 19 | nvidia/OpenMathReasoning|aops_c5_contests_amp_programs | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In a combined Scrum and Kanban methodology, which of the following best describes a balanced approach to project management?
A: The team holds daily stand-ups and uses a Scrum board with fixed sprints, while also implementing a... | <think>
I need to solve this problem about a combined Scrum and Kanban methodology. The question is, "which of the following best describes a balanced approach to project management?" I have options from A to J. I must choose the one that represents a balanced use of both Scrum and Kanban.
First, I should recall what ... | \text{G} | nvidia/OpenScienceReasoning-2 | science | null | |
Find \( \int \frac{\sqrt{x}}{1 + x^6} \, dx \). | <think>
Okay, so I need to solve the integral of sqrt(x)/(1 + x^6) dx. Hmm, let's see. First, maybe I should simplify the expression or look for a substitution that can make this integral more manageable. The denominator is 1 + x^6, which is a bit complicated. The numerator is sqrt(x), which is x^(1/2).
Let me write ... | \frac{\sqrt{2}}{6} \left[ \frac{1}{2} \ln \left| \frac{x^3 + \sqrt{2}x^{3/2} + 1}{x^3 - \sqrt{2}x^{3/2} + 1} \right| + \arctan\left(\sqrt{2}x^{3/2} + 1\right) + \arctan\left(\sqrt{2}x^{3/2} - 1\right) \right] + C | nvidia/OpenMathReasoning|aops_c7_college_math | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Which of the following practices is most effective in reducing the environmental impact of industrial wastewater treatment?
A: Using high-strength chemicals to break down contaminants
B: Implementing advanced filtration systems... | <think>
I need to solve this multiple-choice question: "Which of the following practices is most effective in reducing the environmental impact of industrial wastewater treatment?" with options from A to J.
First, I should understand what the question is asking. It's about reducing the environmental impact, so I need ... | \text{J} | nvidia/OpenScienceReasoning-2 | science | null | |
Vasya wants to buy a new refrigerator. He believes that a refrigerator should be a rectangular parallelepiped with integer edge lengths. Vasya calculated that for daily use he will need a refrigerator with volume of at least V. Moreover, Vasya is a minimalist by nature, so the volume should be no more than V, either — ... | <think>
Okay, I need to solve this programming problem. Let's read the problem carefully.
So the task is, given a volume V (in its prime factorized form), find three integers a, b, c such that a * b * c = V, and the surface area 2(ab + bc + ca) is minimized. Then output the surface area and the three dimensions.
The ... | nvidia/OpenCodeReasoning|codeforces | code | VERY_HARD | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A manufacturing plant uses the Economic Production Quantity (EPQ) model to optimize its production schedule. The annual demand for a product is 12,000 units, the production setup cost per setup is $200, the holding cost per uni... | <think>
I need to solve this EPQ problem. The annual demand is 12,000 units, setup cost per setup is $200, holding cost per unit per year is $1.50, and the production rate is 600 units per month. I need to find the optimal production quantity from the given options.
First, recall the EPQ formula. EPQ is the Economic P... | 1800 | nvidia/OpenScienceReasoning-2 | science | null | |
Let $p$ and $n$ be positive integers such that $p$ is prime and $1 + np$ is a perfect square. If $n + 1$ can be expressed as the sum of $p$ perfect squares, find the smallest possible value of $n + 1$ when $p = 7$. | <think>
Okay, so I need to solve this math problem where p is 7, and we have to find the smallest possible value of n + 1. The conditions are that 1 + np is a perfect square, and n + 1 can be expressed as the sum of p perfect squares, which in this case is 7 perfect squares. Alright, let's break this down step by step.... | 6 | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
- | <think>
Okay, let's see. The problem is to find the number of markets in a city. From the description, a market is a connected component of shops connected by roads. So each connected component counts as one market. Even a single shop with no roads is a market. So the task reduces to finding the number of connected com... | nvidia/OpenCodeReasoning|codechef | code | interview | ||
Evaluate the integral $\int \frac{\ln{x}}{1+x^2}dx$. | <think>
Okay, so I need to evaluate the integral of (ln x)/(1 + x²) dx. Hmm, let's think. I remember that integrals involving ln x often require integration by parts. But sometimes substitutions might work too. Let me start by recalling integration by parts: ∫u dv = uv - ∫v du. So maybe I can set u = ln x here. Then du... | \arctan(x) \ln x - \frac{1}{2i} \left( \text{Li}_2(ix) - \text{Li}_2(-ix) \right) + C | nvidia/OpenMathReasoning|aops_c7_college_math | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Which of the following statements is true regarding the computational complexity of training a support vector machine (SVM)?
A: Training an SVM is always NP-complete.
B: Training an SVM is always in P.
C: Training an SVM is alw... | <think>
I need to determine which statement is true about the computational complexity of training a support vector machine (SVM). The options range from it being NP-complete to being in P, and others.
First, recall that SVMs are used for classification by finding a hyperplane that separates data points. The training ... | \text{D} | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A 72-year-old patient presents with gradually worsening memory loss over 3 years, now struggling to manage finances and medications. Family reports increased confusion in the evenings. Which of the following is **most character... | <think>
First, the question is about a 72-year-old patient with gradually worsening memory loss over 3 years. They're struggling with finances and medications, and there's increased confusion in the evenings. I need to find which option is most characteristic of a dementia syndrome, as opposed to delirium or other cond... | C | nvidia/OpenScienceReasoning-2 | science | null | |
Given that \( f \) is analytic in \( |z| < 2 \), bounded there by 10, and \( f(1) = 0 \), find the best possible upper bound for \( |f(\frac{1}{2})| \). | <think>
Okay, so I have this complex analysis problem here. Let me try to figure it out step by step. The problem says that the function f is analytic in the disk |z| < 2, it's bounded there by 10, meaning |f(z)| ≤ 10 for all |z| < 2, and f(1) = 0. I need to find the best possible upper bound for |f(1/2)|. Hmm, okay.
... | \frac{20}{7} | nvidia/OpenMathReasoning|aops_c7_college_math | math | null | |
Find all quadruples of positive integers $(a,b,m,n)$ such that \[a^mb^n=(a+b)^2+1.\] | <think>
Okay, let's try to tackle this problem. We need to find all quadruples of positive integers (a, b, m, n) such that a^m * b^n = (a + b)^2 + 1. Hmm, this looks interesting. I should start by understanding what the equation is saying. The left side is a product of a raised to the power m and b raised to n, and the... | (13, 5, 1, 2) | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
You are given a permutation p of numbers 1, 2, ..., n. Let's define f(p) as the following sum:
<image>
Find the lexicographically m-th permutation of length n in the set of permutations having the maximum possible value of f(p).
Input
The single line of input contains two integers n and m (1 ≤ m ≤ cntn), where cntn ... | <think>
Okay, I need to solve this programming problem where I have to find the m-th lexicographical permutation of length n that has the maximum possible value of the function f(p). Hmm, let's think about what the function f(p) represents.
So the function f(p) is the sum of |p_i - p_{i+1}| for i from 1 to n-1. Wait, ... | nvidia/OpenCodeReasoning|codeforces | code | MEDIUM_HARD | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In a business negotiation, you notice that the other party is using a strategy where they stress the value of sustainable practices. Which of the following responses is most effective in aligning with this strategy while ensuri... | <think>
I need to solve this business negotiation problem. The other party is stressing the value of sustainable practices, and I have to choose the most effective response that aligns with their strategy while ensuring my own interests are met. The options are A through J.
First, I should understand what it means to ... | \text{B} | nvidia/OpenScienceReasoning-2 | science | null | |
Vova and Marina love offering puzzles to each other. Today Marina offered Vova to cope with the following task.
Vova has a non-directed graph consisting of n vertices and m edges without loops and multiple edges. Let's define the operation of contraction two vertices a and b that are not connected by an edge. As a res... | <think>
Okay, let's try to solve this problem. Hmm. The problem is about contracting vertices in a graph to form the longest possible chain. So, the goal is to find the maximum length of a chain that can be obtained through a series of contractions, and if it's impossible, return -1.
First, I need to understand what a... | nvidia/OpenCodeReasoning|codeforces | code | 11 | ||
Solve the equation:
\[ (2 + \sqrt{2})^{\log_2 x} + x^2 (2 - \sqrt{2})^{\log_2 x} = 1 + x^2 \] | <think>
Okay, let me try to solve this equation step by step. The equation is:
\[
(2 + \sqrt{2})^{\log_2 x} + x^2 (2 - \sqrt{2})^{\log_2 x} = 1 + x^2
\]
Hmm, first, I need to understand the structure of this equation. It has two terms on the left side and a combination of 1 and x² on the right. The exponents are loga... | 1 | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
Kevin Sun has just finished competing in Codeforces Round #334! The round was 120 minutes long and featured five problems with maximum point values of 500, 1000, 1500, 2000, and 2500, respectively. Despite the challenging tasks, Kevin was uncowed and bulldozed through all of them, distinguishing himself from the herd a... | <think>
Okay, let's tackle this problem. Hmm, so I need to calculate Kevin's final score based on the given inputs. Let's break down the steps.
First, the problem mentions the scoring formula for each problem. The maximum points are x, which for the five problems are 500, 1000, 1500, 2000, 2500 respectively. Oh right,... | nvidia/OpenCodeReasoning|codeforces | code | 7 | ||
How many odd integers are there between $\frac{17}{4}$ and $\frac{35}{2}?$ | <think>
Okay, so I need to find out how many odd integers are between 17/4 and 35/2. Hmm, let's start by converting those fractions to decimals to get a better sense of the range.
17 divided by 4 is 4.25, right? Because 4 times 4 is 16, and 17 minus 16 is 1, so 1/4 is 0.25. So the lower bound is 4.25. Then 35 divided... | 7 | nvidia/OpenMathReasoning|MATH_training_set | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Which of the following technological advancements had the most significant impact on the growth of e-commerce in the early 21st century?
A: The invention of the personal computer
B: The introduction of wireless internet (Wi-Fi)... | <think>
I need to solve this multiple-choice question: "Which of the following technological advancements had the most significant impact on the growth of e-commerce in the early 21st century?" The options are A through J. I must box only the answer.
First, I should recall that e-commerce is buying and selling goods o... | \text{G} | nvidia/OpenScienceReasoning-2 | science | null | |
Find the general term of the sum \( \sum_{y_{1} + \cdots + y_{k} = n} y_{1} \cdots y_{k} \) where \( y_1, \ldots, y_k \in \mathbb{N} \). | <think>
Okay, so I need to find the general term of the sum where we're summing the product y1*y2*...*yk over all compositions (since they're in natural numbers) of n into k parts. Hmm, compositions mean the order matters, right? So for example, if n=3 and k=2, the compositions would be (1,2) and (2,1), each contributi... | \binom{n + k - 1}{2k - 1} | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A 45-year-old woman presents with fatigue, weight gain, constipation, and cold intolerance for 6 months. Physical exam is notable for dry skin, mild puffy face, and delayed relaxation of deep tendon reflexes. Lab results show T... | <think>
First, the patient is a 45-year-old woman with symptoms: fatigue, weight gain, constipation, and cold intolerance for 6 months. These symptoms are classic for hypothyroidism because hypothyroidism slows down the body's metabolism.
Physical exam shows dry skin, mild puffy face, and delayed relaxation of deep te... | H | nvidia/OpenScienceReasoning-2 | science | null | |
Find the limit \(\lim_{x \rightarrow 0} \frac{2^{x^2} \cos^2 x - 1}{\sqrt{x^2 + 1} - 1}\). | <think>
Okay, so I need to find the limit as x approaches 0 of [2^(x²) * cos²x - 1] divided by [sqrt(x² +1) -1]. Hmm, let's see. Limits involving square roots and exponents can be tricky. Maybe I should start by expanding the numerator and the denominator using Taylor series or maybe use L'Hospital's Rule since it's 0/... | 2 (\ln 2 - 1) | nvidia/OpenMathReasoning|aops_c7_college_math | math | null | |
Express the surface area $S$ of a right circular cone in terms of the radius $r$ of its base, given that a sphere with radius 1 is inscribed in the cone. | <think>
Okay, let's see. I need to find the surface area of a right circular cone in terms of its base radius r, given that a sphere with radius 1 is inscribed in the cone. Hmm, okay. So the sphere is tangent to the cone from the inside. I remember that when a sphere is inscribed in a cone, there's a specific relations... | \frac{2\pi r^4}{r^2 - 1} | nvidia/OpenMathReasoning|aops_c7_college_math | math | null | |
- | <think>
Okay, I need to solve this problem where I have to determine if an array of integers is sorted in ascending order, descending order, or not sorted. Let's think about how to approach this.
First, the problem states that the array is valid and there's always one correct answer. So I don't have to handle cases wh... | nvidia/OpenCodeReasoning|codewars | code | introductory | ||
The only difference between easy and hard versions is constraints.
Nauuo is a girl who loves random picture websites.
One day she made a random picture website by herself which includes n pictures.
When Nauuo visits the website, she sees exactly one picture. The website does not display each picture with equal proba... | <think>
Okay, let's see. So the problem is about calculating the expected weights of pictures after m visits, considering that each visit's selection affects the weights. Hmm. The selection probability depends on the current weights, and each visit changes a chosen picture's weight by +1 or -1 based on whether Nauuo li... | nvidia/OpenCodeReasoning|codeforces | code | HARD | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A multinational beverage company operates in four regions with distinct water stress characteristics. Using Water Footprint Network methodology, they calculated the following annual operational footprints for their production f... | <think>
First, I need to understand what the question is asking. The company wants to invest in a water stewardship initiative in one region to maximize the reduction in their overall water scarcity footprint. The water scarcity footprint is the scarcity-weighted blue water footprint. Green water is excluded from scarc... | A | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Which of the following is **not** a recommended practice for maintaining heart health?
A: Regular physical exercise
B: Maintaining a healthy diet low in saturated fats
C: Smoking cessation
D: Managing stress through relaxation ... | <think>
I need to determine which option is not recommended for maintaining heart health. The question is multiple-choice, and I must box only the answer.
First, let's review the options:
A: Regular physical exercise
B: Maintaining a healthy diet low in saturated fats
C: Smoking cessation
D: Managing stress throug... | \text{F} | nvidia/OpenScienceReasoning-2 | science | null | |
After Governor's attack on prison, Rick found himself surrounded by walkers. They are coming towards him from all sides. Now, suppose Rick have infinite number of bullets with him. Suppose Rick need 1 bullet to kill each walker (yeah he is good in killing walkers. They need to be shot at head. See, how good he is). Now... | <think>
Okay, let's see. So the problem is about Rick surviving a walker attack. The walkers are at certain distances, and Rick can shoot them one by one. But after each kill, the remaining walkers move 1 meter closer. Also, his gun can fire 6 shots before needing a reload, which takes 1 second. During that reload time... | nvidia/OpenCodeReasoning|hackerearth | code | EASY | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
What is the minimum number of essential health services that must be included in a country's Universal Health Coverage (UHC) package to achieve effective financial protection for non-communicable diseases (NCDs) while ensuring ... | <think>
First, the question is about the minimum number of essential health services that must be included in a country's Universal Health Coverage (UHC) package. Specifically, it's for effective financial protection for non-communicable diseases (NCDs) while ensuring equity across rural and urban populations. This is ... | I | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Consider the hypothetical molecule XY3, where X is a central atom with the electron configuration \([Ne] 3s^2 3p^4\) and Y is a fluorine atom. What is the molecular geometry and hybridization of the central atom X in XY3?
A: Li... | <think>
I need to solve this problem about the molecule XY3. X is the central atom with electron configuration [Ne] 3s^2 3p^4, and Y is fluorine. I need to find the molecular geometry and hybridization of X in XY3. There are multiple choices from A to J.
First, recall that [Ne] stands for the electron configuration of... | \text{E} | nvidia/OpenScienceReasoning-2 | science | null | |
While standing in line to buy concert tickets, Kit moved 60 feet closer to the ticket window over a period of 30 minutes. At this rate, how many minutes will it take her to move the remaining 70 yards to the ticket window? | <think>
Okay, let's see. The problem says that Kit moved 60 feet closer to the ticket window over 30 minutes, and now we need to find out how long it will take her to move the remaining 70 yards at the same rate. Hmm, so first, I need to make sure the units are consistent. The initial movement is in feet and the remain... | 105 | nvidia/OpenMathReasoning|MATH_training_set | math | null | |
In trapezoid $ABCD$ with $AB \parallel CD$ inscribed in circle $\omega$, let point $G$ lie inside triangle $BCD$. Rays $AG$ and $BG$ meet $\omega$ again at points $P$ and $Q$, respectively. The line through $G$ parallel to $AB$ intersects $BD$ and $BC$ at points $R$ and $S$, respectively. If $BG$ bisects $\angle CBD$, ... | <think>
Okay, so I need to solve this geometry problem involving a cyclic trapezoid and some angle bisectors. Let me start by understanding the problem step by step.
First, we have trapezoid ABCD with AB parallel to CD, inscribed in a circle ω. That means ABCD is a cyclic trapezoid. Since it's cyclic and a trapezoid, ... | \frac{6}{5} | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
A mad scientist Dr.Jubal has made a competitive programming task. Try to solve it!
You are given integers n,k. Construct a grid A with size n × n consisting of integers 0 and 1. The very important condition should be satisfied: the sum of all elements in the grid is exactly k. In other words, the number of 1 in the gr... | <think>
Okay, I need to solve this programming problem. Let's read the problem statement carefully.
So, the task is to construct an n x n grid of 0s and 1s such that the total number of 1s is exactly k. Then, we need to minimize the value f(A), which is calculated as (max(R) - min(R))² + (max(C) - min(C))², where R is... | nvidia/OpenCodeReasoning|codeforces | code | 10 | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In the context of pharmaceutical formulations, which thermodynamic parameter is most directly used to predict the spontaneity of a drug dissolution process in an aqueous medium? | <think>
The question is: "In the context of pharmaceutical formulations, which thermodynamic parameter is most directly used to predict the spontaneity of a drug dissolution process in an aqueous medium?"
I need to recall what spontaneity means in thermodynamics. Spontaneity indicates whether a process will occur with... | \text{Gibbs free energy} | nvidia/OpenScienceReasoning-2 | science | null | |
A circle passes through point C of a rectangle ABCD and is tangent to AB and AD at points M and N, respectively. If the distance from C to line segment MN is 25 cm, find the area of rectangle ABCD. | <think>
Okay, let's try to tackle this geometry problem. Hmm, so we have a rectangle ABCD, and a circle that passes through point C. The circle is tangent to sides AB and AD at points M and N, respectively. The distance from point C to the line segment MN is 25 cm. We need to find the area of the rectangle ABCD.
First... | 625 | nvidia/OpenMathReasoning|aops_c4_high_school_math | math | null | |
Mr. Frugal bought a new house. He feels deeply in love with his new house because it has a comfortable living room in which he can put himself completely at ease. He thinks his new house is a really good buy.
But, to his disappointment, the floor of its living room has some scratches on it.
The floor has a rectangle ... | <think>
Okay, let's see. The problem is about covering all the scratched panels (marked as 1) with the minimum number of square carpets. The carpets can't cover any 0s. And the carpets must have sides that are multiples of the panel sizes. So each carpet is a square that covers a certain number of panels. For example, ... | nvidia/OpenCodeReasoning|aizu | code | UNKNOWN_DIFFICULTY | ||
Let \( a, b, c \) be positive real numbers such that \( ab + bc + ca = 3abc \). Find the minimum of
\[ A = \sum \frac{b + c}{a^2 + bc} + \sum \frac{(a - b)^2}{ab(a + b)} \] | <think>
Okay, let's see. The problem is about finding the minimum of this expression A given that ab + bc + ca equals 3abc. Hmm, first I need to understand the condition and the expression to minimize. Let's start by breaking it down.
The condition is ab + bc + ca = 3abc. Maybe I can manipulate this equation to find s... | 3 | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
Bob is a duck. He wants to get to Alice's nest, so that those two can duck! [Image] Duck is the ultimate animal! (Image courtesy of See Bang)
The journey can be represented as a straight line, consisting of $n$ segments. Bob is located to the left of the first segment, while Alice's nest is on the right of the last s... | <think>
Okay, let's see. I need to find the shortest time Bob can reach Alice's nest. Hmm, the problem involves different terrains and movement types with varying stamina costs and gains. So, the key is to model how Bob uses his stamina efficiently while choosing between walking, swimming, and flying.
First, let's und... | nvidia/OpenCodeReasoning|codeforces | code | interview | ||
Unlucky year in Berland is such a year that its number n can be represented as n = xa + yb, where a and b are non-negative integer numbers.
For example, if x = 2 and y = 3 then the years 4 and 17 are unlucky (4 = 20 + 31, 17 = 23 + 32 = 24 + 30) and year 18 isn't unlucky as there is no such representation for it.
Su... | <think>
Okay, so I need to solve this programming problem. Let's see what the problem is asking.
The problem is about finding the longest period (called The Golden Age) within a given range [l, r] where none of the years in that period are unlucky. An unlucky year is one that can be expressed as x^a + y^b, where a and... | nvidia/OpenCodeReasoning|codeforces | code | interview | ||
- | <think>
Okay, I need to solve this problem where given two one-digit integers a and b, I have to create two strings. The first string is made by concatenating b copies of a's digit. The second is a copies of b's digit. Then compare them lexicographically and output the smaller one. If they are equal, just output either... | nvidia/OpenCodeReasoning|atcoder | code | introductory | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A 52-year-old female presents to the Emergency Department with 4 days of progressive dyspnea and pleuritic chest pain. She has a history of stage IV metastatic breast cancer on active chemotherapy (last dose 7 days ago) and rec... | <think>
First, I need to understand the patient's situation. She's a 52-year-old female with stage IV metastatic breast cancer on chemotherapy. She had a minor fall a week ago and has been immobilized. She presents with progressive dyspnea and pleuritic chest pain for 4 days. Vital signs show tachycardia (HR 110), tach... | D | nvidia/OpenScienceReasoning-2 | science | null | |
- | <think>
Okay, I need to solve this problem where I have to generate a playing schedule for m teams each with n players. The key points are that each player must play against all players from other teams, and each round can have a player in at most one game. Also, the total number of rounds must be such that no player h... | nvidia/OpenCodeReasoning|kattis | code | competition | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In William Shakespeare's *The Merchant of Venice*, Portia's "quality of mercy" speech during the trial scene primarily serves to advocate for which concept in the application of law?
A: The inflexible enforcement of contractual... | <think>
First, I need to recall Portia's "quality of mercy" speech from The Merchant of Venice. It's in Act 4, Scene 1, during the trial where Shylock is demanding his pound of flesh from Antonio.
Portia, disguised as a lawyer, gives this famous speech about mercy. She says that mercy is an attribute of God himself, a... | D | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Two surfaces appear identical under a specific illuminant but differ spectrally (metameric pair). Under which of the following conditions is it theoretically possible for these surfaces to appear identical under **all** possibl... | <think>
The problem involves two surfaces that are metameric under a specific illuminant, meaning they look the same under that light but have different spectral reflectance. The question asks under which conditions these surfaces could appear identical under all possible combinations of two arbitrary illuminants A and... | J | nvidia/OpenScienceReasoning-2 | science | null | |
Find all real solutions to the equation
\[ 2(x^2-21)^{1/2} + 3(x^2-17)^{1/3} + 4(x^2-9)^{1/4} = \frac{90}{x}. \] | <think>
Okay, so I need to find all real solutions to this equation:
2 times the square root of (x² - 21) plus 3 times the cube root of (x² - 17) plus 4 times the fourth root of (x² - 9) equals 90 divided by x. Hmm, that looks complicated with all the different roots and the fraction on the right side. Let me try to b... | 5 | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
There are n football teams in the world.
The Main Football Organization (MFO) wants to host at most m games. MFO wants the i-th game to be played between the teams a_i and b_i in one of the k stadiums.
Let s_{ij} be the numbers of games the i-th team played in the j-th stadium. MFO does not want a team to have much... | <think>
Okay, let's see. I need to solve this programming problem where I have to assign stadiums to games to maximize the total money earned, while ensuring that for each team, the difference between the maximum and minimum number of games they play in any stadium doesn't exceed 2. Hmm.
First, let me understand the p... | nvidia/OpenCodeReasoning|codeforces | code | 12 | ||
I’m planning to have a party on my birthday. Many of my friends will come to the party. Some of them will come with one or more pieces of cakes, but it is not certain if the number of the cakes is a multiple of the number of people coming.
I wish to enjoy the cakes equally among the partiers. So, I decided to apply th... | <think>
Okay, let's see. I need to solve this problem where I have to calculate how many pieces of cake I can get based on the given conditions. Let's read the problem statement again carefully.
So, the problem says that there are N friends, and C of them brought cakes. Each of those C friends brought p_i pieces. The ... | nvidia/OpenCodeReasoning|aizu | code | UNKNOWN_DIFFICULTY | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A medical student begins shadowing experienced physicians, learning professional etiquette and communication styles used in hospital settings before starting their residency. This process best illustrates which type of socializ... | <think>
First, the question is about a medical student who is shadowing experienced physicians to learn professional etiquette and communication styles in hospital settings before starting their residency. I need to identify which type of socialization this best illustrates.
The options are:
A: Primary Socialization
... | B | nvidia/OpenScienceReasoning-2 | science | null | |
Find the next term of the sequence $1, 9, 15, 21, 25, 27, \ldots$. | <think>
Okay, let's see. I need to find the next term in the sequence: 1, 9, 15, 21, 25, 27, ... Hmm, let's start by looking at the differences between consecutive terms. That usually helps in these kinds of problems.
So, let's subtract each term from the one after it.
9 - 1 = 8
15 - 9 = 6
21 - 15 = 6
25 - 21 = 4... | 33 | nvidia/OpenMathReasoning|aops_c4_high_school_math | math | null | |
Consider \(2^{2010} + 1\) points in the plane. Let \(A\) be the maximum number of angles (formed by any three points) that are less than \(\frac{2009\pi}{2010}\). Calculate the minimum possible value of \(A\). | <think>
Okay, so I need to find the minimum possible value of A, which is the maximum number of angles less than 2009π/2010 formed by any three points in a set of 2^{2010} + 1 points in the plane. Hmm, that's a mouthful. Let me try to break this down step by step.
First, let me understand the problem. We have a huge n... | 2^{2010} | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Which of the following is **not** a common symptom of vitamin D deficiency?
A: Fatigue
B: Bone pain
C: Muscle weakness
D: Frequent infections
E: Mood changes
F: Excessive sweating
G: Increased bone density
H: Hair loss
I: Slow ... | <think>
First, I need to determine which option is not a common symptom of vitamin D deficiency. The options are A through J: Fatigue, Bone pain, Muscle weakness, Frequent infections, Mood changes, Excessive sweating, Increased bone density, Hair loss, Slow healing of wounds, and Dental issues.
Vitamin D is important ... | \text{G} | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
A 40-year-old man with a history of hypertension and obesity presents with a 6-month history of erectile dysfunction. He is also experiencing fatigue and has noticed somecentral obesity and purple striae on his abdomen. Which o... | <think>
I need to solve this medical problem. The patient is a 40-year-old man with hypertension and obesity. He has a 6-month history of erectile dysfunction, along with fatigue, central obesity, and purple striae on his abdomen. I need to choose the most likely explanation from the options given.
First, let's list t... | \text{D} | nvidia/OpenScienceReasoning-2 | science | null | |
You are given n points on a plane.
Please find the minimum sum of areas of two axis-aligned rectangles, such that each point is contained in at least one of these rectangles.
Note that the chosen rectangles can be degenerate. Rectangle contains all the points that lie inside it or on its boundary.
Input
The first l... | <think>
Okay, let's try to figure out how to solve this problem. The task is to find the minimum sum of the areas of two axis-aligned rectangles such that every point is in at least one of them. Hmm, rectangles can be degenerate, meaning their area could be zero if they're just lines or points. So maybe the optimal sol... | nvidia/OpenCodeReasoning|codeforces | code | VERY_HARD | ||
Given the sequence 1, 4, 13, 40, ..., find a closed-form equation to describe the pattern without depending on the previous value. | <think>
Okay, so I need to find a closed-form equation for the sequence 1, 4, 13, 40, ... Let me think. First, let me look at the differences between the terms to see if there's a pattern.
The first term is 1. The second term is 4. The difference between 4 and 1 is 3. The third term is 13, so the difference between 13... | \frac{3^n - 1}{2} | nvidia/OpenMathReasoning|aops_c4_high_school_math | math | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In the context of family therapy, which of the following strategies is most effective for addressing communication issues within a family system?
A: Cognitive-Behavioral Therapy (CBT) focused on individual members
B: Pharmacolo... | <think>
First, the question is: "In the context of family therapy, which of the following strategies is most effective for addressing communication issues within a family system?"
The options are various therapeutic approaches:
A: Cognitive-Behavioral Therapy (CBT) focused on individual members
B: Pharmacological in... | \text{E} | nvidia/OpenScienceReasoning-2 | science | null | |
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
Two parallel conductors, each carrying a current \( I \), are separated by a distance \( d \). The conductors are in a vacuum and are part of a simple circuit. Considering the magnetic forces between the conductors, which of th... | <think>
I have this problem about two parallel conductors carrying current I, separated by distance d. I need to find the net force per unit length between them and whether it's attractive or repulsive. The answer should be one of the options from A to J.
First, I recall that when two parallel wires carry current, the... | \text{B} | nvidia/OpenScienceReasoning-2 | science | null | |
Evaluate the integral $$\int_0^1{(1-x^3)}^n dx$$ in terms of $n$. | <think>
Okay, so I need to evaluate the integral from 0 to 1 of (1 - x^3)^n dx. Hmm, let me think. I remember that integrating functions raised to a power can sometimes be tricky. Maybe I can use substitution or some known integral formulas. Wait, there's the beta function or the gamma function related to integrals of ... | \frac{\Gamma\left(\frac{1}{3}\right) \Gamma(n + 1)}{3 \Gamma\left(n + \frac{4}{3}\right)} | nvidia/OpenMathReasoning|aops_c7_college_math | math | null | |
What is the value of the Riemann zeta function at \( s = -4 \)? | <think>
Okay, let's see. I need to find the value of the Riemann zeta function at s = -4. Hmm, I remember that the Riemann zeta function is defined as ζ(s) = sum_{n=1}^∞ 1/n^s for Re(s) > 1, but that's only for when the real part of s is greater than 1. For other values, especially negative integers, there's some analy... | 0 | nvidia/OpenMathReasoning|aops_c4_high_school_math | math | null | |
Ksenia has her winter exams. Today she is learning combinatorics. Here's one of the problems she needs to learn to solve.
How many distinct trees are there consisting of n vertices, each with the following properties:
* the tree is marked, that is, the vertices of the tree are numbered from 1 to n;
* each vertex... | <think>
Okay, let's see. So the problem is to count the number of distinct trees with n vertices that meet certain conditions. Hmm, the conditions are:
1. The tree is marked (vertices numbered 1 to n).
2. Each vertex has at most three edges, and vertex 1 has at most two.
3. The maximum matching size is exactly k.
And... | nvidia/OpenCodeReasoning|codeforces | code | VERY_HARD | ||
Vera adores poems. All the poems Vera knows are divided into quatrains (groups of four lines) and in each quatrain some lines contain rhymes.
Let's consider that all lines in the poems consist of lowercase Latin letters (without spaces). Letters "a", "e", "i", "o", "u" are considered vowels.
Two lines rhyme if their ... | <think>
Okay, let's see. I need to solve this problem where I have to determine the rhyme scheme of a poem based on the given quatrains. Hmm. The problem statement says that each quatrain must follow the same rhyme scheme, and if they don't match across all quatrains, the answer is NO. Also, if any quatrain's lines don... | nvidia/OpenCodeReasoning|codeforces | code | MEDIUM_HARD | ||
Solve the following problem. Make sure to put the answer (and only answer) inside \boxed{}.
In a software development project, which combination of practices would best ensure quality assurance and maintain efficient development cycles while fostering team collaboration?
A: Code reviews and pair programming
B: Continu... | <think>
First, the question is about a software development project. The goal is to ensure quality assurance, maintain efficient development cycles, and foster team collaboration. I need to choose the best combination of practices from the options provided.
Here are the options:
A: Code reviews and pair programming
... | \text{H} | nvidia/OpenScienceReasoning-2 | science | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.