id large_stringlengths 7 25 | source large_stringclasses 10
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openr1_math_3974 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
7th Swedish 1967 Problem 1 p parallel lines are drawn in the plane and q lines perpendicular to them are also drawn. How many rectangles are bounded by the lines?<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to figure out how many rectangles are formed when there are p parallel lines and q l... | 7th Swedish 1967 Problem 1 p parallel lines are drawn in the plane and q lines perpendicular to them are also drawn. How many rectangles are bounded by the lines? | <think>
Okay, so I need to figure out how many rectangles are formed when there are p parallel lines and q lines perpendicular to them. Hmm. Let me start by visualizing this. If there are p horizontal lines, say, and q vertical lines, then they intersect each other forming a grid. Each rectangle in this grid is defined... |
openr1_math_3975 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
5. (20 points) The clock shows the time as fifteen minutes past five. Determine the angle between the minute and hour hands at this moment.
---
Note: The translation maintains the original text's formatting and structure.<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to figure out the angle... | 5. (20 points) The clock shows the time as fifteen minutes past five. Determine the angle between the minute and hour hands at this moment.
---
Note: The translation maintains the original text's formatting and structure. | <think>
Okay, so I need to figure out the angle between the minute and hour hands when the time is fifteen minutes past five. Hmm, let's start by visualizing the clock. At 5:15, the minute hand is pointing at the 3, right? Because each number on the clock represents 5 minutes, so 15 minutes would be three numbers away ... |
openr1_math_3976 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
Example 4 As shown in Figure $17-5$, in $\triangle A B C$, $\angle A C B=30^{\circ}, \angle A B C=$ $50^{\circ}, M$ is a point inside the triangle, $\angle M A C=40^{\circ}, \angle M C B=20^{\circ}$. Find the degree measure of $\angle M B C$.
(Mathematical Bulletin, Issue 9, 1999, Problem 1208)<|im_end... | Example 4 As shown in Figure $17-5$, in $\triangle A B C$, $\angle A C B=30^{\circ}, \angle A B C=$ $50^{\circ}, M$ is a point inside the triangle, $\angle M A C=40^{\circ}, \angle M C B=20^{\circ}$. Find the degree measure of $\angle M B C$.
(Mathematical Bulletin, Issue 9, 1999, Problem 1208) | <think>
Alright, let's see. I need to find the measure of angle MBC in triangle ABC. The given angles are angle ACB = 30°, angle ABC = 50°, and inside point M has angles MAC = 40° and MCB = 20°. Hmm, okay. Let me sketch this out first to visualize.
So triangle ABC. Let's label the vertices. Let me recall that in a tri... |
openr1_math_3977 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
9 Let $f(x)=\frac{1}{1+2^{\lg x}}+\frac{1}{1+4^{\lg x}}+\frac{1}{1+8^{\lg x}}$, then $f(x)+f\left(\frac{1}{x}\right)=$<|im_end|>
<|im_start|>assistant
<think>
Okay, so I have this function f(x) which is the sum of three fractions: 1 over (1 + 2^{lg x}), plus 1 over (1 + 4^{lg x}), plus 1 over (1 + 8^{l... | 9 Let $f(x)=\frac{1}{1+2^{\lg x}}+\frac{1}{1+4^{\lg x}}+\frac{1}{1+8^{\lg x}}$, then $f(x)+f\left(\frac{1}{x}\right)=$ | <think>
Okay, so I have this function f(x) which is the sum of three fractions: 1 over (1 + 2^{lg x}), plus 1 over (1 + 4^{lg x}), plus 1 over (1 + 8^{lg x}). And I need to find f(x) + f(1/x). Hmm, let me start by understanding what each part of this function does.
First, let me recall that "lg x" usually means logari... |
openr1_math_3978 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
10.193. Inside a right angle, there is a point $M$, the distances from which to the sides of the angle are 4 and $8 \mathrm{~cm}$. A line passing through point $M$ cuts off a triangle from the right angle with an area of $100 \mathrm{~cm}^{2}$. Find the legs of the triangle.<|im_end|>
<|im_start|>assis... | 10.193. Inside a right angle, there is a point $M$, the distances from which to the sides of the angle are 4 and $8 \mathrm{~cm}$. A line passing through point $M$ cuts off a triangle from the right angle with an area of $100 \mathrm{~cm}^{2}$. Find the legs of the triangle. | <think>
Okay, so I have this problem here. Let me try to parse it step by step. It says: Inside a right angle, there is a point M, and the distances from M to the sides of the angle are 4 cm and 8 cm. Then, a line passing through point M cuts off a triangle from the right angle with an area of 100 cm². We need to find ... |
openr1_math_3979 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
Example 2 A bug crawls along a triangular iron ring, at each vertex the bug has an equal chance of crawling to one of the other two vertices. Then the probability that the bug is back at the starting point after $n$ moves is $\qquad$ [2]<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to find t... | Example 2 A bug crawls along a triangular iron ring, at each vertex the bug has an equal chance of crawling to one of the other two vertices. Then the probability that the bug is back at the starting point after $n$ moves is $\qquad$ [2] | <think>
Okay, so I need to find the probability that a bug, which is crawling along a triangular iron ring, returns to its starting point after n moves. At each vertex, the bug has an equal chance to go to either of the other two vertices. Hmm, let me think about how to approach this.
First, let me visualize the probl... |
openr1_math_3980 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
Example 2.26. $\int_{-\infty}^{+\infty} \frac{d x}{x^{2}+6 x+18}$.<|im_end|>
<|im_start|>assistant
<think>
Okay, let's see. I need to compute the integral from negative infinity to positive infinity of 1 over (x squared plus 6x plus 18) dx. Hmm, integrals over the entire real line... I remember that th... | Example 2.26. $\int_{-\infty}^{+\infty} \frac{d x}{x^{2}+6 x+18}$. | <think>
Okay, let's see. I need to compute the integral from negative infinity to positive infinity of 1 over (x squared plus 6x plus 18) dx. Hmm, integrals over the entire real line... I remember that these are improper integrals, so I might need to take limits. But maybe there's a trick to evaluate it without getting... |
openr1_math_3981 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
[ Properties and characteristics of an isosceles triangle. ]
Through the vertices $A$ and $C$ of triangle $A B C$, lines are drawn perpendicular to the bisector of angle $A B C$ and intersect the lines $C B$ and $B A$ at points $K$ and $M$ respectively. Find $A B$, if $B M=8, K C=1$.<|im_end|>
<|im_st... | [ Properties and characteristics of an isosceles triangle. ]
Through the vertices $A$ and $C$ of triangle $A B C$, lines are drawn perpendicular to the bisector of angle $A B C$ and intersect the lines $C B$ and $B A$ at points $K$ and $M$ respectively. Find $A B$, if $B M=8, K C=1$. | <think>
Okay, let's see. The problem is about an isosceles triangle, but we need to find the length of AB given some other conditions. Let me try to visualize this first.
So, we have triangle ABC. Through vertices A and C, lines are drawn perpendicular to the bisector of angle ABC. These lines intersect CB and BA at p... |
openr1_math_3982 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
11. If in a $4 \times 4$ grid of 16 cells, each cell is filled with a number such that the sum of the numbers in all adjacent cells of each cell is 1, then the sum of the 16 numbers in the grid is $\qquad$
(Note: Adjacent cells refer to cells that share exactly one edge)<|im_end|>
<|im_start|>assistant... | 11. If in a $4 \times 4$ grid of 16 cells, each cell is filled with a number such that the sum of the numbers in all adjacent cells of each cell is 1, then the sum of the 16 numbers in the grid is $\qquad$
(Note: Adjacent cells refer to cells that share exactly one edge) | <think>
Okay, so I need to solve this problem about a 4x4 grid where each cell has a number, and the sum of the numbers in all adjacent cells for each cell is 1. Then I have to find the total sum of all 16 numbers in the grid. Hmm, let's start by understanding the problem step by step.
First, let me visualize the grid... |
openr1_math_3983 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
5. In the number $2 * 0 * 1 * 6 * 0 *$, each of the 5 asterisks needs to be replaced with any of the digits $0,1,2,3,4,5,6,7,8$ (digits can repeat) so that the resulting 10-digit number is divisible by 18. In how many ways can this be done?<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to fig... | 5. In the number $2 * 0 * 1 * 6 * 0 *$, each of the 5 asterisks needs to be replaced with any of the digits $0,1,2,3,4,5,6,7,8$ (digits can repeat) so that the resulting 10-digit number is divisible by 18. In how many ways can this be done? | <think>
Okay, so I need to figure out how many ways I can replace the five asterisks in the number 2*0*1*6*0* with digits from 0 to 9 (but wait, the problem says digits 0 through 8, actually. Let me check that again. The original problem says: each of the 5 asterisks needs to be replaced with any of the digits 0,1,2,3,... |
openr1_math_3984 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
A triangle has side lengths $a, a$ and $b$. It has perimeter $P$ and area $A$. Given that $b$ and $P$ are integers, and that $P$ is numerically equal to $A^{2}$, find all possible pairs $(a, b)$.<|im_end|>
<|im_start|>assistant
<think>
Alright, let me try to figure out this problem. So, we have a trian... | A triangle has side lengths $a, a$ and $b$. It has perimeter $P$ and area $A$. Given that $b$ and $P$ are integers, and that $P$ is numerically equal to $A^{2}$, find all possible pairs $(a, b)$. | <think>
Alright, let me try to figure out this problem. So, we have a triangle with two sides of length a and one side of length b. That makes it an isosceles triangle. The perimeter P and area A are related such that P is equal to A squared. Also, both b and P are integers. We need to find all possible pairs (a, b).
... |
openr1_math_3985 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
Let $1 = d_1 < d_2 < ...< d_k = n$ be all natural divisors of the natural number $n$. Find all possible values of the number $k$ if $n=d_2d_3 + d_2d_5+d_3d_5$.<|im_end|>
<|im_start|>assistant
<think>
Okay, let me try to work through this problem step by step. So, we have a natural number n, and its ... | Let $1 = d_1 < d_2 < ...< d_k = n$ be all natural divisors of the natural number $n$. Find all possible values of the number $k$ if $n=d_2d_3 + d_2d_5+d_3d_5$. | <think>
Okay, let me try to work through this problem step by step. So, we have a natural number n, and its divisors listed in order: 1 = d₁ < d₂ < ... < d_k = n. We need to find all possible values of k (which is the number of divisors) given that n = d₂d₃ + d₂d₅ + d₃d₅.
First, let me make sure I understand the prob... |
openr1_math_3986 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
# Task 9.2
Factorize $x^{4}+2021 x^{2}+2020 x+2021$.
## Number of points 7
#<|im_end|>
<|im_start|>assistant
<think>
Okay, let's see. I need to factorize the polynomial x⁴ + 2021x² + 2020x + 2021. Hmm, quartic polynomial. Factoring quartics can be tricky. Let me start by checking if there are any ob... | # Task 9.2
Factorize $x^{4}+2021 x^{2}+2020 x+2021$.
## Number of points 7
# | <think>
Okay, let's see. I need to factorize the polynomial x⁴ + 2021x² + 2020x + 2021. Hmm, quartic polynomial. Factoring quartics can be tricky. Let me start by checking if there are any obvious rational roots using the Rational Root Theorem. The possible roots would be factors of 2021 over factors of 1, so ±1, ±2021... |
openr1_math_3987 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
11. Find the sum of the values of the polynomial \(x^{5}-1.7 \cdot x^{3}+2.5\) at \(x=19.1\) and \(x=-19.1\).<|im_end|>
<|im_start|>assistant
<think>
Okay, let's see. I need to find the sum of the values of the polynomial \(x^{5} - 1.7x^{3} + 2.5\) at \(x = 19.1\) and \(x = -19.1\). Hmm, so basically, ... | 11. Find the sum of the values of the polynomial \(x^{5}-1.7 \cdot x^{3}+2.5\) at \(x=19.1\) and \(x=-19.1\). | <think>
Okay, let's see. I need to find the sum of the values of the polynomial \(x^{5} - 1.7x^{3} + 2.5\) at \(x = 19.1\) and \(x = -19.1\). Hmm, so basically, I have to compute the polynomial at both these points and then add the results together. But wait, maybe there's a smarter way than just plugging in each value... |
openr1_math_3988 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
4. Two classes are planting trees. Class one plants 3 trees per person, and class two plants 5 trees per person, together planting a total of 115 trees. The maximum sum of the number of people in the two classes is $\qquad$ .<|im_end|>
<|im_start|>assistant
<think>
Okay, so there's this problem about t... | 4. Two classes are planting trees. Class one plants 3 trees per person, and class two plants 5 trees per person, together planting a total of 115 trees. The maximum sum of the number of people in the two classes is $\qquad$ . | <think>
Okay, so there's this problem about two classes planting trees. Class one plants 3 trees per person, and class two plants 5 trees per person. Together, they planted a total of 115 trees. We need to find the maximum sum of the number of people in the two classes. Hmm, let me try to figure this out step by step.
... |
openr1_math_3989 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
GS. 4 Calculate the value of $\frac{2008^{3}+4015^{3}}{2007^{3}+4015^{3}}$.<|im_end|>
<|im_start|>assistant
<think>
Alright, let me try to figure out how to solve this problem: Calculate the value of (2008³ + 4015³) divided by (2007³ + 4015³). Hmm, that's an interesting expression. At first glance, it ... | GS. 4 Calculate the value of $\frac{2008^{3}+4015^{3}}{2007^{3}+4015^{3}}$. | <think>
Alright, let me try to figure out how to solve this problem: Calculate the value of (2008³ + 4015³) divided by (2007³ + 4015³). Hmm, that's an interesting expression. At first glance, it looks like two large cubes in the numerator and denominator, each added to another cube. Maybe there's a way to simplify this... |
openr1_math_3990 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
4. In the Cartesian coordinate system, the curve represented by the equation $m\left(x^{2}+y^{2}+2 y\right.$ $+1)=(x-2 y+3)^{2}$ is an ellipse, then the range of $m$ is .
(A) $(0,1)$
(B) $(1,+\infty)$
(C) $(0,5)$
(D) $(5,+\infty)$
(Hunan contribution)<|im_end|>
<|im_start|>assistant
<think>
Okay, let's... | 4. In the Cartesian coordinate system, the curve represented by the equation $m\left(x^{2}+y^{2}+2 y\right.$ $+1)=(x-2 y+3)^{2}$ is an ellipse, then the range of $m$ is .
(A) $(0,1)$
(B) $(1,+\infty)$
(C) $(0,5)$
(D) $(5,+\infty)$
(Hunan contribution) | <think>
Okay, let's try to figure out the range of m for which the given equation represents an ellipse. The equation is m(x² + y² + 2y + 1) = (x - 2y + 3)². Hmm, first, I remember that the general form of a conic section is Ax² + Bxy + Cy² + Dx + Ey + F = 0. Depending on the coefficients, we can determine whether it's... |
openr1_math_3991 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
14. Insert parentheses in the equation: $1: 2: 3: 4: 5: 6: 7: 8: 9: 10=7$, to make it true.<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to figure out where to put parentheses in this equation: 1:2:3:4:5:6:7:8:9:10=7. The colons represent division, right? So it's like 1 ÷ 2 ÷ 3 ÷ 4 ÷ 5 ÷ 6 ÷... | 14. Insert parentheses in the equation: $1: 2: 3: 4: 5: 6: 7: 8: 9: 10=7$, to make it true. | <think>
Okay, so I need to figure out where to put parentheses in this equation: 1:2:3:4:5:6:7:8:9:10=7. The colons represent division, right? So it's like 1 ÷ 2 ÷ 3 ÷ 4 ÷ 5 ÷ 6 ÷ 7 ÷ 8 ÷ 9 ÷ 10 = 7. But obviously, if you just divide all those numbers sequentially, the result would be a tiny fraction, way less than 1. ... |
openr1_math_3992 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
【Question 18】
Two natural numbers are divided, the quotient is 15, and the remainder is 5. It is known that the sum of the dividend, divisor, quotient, and remainder is 2169. Find the dividend.<|im_end|>
<|im_start|>assistant
<think>
Okay, so there's this problem here where two natural numbers are divi... | 【Question 18】
Two natural numbers are divided, the quotient is 15, and the remainder is 5. It is known that the sum of the dividend, divisor, quotient, and remainder is 2169. Find the dividend. | <think>
Okay, so there's this problem here where two natural numbers are divided, giving a quotient of 15 and a remainder of 5. The sum of the dividend, divisor, quotient, and remainder is 2169. We need to find the dividend. Hmm, let me think step by step how to approach this.
First, let me recall some basics about di... |
openr1_math_3993 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
$28 \cdot 5$ A cube is formed by welding 12 pieces of wire, each 3 inches long. A fly first lands on one vertex, then crawls along the wires. If it does not turn back and does not walk on the same path, the maximum distance it can crawl to return to the original landing point is
(A) 24 inches.
(B) 12 ... | $28 \cdot 5$ A cube is formed by welding 12 pieces of wire, each 3 inches long. A fly first lands on one vertex, then crawls along the wires. If it does not turn back and does not walk on the same path, the maximum distance it can crawl to return to the original landing point is
(A) 24 inches.
(B) 12 inches.
(C) 30 in... | <think>
Okay, let me try to figure out this cube problem. So, the question is about a cube made by welding 12 pieces of wire, each 3 inches long. A fly lands on one vertex and crawls along the wires without turning back or walking on the same path. We need to find the maximum distance it can crawl to return to the orig... |
openr1_math_3994 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
Task B-4.4. Determine all natural numbers $a$ for which the number $a^{3}+1$ is a power of 3.<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to find all natural numbers a such that a cubed plus one is a power of three. Hmm, let's start by understanding what the problem is asking. A power of th... | Task B-4.4. Determine all natural numbers $a$ for which the number $a^{3}+1$ is a power of 3. | <think>
Okay, so I need to find all natural numbers a such that a cubed plus one is a power of three. Hmm, let's start by understanding what the problem is asking. A power of three means numbers like 3, 9, 27, 81, etc., which can be written as 3^k where k is a natural number. So, I need to find all a in natural numbers... |
openr1_math_3995 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
2. (3 points) A student, while solving a calculation problem, was supposed to divide by 20 in the last step, but mistakenly added 20, thus obtaining an incorrect result of 180. What should the correct answer to this calculation problem be? $\qquad$ .<|im_end|>
<|im_start|>assistant
<think>
Okay, let me... | 2. (3 points) A student, while solving a calculation problem, was supposed to divide by 20 in the last step, but mistakenly added 20, thus obtaining an incorrect result of 180. What should the correct answer to this calculation problem be? $\qquad$ . | <think>
Okay, let me try to figure this problem out. So, the student was supposed to divide by 20 in the last step but instead added 20 and got 180. I need to find what the correct answer should be. Hmm, let's break it down step by step.
First, let me understand what's happening here. There's a calculation problem whe... |
openr1_math_3996 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
11.8. A student was supposed to multiply a three-digit number by a four-digit number (the numbers do not start with 0). Instead of doing so, he simply appended the four-digit number to the right of the three-digit number, obtaining a seven-digit number, which is $N$ times ($N \in \mathbb{Z}$) larger th... | 11.8. A student was supposed to multiply a three-digit number by a four-digit number (the numbers do not start with 0). Instead of doing so, he simply appended the four-digit number to the right of the three-digit number, obtaining a seven-digit number, which is $N$ times ($N \in \mathbb{Z}$) larger than the correct re... | <think>
Okay, let's tackle this problem step by step. So, part a) is asking if N can be equal to 2 or 10. Hmm. Let me first understand what the problem is saying. A student was supposed to multiply a three-digit number by a four-digit number, but instead, he just appended the four-digit number to the right of the three... |
openr1_math_3997 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
$a_1=-1$, $a_2=2$, and $a_n=\frac {a_{n-1}}{a_{n-2}}$ for $n\geq 3$. What is $a_{2006}$?
$
\textbf{(A)}\ -2
\qquad\textbf{(B)}\ -1
\qquad\textbf{(C)}\ -\frac 12
\qquad\textbf{(D)}\ \frac 12
\qquad\textbf{(E)}\ 2
$<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to find the value of the 2006th... | $a_1=-1$, $a_2=2$, and $a_n=\frac {a_{n-1}}{a_{n-2}}$ for $n\geq 3$. What is $a_{2006}$?
$
\textbf{(A)}\ -2
\qquad\textbf{(B)}\ -1
\qquad\textbf{(C)}\ -\frac 12
\qquad\textbf{(D)}\ \frac 12
\qquad\textbf{(E)}\ 2
$ | <think>
Okay, so I need to find the value of the 2006th term in this sequence. Let me start by writing down the given information. The first term, a₁, is -1, and the second term, a₂, is 2. Then for any n greater than or equal to 3, each term aₙ is equal to the previous term divided by the term before that, so aₙ = aₙ₋₁... |
openr1_math_3998 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
8. (10 points) In the inscribed quadrilateral $A B C D$, the degree measures of the angles are in the ratio $\angle A: \angle B: \angle C=2: 3: 4$. Find the length of $A C$, if $C D=8, B C=7.5 \sqrt{3}-4$.<|im_end|>
<|im_start|>assistant
<think>
Okay, so I have this problem about an inscribed quadrilat... | 8. (10 points) In the inscribed quadrilateral $A B C D$, the degree measures of the angles are in the ratio $\angle A: \angle B: \angle C=2: 3: 4$. Find the length of $A C$, if $C D=8, B C=7.5 \sqrt{3}-4$. | <think>
Okay, so I have this problem about an inscribed quadrilateral ABCD. The angles at A, B, and C are in the ratio 2:3:4. I need to find the length of AC, given that CD is 8 and BC is 7.5√3 - 4. Alright, let's start by recalling some properties of cyclic quadrilaterals.
First off, in a cyclic quadrilateral, the o... |
openr1_math_3999 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
$1 \cdot 20$ If positive numbers $a, b, c$ satisfy the equation $a^{3}+b^{3}+c^{3}-3 a b c=0$, then
(A) $a=b=c$.
(B) $a=b \neq c$.
(C) $b=c \neq a$.
(D) $a, b, c$ are all unequal.
(1st "Five Sheep Cup" Junior High School Mathematics Competition, 1989)<|im_end|>
<|im_start|>assistant
<think>
Okay, let's... | $1 \cdot 20$ If positive numbers $a, b, c$ satisfy the equation $a^{3}+b^{3}+c^{3}-3 a b c=0$, then
(A) $a=b=c$.
(B) $a=b \neq c$.
(C) $b=c \neq a$.
(D) $a, b, c$ are all unequal.
(1st "Five Sheep Cup" Junior High School Mathematics Competition, 1989) | <think>
Okay, let's see. I have this problem here: If positive numbers a, b, c satisfy the equation a³ + b³ + c³ - 3abc = 0, then which of the options (A) to (D) is correct? The options are about whether they are all equal, two equal and one different, or all unequal. Hmm.
First, I remember there's a formula related t... |
openr1_math_4000 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
14. (1993 German Mathematical Olympiad) Every natural number $n$ greater than 2 can be expressed as the sum of several distinct natural numbers. Let the maximum number of these distinct natural numbers be $A(n)$. Find $A(n)$ (expressed in terms of $n$).<|im_end|>
<|im_start|>assistant
<think>
Okay, so ... | 14. (1993 German Mathematical Olympiad) Every natural number $n$ greater than 2 can be expressed as the sum of several distinct natural numbers. Let the maximum number of these distinct natural numbers be $A(n)$. Find $A(n)$ (expressed in terms of $n$). | <think>
Okay, so I have this problem from the 1993 German Mathematical Olympiad. The question is about expressing every natural number n greater than 2 as a sum of several distinct natural numbers, and then finding the maximum number of such distinct numbers, denoted as A(n). The task is to find A(n) expressed in terms... |
openr1_math_4001 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
The number $2^{1997}$ has $m$ decimal digits, while the number $5^{1997}$ has $n$ digits. Evaluate $m+n$.<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to find out how many digits the numbers 2^1997 and 5^1997 have, and then add those two numbers of digits together. Hmm, let's think. I rememb... | The number $2^{1997}$ has $m$ decimal digits, while the number $5^{1997}$ has $n$ digits. Evaluate $m+n$. | <think>
Okay, so I need to find out how many digits the numbers 2^1997 and 5^1997 have, and then add those two numbers of digits together. Hmm, let's think. I remember that the number of digits in a number can be found using logarithms. Specifically, the formula is something like taking the floor of the base-10 logarit... |
openr1_math_4002 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
Let the notation $|X|$ represent the number of elements in the set $X$. Suppose $|X|=n\left(n \in \mathbf{N}_{+}\right)$, and all subsets of $X$ are $\left\{A_{1}, A_{2}, \cdots, A_{m}\right\}\left(m=2^{n}\right)$. It is known that the sum of the number of elements in the intersections of these subsets... | Let the notation $|X|$ represent the number of elements in the set $X$. Suppose $|X|=n\left(n \in \mathbf{N}_{+}\right)$, and all subsets of $X$ are $\left\{A_{1}, A_{2}, \cdots, A_{m}\right\}\left(m=2^{n}\right)$. It is known that the sum of the number of elements in the intersections of these subsets is
$$
S=\sum_{i=... | <think>
Okay, so I need to find the sum T, which is the sum over all pairs of distinct subsets A_i and A_j of the sizes of their intersections. The problem gives me that the sum S, which is the sum over all i and j (including when i=j) of |A_i ∩ A_j|, equals n * 2^(2(n-1)). They want me to find T, which is the same sum... |
openr1_math_4003 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
5. Let $a, b$ be real numbers, and the function $f(x)=a x+b$ satisfies: for any $x \in[0,1]$, we have $|f(x)| \leq 1$. Then the maximum value of $a b$ is $\qquad$ .<|im_end|>
<|im_start|>assistant
<think>
Okay, so I have this problem where I need to find the maximum value of the product \( ab \) given ... | 5. Let $a, b$ be real numbers, and the function $f(x)=a x+b$ satisfies: for any $x \in[0,1]$, we have $|f(x)| \leq 1$. Then the maximum value of $a b$ is $\qquad$ . | <think>
Okay, so I have this problem where I need to find the maximum value of the product \( ab \) given that the function \( f(x) = ax + b \) satisfies \( |f(x)| \leq 1 \) for all \( x \) in the interval [0, 1]. Let me try to work through this step by step.
First, let me understand the constraints. The function is l... |
openr1_math_4004 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
2.31. The side of the base of a regular triangular pyramid is equal to $a$. A plane is drawn through one of the sides of the base, perpendicular to the opposite lateral edge and dividing this edge in the ratio $\boldsymbol{m}: \boldsymbol{n}$, counting from the vertex of the base. Determine the total s... | 2.31. The side of the base of a regular triangular pyramid is equal to $a$. A plane is drawn through one of the sides of the base, perpendicular to the opposite lateral edge and dividing this edge in the ratio $\boldsymbol{m}: \boldsymbol{n}$, counting from the vertex of the base. Determine the total surface area of th... | <think>
Okay, so I need to find the total surface area of a regular triangular pyramid where the base side is length 'a'. A plane is drawn through one side of the base, perpendicular to the opposite lateral edge, and divides this edge in the ratio m:n from the vertex of the base. Hmm, that sounds a bit complicated, but... |
openr1_math_4005 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
6. Find the set of values of the function $f(x)=1 / g(64 g(g(\ln x)) / 1025)$, where
$$
g(x)=x^{5}+1 / x^{5} \cdot(10 \text { points })
$$<|im_end|>
<|im_start|>assistant
<think>
Okay, let's try to figure out this problem. So, we have the function f(x) = 1 / g(64 g(g(ln x)) / 1025), and g(x) is define... | 6. Find the set of values of the function $f(x)=1 / g(64 g(g(\ln x)) / 1025)$, where
$$
g(x)=x^{5}+1 / x^{5} \cdot(10 \text { points })
$$ | <think>
Okay, let's try to figure out this problem. So, we have the function f(x) = 1 / g(64 g(g(ln x)) / 1025), and g(x) is defined as x⁵ + 1/x⁵. We need to find the set of values that f(x) can take. Hmm, that seems a bit complicated with all the nested functions. Let me break it down step by step.
First, let me writ... |
openr1_math_4006 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
2. The sum of the terms of an infinite geometric series is 2 and the sum of the squares of the terms of this series is 6 . Find the sum of the cubes of the terms of this series.<|im_end|>
<|im_start|>assistant
<think>
Okay, so I have this problem here about an infinite geometric series. The sum of the ... | 2. The sum of the terms of an infinite geometric series is 2 and the sum of the squares of the terms of this series is 6 . Find the sum of the cubes of the terms of this series. | <think>
Okay, so I have this problem here about an infinite geometric series. The sum of the series is 2, and the sum of the squares of the terms is 6. I need to find the sum of the cubes of the terms. Hmm, let me think. Alright, let's start by recalling some formulas related to geometric series.
First, an infinite ge... |
openr1_math_4007 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
Let $T=\frac{1}{4}x^{2}-\frac{1}{5}y^{2}+\frac{1}{6}z^{2}$ where $x,y,z$ are real numbers such that $1 \leq x,y,z \leq 4$ and $x-y+z=4$.
Find the smallest value of $10 \times T$.<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to find the smallest value of 10 times T, where T is given by the ex... | Let $T=\frac{1}{4}x^{2}-\frac{1}{5}y^{2}+\frac{1}{6}z^{2}$ where $x,y,z$ are real numbers such that $1 \leq x,y,z \leq 4$ and $x-y+z=4$.
Find the smallest value of $10 \times T$. | <think>
Okay, so I need to find the smallest value of 10 times T, where T is given by the expression (1/4)x² - (1/5)y² + (1/6)z². The variables x, y, z are real numbers between 1 and 4, inclusive, and they have to satisfy the equation x - y + z = 4. Alright, let's break this down step by step.
First, I should understa... |
openr1_math_4008 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
1. Given $\sin \alpha \cdot \cos \beta=-\frac{1}{2}$. Then the range of $\cos \alpha \cdot \sin \beta$ is ( ).
(A) $\left[-1, \frac{1}{2}\right]$
(B) $\left[-\frac{1}{2}, 1\right]$
(C) $\left[-\frac{3}{4}, \frac{3}{4}\right]$
(D) $\left[-\frac{1}{2}, \frac{1}{2}\right]$<|im_end|>
<|im_start|>assistant
... | 1. Given $\sin \alpha \cdot \cos \beta=-\frac{1}{2}$. Then the range of $\cos \alpha \cdot \sin \beta$ is ( ).
(A) $\left[-1, \frac{1}{2}\right]$
(B) $\left[-\frac{1}{2}, 1\right]$
(C) $\left[-\frac{3}{4}, \frac{3}{4}\right]$
(D) $\left[-\frac{1}{2}, \frac{1}{2}\right]$ | <think>
Okay, let's try to figure out this problem. So, we have sin α multiplied by cos β equals -1/2, and we need to find the range of cos α times sin β. The options are given from A to D. Hmm, trigonometry product identities, maybe? Let's see.
First, I remember that there are product-to-sum formulas in trigonometry.... |
openr1_math_4009 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
6. (20 points) Each of the two baskets contains white and black balls, and the total number of balls in both baskets is 25. A ball is randomly drawn from each basket. It is known that the probability that both drawn balls will be white is 0.54. Find the probability that both drawn balls will be black.<... | 6. (20 points) Each of the two baskets contains white and black balls, and the total number of balls in both baskets is 25. A ball is randomly drawn from each basket. It is known that the probability that both drawn balls will be white is 0.54. Find the probability that both drawn balls will be black. | <think>
Okay, so I need to find the probability that both drawn balls will be black, given that there are two baskets each containing white and black balls, the total number of balls in both baskets is 25, and the probability that both drawn balls are white is 0.54. Hmm, let's try to break this down step by step.
Firs... |
openr1_math_4010 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
a) Verify that if we choose 3 or more integers from the set $\{6 k+1,6 k+2,6 k+3,6 k+4,6 k+5,6 k+6\}$, at least two will differ by 1, 4, or 5.
b) What is the largest number of positive integers less than or equal to 2022 that we can choose so that there are no two numbers whose difference is 1, 4, or ... | a) Verify that if we choose 3 or more integers from the set $\{6 k+1,6 k+2,6 k+3,6 k+4,6 k+5,6 k+6\}$, at least two will differ by 1, 4, or 5.
b) What is the largest number of positive integers less than or equal to 2022 that we can choose so that there are no two numbers whose difference is 1, 4, or 5? | <think>
Okay, let's try to tackle part a) first. The problem says that if we choose 3 or more integers from the set {6k+1, 6k+2, 6k+3, 6k+4, 6k+5, 6k+6}, then at least two of them will differ by 1, 4, or 5. Hmm, so we need to verify this statement. Let me think.
First, let me understand the structure of the set. The s... |
openr1_math_4011 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
3. In a convex quadrilateral $A B C D$, the lengths of sides $A B$ and $B C$ are equal, $D B$ is the bisector of angle $A D C$, and $A D: D C=4: 3$. Find the cosine of angle $A K B$, where $K$ is the intersection point of diagonals $A C$ and $B D$, and $B K: K D=1: 3$. (16 points)<|im_end|>
<|im_start|... | 3. In a convex quadrilateral $A B C D$, the lengths of sides $A B$ and $B C$ are equal, $D B$ is the bisector of angle $A D C$, and $A D: D C=4: 3$. Find the cosine of angle $A K B$, where $K$ is the intersection point of diagonals $A C$ and $B D$, and $B K: K D=1: 3$. (16 points) | <think>
Alright, so I have this geometry problem here. Let me try to parse it step by step. The problem is about a convex quadrilateral ABCD. Let me jot down the given information:
1. AB = BC. So, sides AB and BC are equal in length. That might mean that triangle ABC is isosceles with AB = BC. Hmm.
2. DB is the bisect... |
openr1_math_4012 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
Problem 2. The numbers $d$ and $e$ are the roots of the quadratic trinomial $a x^{2}+b x+c$. Could it be that $a, b, c, d, e$ are consecutive integers in some order?<|im_end|>
<|im_start|>assistant
<think>
Alright, let me try to figure this out. So the problem says that numbers d and e are the roots of... | Problem 2. The numbers $d$ and $e$ are the roots of the quadratic trinomial $a x^{2}+b x+c$. Could it be that $a, b, c, d, e$ are consecutive integers in some order? | <think>
Alright, let me try to figure this out. So the problem says that numbers d and e are the roots of the quadratic trinomial ax² + bx + c. The question is asking if it's possible that a, b, c, d, e are consecutive integers in some order. Hmm, okay. Let me start by recalling some properties of quadratic equations.
... |
openr1_math_4013 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
(4) Let $(1+x)^{16}=\sum_{i=0}^{16} a_{i} x^{i}$, then $\sum_{i=1}^{8} i a_{i}=$ $\qquad$<|im_end|>
<|im_start|>assistant
<think>
Okay, so I need to find the sum from i=1 to 8 of i times a_i, where the coefficients a_i come from the expansion of (1 + x)^16. Let me think about how to approach this.
Fir... | (4) Let $(1+x)^{16}=\sum_{i=0}^{16} a_{i} x^{i}$, then $\sum_{i=1}^{8} i a_{i}=$ $\qquad$ | <think>
Okay, so I need to find the sum from i=1 to 8 of i times a_i, where the coefficients a_i come from the expansion of (1 + x)^16. Let me think about how to approach this.
First, I remember that in the binomial expansion, (1 + x)^n = sum_{k=0}^n C(n, k) x^k. So in this case, a_i is just C(16, i), the combination ... |
openr1_math_4014 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
Problem 8.7.1. Given trapezoid $A B C D (B C \| A D)$. Point $H$ on side $A B$ is such that $\angle D H A=$ $90^{\circ}$. It is known that $C H=C D=13$ and $A D=19$. Find the length of segment $B C$.
$. Point $H$ on side $A B$ is such that $\angle D H A=$ $90^{\circ}$. It is known that $C H=C D=13$ and $A D=19$. Find the length of segment $B C$.
 that approach zero as x approaches zero for the equation x⁵ + ... | Investigate the asymptotic behaviour of the solutions $y$ of the equation $x^5 + x^2y^2 = y^6$ that tend to zero as $x\to0$. | <think>
Okay, so I need to figure out the asymptotic behavior of the solutions y(x) that approach zero as x approaches zero for the equation x⁵ + x²y² = y⁶. Hmm, asymptotic behavior near x = 0. That probably means I need to approximate how y behaves when x is very small, right? Since y tends to zero as x approaches zer... |
openr1_math_4016 | DeepSeek-R1-OpenR1-Math-220k | mathematics | <|im_start|>user
A circle centered at $A$ with a radius of 1 and a circle centered at $B$ with a radius of 4 are externally tangent. A third circle is tangent to the first two and to one of their common external tangents as shown. What is the radius of the third circle?
$\text{(A) }\frac {1}{3} \qquad \text{(B) }\frac... | A circle centered at $A$ with a radius of 1 and a circle centered at $B$ with a radius of 4 are externally tangent. A third circle is tangent to the first two and to one of their common external tangents as shown. What is the radius of the third circle?
$\text{(A) }\frac {1}{3} \qquad \text{(B) }\frac {2}{5} \qquad \t... | <think>
Okay, so there's a problem about two circles that are externally tangent. One has a radius of 1 centered at A, and the other has a radius of 4 centered at B. There's a third circle that's tangent to both of these circles and also to one of their common external tangents. We need to find the radius of this third... |
mgsm_es_0 | MGSM_Multilingual_ES | multilingual_reasoning | <|im_start|>user
Pregunta: Roger tiene 5 pelotas de tenis. Compra 2 tubos más de pelotas de tenis. Cada tubo contiene 3 pelotas de tenis. ¿Cuántas pelotas de tenis tiene ahora?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Roger comenzó con 5 pelotas. 2 tu... | Pregunta: Roger tiene 5 pelotas de tenis. Compra 2 tubos más de pelotas de tenis. Cada tubo contiene 3 pelotas de tenis. ¿Cuántas pelotas de tenis tiene ahora? | <think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Roger comenzó con 5 pelotas. 2 tubos de 3 pelotas de tenis cada uno equivale a 6 pelotas de tenis. 5 + 6 = 11. La respuesta es 11.
</think>
**Answer:** Respuesta paso a paso: Roger comenzó con 5 pelotas. 2 tubos de 3 pelotas de tenis cada un... |
mgsm_es_1 | MGSM_Multilingual_ES | multilingual_reasoning | <|im_start|>user
Pregunta: Había nueve computadoras en la sala de servidores. Se instalaron cinco computadoras cada día, de lunes a jueves. ¿Cuántas computadoras hay ahora en la sala de servidores?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Hay 4 días d... | Pregunta: Había nueve computadoras en la sala de servidores. Se instalaron cinco computadoras cada día, de lunes a jueves. ¿Cuántas computadoras hay ahora en la sala de servidores? | <think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Hay 4 días de lunes a jueves. Se agregaron 5 computadoras cada día. Eso significa que en total se agregaron 4 * 5 = 20 computadoras. Al principio, había 9 computadoras, por lo que ahora hay 9 + 20 = 29 computadoras. La respuesta es 29.
</thin... |
mgsm_es_2 | MGSM_Multilingual_ES | multilingual_reasoning | <|im_start|>user
Pregunta: Leah tenía 32 chocolates y su hermana tenía 42. Si se comieron 35, ¿cuántos chocolates les quedan en total?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Leah tenía 32 chocolates y la hermana de Leah tenía 42. Quiere decir que or... | Pregunta: Leah tenía 32 chocolates y su hermana tenía 42. Si se comieron 35, ¿cuántos chocolates les quedan en total? | <think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Leah tenía 32 chocolates y la hermana de Leah tenía 42. Quiere decir que originalmente había 32 + 42 = 74 chocolates. Se comieron 35. Por lo tanto, en total todavía tienen 74 - 35 = 39 chocolates. La respuesta es 39.
</think>
**Answer:** Res... |
mgsm_es_3 | MGSM_Multilingual_ES | multilingual_reasoning | <|im_start|>user
Pregunta: Shawn tiene cinco juguetes. Para Navidad, recibió dos juguetes de su mamá y dos de su papá. ¿Cuántos juguetes tiene ahora?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Tiene 5 juguetes. Recibió 2 de la mamá, por lo que después d... | Pregunta: Shawn tiene cinco juguetes. Para Navidad, recibió dos juguetes de su mamá y dos de su papá. ¿Cuántos juguetes tiene ahora? | <think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Tiene 5 juguetes. Recibió 2 de la mamá, por lo que después de eso tiene 5 + 2 = 7 juguetes. Luego, recibió 2 más del papá, así que en total tiene 7 + 2 = 9 juguetes. La respuesta es 9.
</think>
**Answer:** Respuesta paso a paso: Tiene 5 jugu... |
mgsm_es_4 | MGSM_Multilingual_ES | multilingual_reasoning | <|im_start|>user
Pregunta: Michael tenía 58 pelotas de golf. El martes, perdió 23 pelotas de golf. El miércoles, perdió 2 más. ¿Cuántas pelotas de golf tenía al final del miércoles?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Michael comenzó con 58 pelot... | Pregunta: Michael tenía 58 pelotas de golf. El martes, perdió 23 pelotas de golf. El miércoles, perdió 2 más. ¿Cuántas pelotas de golf tenía al final del miércoles? | <think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Michael comenzó con 58 pelotas de golf y perdió 23, por lo tanto tiene 58 - 23 = 35. Después de perder 2 más, ahora tiene 35 - 2 = 33 pelotas. La respuesta es 33.
</think>
**Answer:** Respuesta paso a paso: Michael comenzó con 58 pelotas de ... |
mgsm_es_5 | MGSM_Multilingual_ES | multilingual_reasoning | <|im_start|>user
Pregunta: Olivia tiene $23. Compró cinco roscas a $3 cada una. ¿Cuánto dinero le queda?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: 5 roscas a $3 cada una deben costar 5 * 3 = 15 dólares. Olivia tenía $23 al principio, por lo tanto ahora... | Pregunta: Olivia tiene $23. Compró cinco roscas a $3 cada una. ¿Cuánto dinero le queda? | <think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: 5 roscas a $3 cada una deben costar 5 * 3 = 15 dólares. Olivia tenía $23 al principio, por lo tanto ahora le quedan 23 - 15 = 8 dólares. La respuesta es 8.
</think>
**Answer:** Respuesta paso a paso: 5 roscas a $3 cada una deben costar 5 * 3... |
mgsm_es_6 | MGSM_Multilingual_ES | multilingual_reasoning | <|im_start|>user
Pregunta: Jason tenía 20 chupetines. Le dio algunos chupetines a Denny. Ahora Jason tiene 12 chupetines. ¿Cuántos chupetines le dio Jason a Denny?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Jason comenzó con 20 chupetines, pero ahora so... | Pregunta: Jason tenía 20 chupetines. Le dio algunos chupetines a Denny. Ahora Jason tiene 12 chupetines. ¿Cuántos chupetines le dio Jason a Denny? | <think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Jason comenzó con 20 chupetines, pero ahora solo tiene 12, por lo tanto le dio a Denny 20 - 12 = 8 chupetines. La respuesta es 8.
</think>
**Answer:** Respuesta paso a paso: Jason comenzó con 20 chupetines, pero ahora solo tiene 12, por lo t... |
mgsm_es_7 | MGSM_Multilingual_ES | multilingual_reasoning | <|im_start|>user
Pregunta: Si hay 3 autos en el estacionamiento y llegan 2 autos más, ¿cuántos autos hay en el estacionamiento?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Hay 3 autos al principio, llegan 2 más, por lo tanto ahora debe haber 3 + 2 = 5 au... | Pregunta: Si hay 3 autos en el estacionamiento y llegan 2 autos más, ¿cuántos autos hay en el estacionamiento? | <think>
Analyze problem in es. Calculate step by step.
Respuesta paso a paso: Hay 3 autos al principio, llegan 2 más, por lo tanto ahora debe haber 3 + 2 = 5 autos. La respuesta es 5.
</think>
**Answer:** Respuesta paso a paso: Hay 3 autos al principio, llegan 2 más, por lo tanto ahora debe haber 3 + 2 = 5 autos. La r... |
mgsm_de_0 | MGSM_Multilingual_DE | multilingual_reasoning | <|im_start|>user
Frage: Roger hat 5 Tennisbälle. Er kauft noch 2 Dosen Tennisbälle. In jeder Dose sind 3 Tennisbälle. Wie viele Tennisbälle hat er jetzt?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Roger begann mit 5 Bällen. 2 Dosen von jeweils 3 T... | Frage: Roger hat 5 Tennisbälle. Er kauft noch 2 Dosen Tennisbälle. In jeder Dose sind 3 Tennisbälle. Wie viele Tennisbälle hat er jetzt? | <think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Roger begann mit 5 Bällen. 2 Dosen von jeweils 3 Tennisbällen macht 6 Tennisbälle. 5 + 6 = 11. Die Antwort ist 11.
</think>
**Answer:** Schritt-für-Schritt-Antwort: Roger begann mit 5 Bällen. 2 Dosen von jeweils 3 Tennisbällen macht 6 ... |
mgsm_de_1 | MGSM_Multilingual_DE | multilingual_reasoning | <|im_start|>user
Frage: Es waren neun Computer im Serverraum. Von Montag bis Donnerstag wurden jeden Tag noch fünf Computer installiert. Wie viele Computer sind jetzt im Serverraum?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Von Montag bis Donners... | Frage: Es waren neun Computer im Serverraum. Von Montag bis Donnerstag wurden jeden Tag noch fünf Computer installiert. Wie viele Computer sind jetzt im Serverraum? | <think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Von Montag bis Donnerstag sind es 4 Tage. Jeden Tag kamen 5 neue Computer hinzu. Das macht insgesamt 4 x 5 = 20 Computer, die hinzugefügt wurden. Am Anfang waren es 9 Computer, also sind es jetzt 9 + 20 =29 Computer. Die Antwort lautet ... |
mgsm_de_2 | MGSM_Multilingual_DE | multilingual_reasoning | <|im_start|>user
Frage: Leah hat 32 Pralinen und ihre Schwester hat 42. Wenn sie 35 essen, wie viele sind dann insgesamt noch übrig?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Leah hat 32 Pralinen und Leahs Schwester 42. Das bedeutet, dass es ursp... | Frage: Leah hat 32 Pralinen und ihre Schwester hat 42. Wenn sie 35 essen, wie viele sind dann insgesamt noch übrig? | <think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Leah hat 32 Pralinen und Leahs Schwester 42. Das bedeutet, dass es ursprünglich 32 + 42 =74 Pralinen waren. 35 wurden gegessen. Also haben sie insgesamt noch 74 - 35 = 39 Pralinen übrig. Die Antwort lautet 39.
</think>
**Answer:** Schr... |
mgsm_de_3 | MGSM_Multilingual_DE | multilingual_reasoning | <|im_start|>user
Frage: Shawn hat fünf Spielzeuge. Zu Weihnachten hat er von seiner Mama und seinem Papa jeweils zwei Spielzeuge bekommen. Wie viele Spielzeuge hat er jetzt?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Er hat 5 Spielzeuge. Er hat 2 ... | Frage: Shawn hat fünf Spielzeuge. Zu Weihnachten hat er von seiner Mama und seinem Papa jeweils zwei Spielzeuge bekommen. Wie viele Spielzeuge hat er jetzt? | <think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Er hat 5 Spielzeuge. Er hat 2 von seiner Mama bekommen, sodass er nun 5 + 2 = 7 Spielzeuge hat. Dann hat er noch 2 von seinem Papa bekommen, also hat er insgesamt 7 + 2 = 9 Spielzeuge. Die Antwort lautet 9.
</think>
**Answer:** Schritt... |
mgsm_de_4 | MGSM_Multilingual_DE | multilingual_reasoning | <|im_start|>user
Frage: Michael hat 58 Golfbälle. Am Dienstag hat er 23 Golfbälle verloren. Am Mittwoch hat er 2 weitere verloren. Wie viele Golfbälle hat er Mittwoch am Ende des Tages?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Michael hatte anfa... | Frage: Michael hat 58 Golfbälle. Am Dienstag hat er 23 Golfbälle verloren. Am Mittwoch hat er 2 weitere verloren. Wie viele Golfbälle hat er Mittwoch am Ende des Tages? | <think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Michael hatte anfangs 58 Golfbälle und hat 23 verloren, sodass er 58 - 23 = 35 hat. Nachdem er 2 weitere verloren hat, hat er jetzt 35 - 2 = 33 Bälle. Die Antwort lautet 33.
</think>
**Answer:** Schritt-für-Schritt-Antwort: Michael hat... |
mgsm_de_5 | MGSM_Multilingual_DE | multilingual_reasoning | <|im_start|>user
Frage: Olivia hat 23 US-Dollar. Sie hat fünf Bagels für 3 US-Dollar pro Stück gekauft. Wie viel Geld hat sie übrig?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: 5 Bagels für 3 US-Dollar pro Stück kosten 5 x 3 = 15 Dollar. Olivia hat... | Frage: Olivia hat 23 US-Dollar. Sie hat fünf Bagels für 3 US-Dollar pro Stück gekauft. Wie viel Geld hat sie übrig? | <think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: 5 Bagels für 3 US-Dollar pro Stück kosten 5 x 3 = 15 Dollar. Olivia hat anfangs 23 US-Dollar, also hat sie jetzt 23 - 15 = 8 Dollar übrig. Die Antwort lautet 8.
</think>
**Answer:** Schritt-für-Schritt-Antwort: 5 Bagels für 3 US-Dollar... |
mgsm_de_6 | MGSM_Multilingual_DE | multilingual_reasoning | <|im_start|>user
Frage: Jason hatte 20 Lutscher. Er hat Denny einige Lutscher gegeben. Jetzt hat Jason 12 Lutscher. Wie viele Lutscher hat Jason Denny gegeben?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Jason hat mit 20 Lutschern angefangen, aber ... | Frage: Jason hatte 20 Lutscher. Er hat Denny einige Lutscher gegeben. Jetzt hat Jason 12 Lutscher. Wie viele Lutscher hat Jason Denny gegeben? | <think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Jason hat mit 20 Lutschern angefangen, aber jetzt hat er nur 12, also hat er Denny 20 - 12 = 8 Lutscher abgegeben. Die Antwort lautet 8.
</think>
**Answer:** Schritt-für-Schritt-Antwort: Jason hat mit 20 Lutschern angefangen, aber jetz... |
mgsm_de_7 | MGSM_Multilingual_DE | multilingual_reasoning | <|im_start|>user
Frage: Wenn 3 Autos auf dem Parkplatz stehen und 2 weitere Autos ankommen, wie viele Autos stehen dann auf dem Parkplatz?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Anfangs sind 3 Autos da, 2 weitere kommen an, also sind jetzt 3 +... | Frage: Wenn 3 Autos auf dem Parkplatz stehen und 2 weitere Autos ankommen, wie viele Autos stehen dann auf dem Parkplatz? | <think>
Analyze problem in de. Calculate step by step.
Schritt-für-Schritt-Antwort: Anfangs sind 3 Autos da, 2 weitere kommen an, also sind jetzt 3 + 2 = 5 Autos da. Die Antwort lautet 5.
</think>
**Answer:** Schritt-für-Schritt-Antwort: Anfangs sind 3 Autos da, 2 weitere kommen an, also sind jetzt 3 + 2 = 5 Autos da.... |
mgsm_fr_0 | MGSM_Multilingual_FR | multilingual_reasoning | <|im_start|>user
Question : Roger a 5 balles de tennis. Il achète 2 autres boîtes de balles de tennis en plus. Si chaque boîte contient 3 balles de tennis, combien de balles de tennis a-t-il maintenant ?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Rog... | Question : Roger a 5 balles de tennis. Il achète 2 autres boîtes de balles de tennis en plus. Si chaque boîte contient 3 balles de tennis, combien de balles de tennis a-t-il maintenant ? | <think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Roger a commencé avec 5 balles. 2 boîtes de 3 balles de tennis chacune représentent 6 balles de tennis. 5 + 6 = 11. La réponse est 11.
</think>
**Answer:** Réponse étape par étape : Roger a commencé avec 5 balles. 2 boîtes de 3 balles de ... |
mgsm_fr_1 | MGSM_Multilingual_FR | multilingual_reasoning | <|im_start|>user
Question : Il y avait neuf ordinateurs dans la salle des serveurs. Cinq ordinateurs supplémentaires ont été installés chaque jour, du lundi au jeudi. Combien d'ordinateurs y a-t-il maintenant dans la salle des serveurs ?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in fr. Calculate step by s... | Question : Il y avait neuf ordinateurs dans la salle des serveurs. Cinq ordinateurs supplémentaires ont été installés chaque jour, du lundi au jeudi. Combien d'ordinateurs y a-t-il maintenant dans la salle des serveurs ? | <think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : De lundi à jeudi, il y a 4 jours. 5 ordinateurs ont été ajoutés par jour. Cela signifie qu'au total, 4 x 5 = 20 ordinateurs ont été ajoutés. Comme il y avait 9 ordinateurs au départ, il y a maintenant 9 + 20 = 29 ordinateurs. La réponse es... |
mgsm_fr_2 | MGSM_Multilingual_FR | multilingual_reasoning | <|im_start|>user
Question : Léa avait 32 chocolats et sa sœur en avait 42. Si elles en ont mangé 35, combien de morceaux leur reste-t-il en tout ?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Léa avait 32 chocolats et sa sœur en avait 42. Cela signifie... | Question : Léa avait 32 chocolats et sa sœur en avait 42. Si elles en ont mangé 35, combien de morceaux leur reste-t-il en tout ? | <think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Léa avait 32 chocolats et sa sœur en avait 42. Cela signifie qu'il y avait à l'origine 32 + 42 = 74 chocolats. 35 chocolats ont été mangés. Il leur en reste donc au total 74 - 35 = 39 chocolats. La réponse est 39.
</think>
**Answer:** Rép... |
mgsm_fr_3 | MGSM_Multilingual_FR | multilingual_reasoning | <|im_start|>user
Question : Shawn a cinq jouets. Pour Noël, papa et maman lui ont offert deux jouets chacun. Combien de jouets a-t-il maintenant ?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Il a 5 jouets. Il en a reçu 2 de maman, ce qui fait qu'il a ... | Question : Shawn a cinq jouets. Pour Noël, papa et maman lui ont offert deux jouets chacun. Combien de jouets a-t-il maintenant ? | <think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Il a 5 jouets. Il en a reçu 2 de maman, ce qui fait qu'il a 5 + 2 = 7 jouets. Ensuite, il a reçu 2 autres jouets de papa. Cela fait donc un total de 7 + 2 = 9 jouets. La réponse est 9.
</think>
**Answer:** Réponse étape par étape : Il a 5... |
mgsm_fr_4 | MGSM_Multilingual_FR | multilingual_reasoning | <|im_start|>user
Question : Michael avait 58 balles de golf. Mardi, il a perdu 23 balles de golf. Mercredi, il en a perdu 2 autres. De combien de balles de golf disposait-il à la fin du mercredi ?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Michael a ... | Question : Michael avait 58 balles de golf. Mardi, il a perdu 23 balles de golf. Mercredi, il en a perdu 2 autres. De combien de balles de golf disposait-il à la fin du mercredi ? | <think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Michael a commencé avec 58 balles de golf et en a perdu 23. Il lui reste donc 58 - 23 = 35. Après en avoir perdu 2 autres, il lui reste 35 - 2 = 33 balles. La réponse est 33.
</think>
**Answer:** Réponse étape par étape : Michael a commen... |
mgsm_fr_5 | MGSM_Multilingual_FR | multilingual_reasoning | <|im_start|>user
Question : Olivia a 23 $. Elle a acheté cinq bagels à 3 $ chacun. Combien d'argent lui reste-t-il ?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : 5 bagels à 3 $ chacun coûtent 5 x 3 = 15 dollars. Olivia avait 23 dollars au départ, il lu... | Question : Olivia a 23 $. Elle a acheté cinq bagels à 3 $ chacun. Combien d'argent lui reste-t-il ? | <think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : 5 bagels à 3 $ chacun coûtent 5 x 3 = 15 dollars. Olivia avait 23 dollars au départ, il lui reste donc 23 - 15 = 8 dollars. La réponse est 8.
</think>
**Answer:** Réponse étape par étape : 5 bagels à 3 $ chacun coûtent 5 x 3 = 15 dollars.... |
mgsm_fr_6 | MGSM_Multilingual_FR | multilingual_reasoning | <|im_start|>user
Question : Jason avait 20 sucettes. Il en a donné à Denny et il ne lui en reste plus que 12 à présent. Combien de sucettes Jason a-t-il donné à Denny ?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Au départ, Jason avait 20 sucettes. Il... | Question : Jason avait 20 sucettes. Il en a donné à Denny et il ne lui en reste plus que 12 à présent. Combien de sucettes Jason a-t-il donné à Denny ? | <think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Au départ, Jason avait 20 sucettes. Il n'en a plus que 12, alors il a donné à Denny 20 - 12 = 8 sucettes. La réponse est 8.
</think>
**Answer:** Réponse étape par étape : Au départ, Jason avait 20 sucettes. Il n'en a plus que 12, alors il... |
mgsm_fr_7 | MGSM_Multilingual_FR | multilingual_reasoning | <|im_start|>user
Question : S'il y a 3 voitures dans le parking et que 2 autres arrivent, combien de voitures y a-t-il maintenant dans le parking ?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Au début, il y a 3 voitures, puis 2 autres arrivent. Ça fai... | Question : S'il y a 3 voitures dans le parking et que 2 autres arrivent, combien de voitures y a-t-il maintenant dans le parking ? | <think>
Analyze problem in fr. Calculate step by step.
Réponse étape par étape : Au début, il y a 3 voitures, puis 2 autres arrivent. Ça fait donc 3 + 2 = 5 voitures. La réponse est 5.
</think>
**Answer:** Réponse étape par étape : Au début, il y a 3 voitures, puis 2 autres arrivent. Ça fait donc 3 + 2 = 5 voitures. L... |
mgsm_ru_0 | MGSM_Multilingual_RU | multilingual_reasoning | <|im_start|>user
Задача: у Роджера 5 теннисных мячей. Он покупает еще 2 банки теннисных мячей. В каждой банке 3 теннисных мяча. Сколько теннисных мячей у него сейчас?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: в начале у Роджера было 5 мячей. 2 банки по 3 т... | Задача: у Роджера 5 теннисных мячей. Он покупает еще 2 банки теннисных мячей. В каждой банке 3 теннисных мяча. Сколько теннисных мячей у него сейчас? | <think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: в начале у Роджера было 5 мячей. 2 банки по 3 теннисных мяча каждая — это 6 теннисных мячей. 5 + 6 = 11. Ответ — 11.
</think>
**Answer:** Пошаговое решение: в начале у Роджера было 5 мячей. 2 банки по 3 теннисных мяча каждая — это 6 теннисных мя... |
mgsm_ru_1 | MGSM_Multilingual_RU | multilingual_reasoning | <|im_start|>user
Задача: в серверной было девять компьютеров. Каждый день с понедельника по четверг устанавливалось еще по пять компьютеров. Сколько компьютеров сейчас в серверной?компьютеров.<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: с понедельника по чет... | Задача: в серверной было девять компьютеров. Каждый день с понедельника по четверг устанавливалось еще по пять компьютеров. Сколько компьютеров сейчас в серверной?компьютеров. | <think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: с понедельника по четверг прошло 4 дня. Каждый день добавляли по 5 компьютеров. То есть всего добавили 4 * 5 = 20 компьютеров. Вначале было 9 компьютеров, значит, теперь стало 9 + 20 = 29 компьютеров. Ответ — 29.
</think>
**Answer:** Пошаговое р... |
mgsm_ru_2 | MGSM_Multilingual_RU | multilingual_reasoning | <|im_start|>user
Задача: у Лии было 32 шоколадных конфеты, а у ее сестры — 42. Если 35 они съели, сколько всего штук у них осталось?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: у Лии было 32 шоколадных конфеты, а у сестры Лии — 42. Значит, первоначально было... | Задача: у Лии было 32 шоколадных конфеты, а у ее сестры — 42. Если 35 они съели, сколько всего штук у них осталось? | <think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: у Лии было 32 шоколадных конфеты, а у сестры Лии — 42. Значит, первоначально было 32 + 42 = 74 шоколадных конфеты. 35 съели. Значит, всего осталось 74 - 35 = 39 шоколадных конфет. Ответ — 39.
</think>
**Answer:** Пошаговое решение: у Лии было 32... |
mgsm_ru_3 | MGSM_Multilingual_RU | multilingual_reasoning | <|im_start|>user
Задача: у Шона было пять игрушек. На Рождество он получил по две игрушки от мамы и от папы. Сколько у него сейчас игрушек?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: у него было 5 игрушек. Он получил 2 от мамы, и после этого у него стало 5 ... | Задача: у Шона было пять игрушек. На Рождество он получил по две игрушки от мамы и от папы. Сколько у него сейчас игрушек? | <think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: у него было 5 игрушек. Он получил 2 от мамы, и после этого у него стало 5 + 2 = 7 игрушек. Потом он получил еще 2 от папы, так что в общей сложности у него стало 7 + 2 = 9 игрушек. Ответ — 9.
</think>
**Answer:** Пошаговое решение: у него было 5... |
mgsm_ru_4 | MGSM_Multilingual_RU | multilingual_reasoning | <|im_start|>user
Задача: у Майкла было 58 мячей для гольфа. Во вторник он потерял 23 мяча для гольфа. В среду он потерял еще 2. Сколько мячей для гольфа осталось у него к концу среды?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: вначале у Майкла было 58 мячей... | Задача: у Майкла было 58 мячей для гольфа. Во вторник он потерял 23 мяча для гольфа. В среду он потерял еще 2. Сколько мячей для гольфа осталось у него к концу среды? | <think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: вначале у Майкла было 58 мячей для гольфа, 23 он потерял, и у него осталось 58 - 23 = 35. После этого он потерял еще 2, и теперь у него осталось 35 - 2 = 33 мяча. Ответ — 33.
</think>
**Answer:** Пошаговое решение: вначале у Майкла было 58 мячей... |
mgsm_ru_5 | MGSM_Multilingual_RU | multilingual_reasoning | <|im_start|>user
Задача: у Оливии было 23 $. Она купила пять рогаликов по 3 $. Сколько денег у нее осталось?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: 5 рогаликов по 3 $ стоят 5 * 3 = 15 долларов. Вначале у Оливии было 23 $, значит, теперь у нее осталось 2... | Задача: у Оливии было 23 $. Она купила пять рогаликов по 3 $. Сколько денег у нее осталось? | <think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: 5 рогаликов по 3 $ стоят 5 * 3 = 15 долларов. Вначале у Оливии было 23 $, значит, теперь у нее осталось 23 - 15 = 8 $. Ответ — 8.
</think>
**Answer:** Пошаговое решение: 5 рогаликов по 3 $ стоят 5 * 3 = 15 долларов. Вначале у Оливии было 23 $, з... |
mgsm_ru_6 | MGSM_Multilingual_RU | multilingual_reasoning | <|im_start|>user
Задача: у Джейсона было 20 леденцов. Он дал несколько леденцов Дэнни. Теперь у Джейсона осталось 12 леденцов. Сколько леденцов Джейсон дал Дэнни?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: вначале у Джейсона было 20 леденцов, а теперь остал... | Задача: у Джейсона было 20 леденцов. Он дал несколько леденцов Дэнни. Теперь у Джейсона осталось 12 леденцов. Сколько леденцов Джейсон дал Дэнни? | <think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: вначале у Джейсона было 20 леденцов, а теперь осталось только 12, значит, он дал Дэнни 20 - 12 = 8 леденцов. Ответ — 8.
</think>
**Answer:** Пошаговое решение: вначале у Джейсона было 20 леденцов, а теперь осталось только 12, значит, он дал Дэнн... |
mgsm_ru_7 | MGSM_Multilingual_RU | multilingual_reasoning | <|im_start|>user
Задача: если на парковке 3 автомобиля и подъезжают еще 2, сколько автомобилей на парковке?<|im_end|>
<|im_start|>assistant
<think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: вначале есть 3 автомобиля, подъезжают еще 2, значит, теперь там должно быть 3 + 2 = 5 автомобилей. Ответ —... | Задача: если на парковке 3 автомобиля и подъезжают еще 2, сколько автомобилей на парковке? | <think>
Analyze problem in ru. Calculate step by step.
Пошаговое решение: вначале есть 3 автомобиля, подъезжают еще 2, значит, теперь там должно быть 3 + 2 = 5 автомобилей. Ответ — 5.
</think>
**Answer:** Пошаговое решение: вначале есть 3 автомобиля, подъезжают еще 2, значит, теперь там должно быть 3 + 2 = 5 автомобил... |
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