inclusionAI/Ring-lite-rl-data huggingface dataset:
At the beginning of January 2020, Boris and Victor started saving money for a new phone. Every month, Boris saved 200 rubles and Victor saved 300 rubles. One day, Boris got tired of saving and stopped putting aside money (but he did not spend the money he had already saved). Victor continued to save. On May 11, 2021, Victor's savings became 6 times greater than Boris's savings. In which month did Boris stop saving? Indicate the month and year.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\text{May 2020}}
If there are three squares with different side lengths that need to be fenced, and the cost of fencing each side varies as follows: the first side costs 79 dollars, the second side costs 92 dollars, the third side costs 85 dollars, and the fourth side costs 96 dollars. Calculate the total cost of fencing each of the three squares if their side lengths are 5 meters, 7 meters, and 9 meters respectively.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3168}
$99$  identical balls lie on a table.  $50$  balls are made of copper, and  $49$  balls are made of zinc. The assistant numbered the balls. Once spectrometer test is applied to  $2$  balls and allows to determine whether they are made of the same metal or not. However, the results of the test can be obtained only the next day. What minimum number of tests is required to determine the material of each ball if all the tests should be performed today?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{98}
Mr. Lee V. Soon starts his morning commute at 7:00 AM to arrive at work by 8:00 AM. If he drives at an average speed of 30 miles per hour, he is late by 5 minutes, and if he drives at an average speed of 70 miles per hour, he is early by 4 minutes. Find the speed he needs to maintain to arrive exactly at 8:00 AM.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{32.5}
Four siblings inherited a plot of land shaped like a convex quadrilateral. By connecting the midpoints of the opposite sides of the plot, they divided the inheritance into four quadrilaterals. The first three siblings received plots of $360 \, \mathrm{m}^{2}$, $720 \, \mathrm{m}^{2}$, and $900 \, \mathrm{m}^{2}$ respectively. What is the area of the plot received by the fourth sibling?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{540 \, \text{m}^2}
Johnny is a dog walker. He can walk 3 dogs at once. He gets paid $15 for a 30-minute walk and $20 for a 60-minute walk. Johnny works for 4 hours per day. If he always walks the maximum number of dogs possible and 6 dogs have 60-minute walks per day, how much money does he make in a week where he works 5 days?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1500}
Evaluate $\int_1^4 \frac{x-2}{(x^2+4)\sqrt{x}}\,dx.$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
We are given triangle $A B C$, with $A B=9, A C=10$, and $B C=12$, and a point $D$ on $B C . B$ and $C$ are reflected in $A D$ to $B^{\prime}$ and $C^{\prime}$, respectively. Suppose that lines $B C^{\prime}$ and $B^{\prime} C$ never meet (i.e., are parallel and distinct). Find $B D$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
There's a tape with  $n^2$  cells labeled by  $1,2,\ldots,n^2$ . Suppose that  $x,y$  are two distinct positive integers less than or equal to  $n$ . We want to color the cells of the tape such that any two cells with label difference of  $x$  or  $y$  have different colors. Find the minimum number of colors needed to do so.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
一只蚂蚁在正方体 $A B C D-E F G H$ 的顶点 A 处，每次等概率地爬行到相邻三个顶点中的一个，那么六次爬行之后回到顶点 A 的概率为?.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{304}
Triangle $ABC$ has $\overline{AB} = 5, \overline{BC} = 4, \overline{CA} = 6$. Points $D$ and $E$ are on sides $AB$ and $AC$, respectively, such that $\overline{AD} = \overline{AE} = \overline{BC}$. Let $CD$ and $BE$ intersect at $F$ and let $AF$ and $DE$ intersect at $G$. The length of $FG$ can be expressed in the form $\tfrac{a\sqrt{b}}{c}$ in simplified form. What is $a + b + c$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{255}
How many rearrangements \((p_1, p_2, \ldots, p_{1000})\) of the sequence \(1, 2, \ldots, 1000\) satisfy that for any integer \(1 \leq i \leq 999\), we have \(i \mid p_i\)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Given that the function f(x) is differentiable on R with its derivative f'(x), and f(x) satisfies: (x-1)[f'(x)-f(x)] > 0, f(2-x) = f(x)e^(2-2x), determine the solution set of the inequality e^2f(ln x) < xf(2). Express your answer in interval notation.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(1,e^2)}
Paige and her mom planted flowers in several garden areas around their house. In the front yard flower bed, they planted 120 seeds and 75% grew into flowers. In the herb garden, they planted 45 seeds and 90% sprouted. In the backyard, they put 80 seeds with 60% success rate. They also planted 60 seeds around the mailbox and saw 80% success rate. How many flowers did they grow in total?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{226}
The new PUMaC tournament hosts $2020$ students, numbered by the following set of labels $1, 2, . . . , 2020$. The students are initially divided up into $20$ groups of $101$, with each division into groups equally likely. In each of the groups, the contestant with the lowest label wins, and the winners advance to the second round. Out of these $20$ students, we chose the champion uniformly at random. If the expected value of champion’s number can be written as $\frac{a}{b}$, where $a, b$ are relatively prime integers, determine $a + b$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2123}
Three circles $C_i$ are given in the plane: $C_1$ has diameter $AB$ of length $1$; $C_2$ is concentric and has diameter $k$ ($1 < k < 3$); $C_3$ has center $A$ and diameter $2k$. We regard $k$ as fixed. Consider all straight line segments $XY$ which have one endpoint $X$ on $C_2$, one endpoint $Y$ on $C_3$, and contain the point $B$. For what ratio $\frac{XB}{BY}$ will the segment $XY$ have minimal length?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
The calendar of the year 2060 can be used again in which year?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2088}
From the numbers $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, four different numbers are selected, denoted as $a$, $b$, $c$, $d$ respectively. If the parity of $a+b$ is the same as the parity of $c+d$, then the total number of ways to select $a$, $b$, $c$, $d$ is ______ (provide the answer in numerical form).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{912}
On the Island of Misfortune, there are knights, who always tell the truth, and liars, who always lie. One day, $n$ islanders gathered in a room.

The first one said, "Exactly every first person present in this room is a liar."

The second one said, "Exactly every second person present in this room is a liar," and so on.

The person with number $n$ said, "Exactly every $n$-th person present in this room is a liar." How many people could have been in the room?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Let \(ABCDEF\) be a regular hexagon. A frog starts at vertex \(A\) and can randomly jump to any one of the two adjacent vertices each time. If the frog reaches point \(D\) within 5 jumps, it stops jumping. If it cannot reach point \(D\) within 5 jumps, it stops after completing the 5 jumps. How many different possible sequences of jumps can the frog make from the start to stopping?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{26}
The total dining bill of 9 people was $139.00 and they added a 10% tip. They divided the bill evenly. What is the bill amount each person shared (approximately)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$16.99}
In the complex plane, the points corresponding to the complex number $1+ \sqrt {3}i$ and $- \sqrt {3}+i$ are $A$ and $B$, respectively, with $O$ as the coordinate origin. Calculate the measure of $\angle AOB$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac {\pi}{2}}
A game begins with seven coins lined up on a table, all showing heads up. To win the game, you need to flip some coins such that, in the end, two adjacent coins always show different faces. The rule of the game is to flip two adjacent coins in each move. What is the minimum number of moves required to win the game?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Find $\sum_{k \in A} \frac{1}{k-1}$ where $A= \{ m^n : m,n \in \mathbb{Z}, m,n \geq 2 \}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Determine the sum of all possible surface areas of a cube, given that two of its vertices are $(1,2,0)$ and $(3,3,2)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{99}
$D$ and $E$ are on sides $AB$ and $AC$ of $\angle CAB$ respectively. The angle bisector of $\angle BDE$ intersects the angle bisector of $\angle CED$ at $F$. If $\angle BAC = 38^\circ$, then what is the measure of $\angle DFE$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{71^\circ}
In the right triangle \(ABC\), a circle is constructed with \(AC\) as its diameter. The circle intersects side \(AB\) at point \(E\). Point \(G\) is taken on side \(BC\) such that segment \(AG\) intersects the circle at point \(F\). Given that segments \(EF\) and \(AC\) are parallel, \(BG = 2CG\), and \(AC = 2\sqrt{3}\), find \(GF\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
When travelling from London to Edinburgh by train, you pass a sign saying 'Edinburgh 200 miles'. Then, 3 1/2 miles later, you pass another sign saying 'Half way between London and Edinburgh'. How many miles is it by train from London to Edinburgh?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{393}
A factory's total output value was $a$ last year. It is planned that for each of the next 5 years, the output will increase by 10% compared to the previous year. Calculate the total output value of the factory in the last of these 5 years. Express your answer as an algebraic expression in terms of $a$, including the base and exponent.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1.1^5a}
If the line $l$ passes through the point $(0,2)$ and intersects the ellipse $C: \frac{{x}^{2}}{7}+\frac{{y}^{2}}{2}=1$ at only one point, then the slope of the line $l$ is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{±\frac{\sqrt{14}}{7}}
Consider a cube with two particles positioned at opposite vertices of the same face. At any given time $t$, if the particles occupy the same edge, they remain there until time $t + 1$. Otherwise, one particle is randomly selected with equal probability and moves to one of its three neighboring vertices with equal probability. What is the expected value for the least amount of time it will take for the particles to be in the same edge?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
As shown in the diagram, circles \( \odot O_{1} \) and \( \odot O_{2} \) are externally tangent. The line segment \( O_{1}O_{2} \) intersects \( \odot O_{1} \) at points \( A \) and \( B \), and intersects \( \odot O_{2} \) at points \( C \) and \( D \). Circle \( \odot O_{3} \) is internally tangent to \( \odot O_{1} \) at point \( B \), and circle \( \odot O_{4} \) is internally tangent to \( \odot O_{2} \) at point \( C \). The common external tangent of \( \odot O_{2} \) and \( \odot O_{3} \) passes through point \( A \), tangent to \( \odot O_{3} \) at point \( E \) and tangent to \( \odot O_{2} \) at point \( F \). The common external tangent of \( \odot O_{1} \) and \( \odot O_{4} \) passes through point \( D \). If the radius of circle \( \odot O_{3} \) is 1.2, what is the radius of circle \( \odot O_{4} \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1.2}
How do you determine the minimum number of times a fair die must be rolled such that the mean score differs from 3.5 by no more than 0.1 with less than a 1% probability?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1936}
Five girls ran a race. Fiona started first, followed by Gertrude, then Hannah, then India, and lastly Janice. Whenever a girl overtook another girl, she was awarded a point. India was first to finish, followed by Gertrude, Fiona, Janice, and lastly Hannah. Calculate the minimum total number of points that could have been awarded. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
4. Vasya, a bibliophile, has 1300 books arranged on $k$ bookshelves in his cabinets. One day, Vasya moved the cabinets to a new place, taking all the books out beforehand. In the process, he completely forgot how the books were arranged before and placed them in the cabinets in a different order. For what maximum $k$ will there definitely be 5 books that were on the same shelf both before and after the rearrangement?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
Find the greatest positive integer $m$ with the following property:
For every permutation $a_1, a_2, \cdots, a_n,\cdots$ of the set of positive integers, there exists positive integers $i_1<i_2<\cdots <i_m$ such that $a_{i_1}, a_{i_2}, \cdots, a_{i_m}$ is an arithmetic progression with an odd common difference.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{ 3 }
There is a magical flower that blooms on Wednesdays and Fridays in odd-numbered months and on Tuesdays and Thursdays in even-numbered months. For example, October 1st, which is a Tuesday, is a blooming day. How many days will this flower bloom from November 1, 2013, to December 31, 2013?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
Vasya has chosen four numbers and for each pair calculated the logarithm of the larger number to the base of the smaller number. This resulted in six logarithms. Four of them are equal to 15, 20, 21, and 28. What possible values can the largest of all six logarithms take?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{420}}
Call a fraction $\frac{a}{b}$, not necessarily in the simplest form, <i>special</i> if $a$ and $b$ are positive integers whose sum is $15$. How many distinct integers can be written as the sum of two, not necessarily different, special fractions?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$11$}
Given that the odd function $f(x)$ has a domain of $[-2, 2]$ and is decreasing in the interval $[-2, 0]$. If $f(1-m) + f(1-m^2) < 0$, find the range of the real number $m$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-1 \leq m < 1}
An underground line has $26$ stops, including the first and the final one, and all the stops are numbered from $1$ to $26$ according to their order. Inside the train, for each pair $(x,y)$ with $1 \leq x < y \leq 26$, there is exactly one passenger that goes from the $x$-th stop to the $y$-th one. If every passenger wants to take a seat during his journey, find the minimum number of seats that must be available on the train.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{169}
a, b, c, and d rent a pasture for a total of Rs. 725. a put in 12 horses for 8 months at a rate of Rs. 5 per month, b puts in 16 horses for 9 months at a rate of Rs. 6 per month, c puts in 18 horses for 6 months at a rate of Rs. 7 per month, and d puts in 20 horses for 4 months at a rate of Rs. 4 per month. How much should b pay?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{259}
已知实数 $x 、 y$ 满足 $x|x|+\frac{y|y|}{3}=1$. 则 $|\sqrt{3} x+y-4|$ 的取值范围是 $\qquad$. 答案标准形式为[\a-\sqrt{b},c]，请给出区间端点a+b+c之和的值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14}
Evaluate $$1^{2018}+2^{2018}+...+500^{2018}(\text{mod}\; 1024)$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Call a polynomial $P\left(x_{1}, \ldots, x_{k}\right)$ good if there exist $2 \times 2$ real matrices $A_{1}, \ldots, A_{k}$ such that $$ P\left(x_{1}, \ldots, x_{k}\right)=\operatorname{det}\left(\sum_{i=1}^{k} x_{i} A_{i}\right) $$ Find all values of $k$ for which all homogeneous polynomials with $k$ variables of degree 2 are good. Please provide the sum of all possible values of $k$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Ten test papers are to be prepared for the National Olympiad. Each paper contains 4 problems, and no two papers have more than one problem in common. What is the minimum number of problems needed?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
Let $P$ be a $10$-degree monic polynomial with roots $r_1, r_2, \ldots, r_{10}$, and let $Q$ be a $45$-degree monic polynomial with roots $\frac{1}{r_i} + \frac{1}{r_j} - \frac{1}{r_i r_j}$ where $i < j$ and $i, j \in \{1, \ldots, 10\}$. If $P(0) = Q(1) = 2$, then $\log_2 (|P(1)|)$ can be written as $\frac{a}{b}$ for relatively prime integers $a, b$. Find $a + b$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19}
What is the value of the following expression: $1 - 3 + 5 - 7 + 9 - \cdots - 43 + 45 - 47 + 49$ ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
Given the function
$$
f(x)=x^{4}+a x^{3}+b x^{2}+a x+1 \quad (a, b \in \mathbf{R})
$$

which has at least one root, find the minimum value of \( a^2 - b \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
The number of apples produced by a group of farmers is less than 1000. It is known that they shared the apples in the following way. In turn, each farmer took from the collection of apples either exactly one-half or exactly one-third of the apples remaining in the collection. No apples were cut into pieces. After each farmer had taken his share, the rest was given to charity. Find the greatest number of farmers that could take part in the apple sharing.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
The graphs of the functions y = |x^2 - x - 2| and y = |x^2 - x| enclose a finite area. Within this enclosed area (including the boundary), how many points have both integer coordinates? Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Let  $a_n = n(2n+1)$ .  Evaluate
\[
  \biggl | \sum_{1 \le j < k \le 36} \sin\bigl( \frac{\pi}{6}(a_k-a_j) \bigr) \biggr |.
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
(solved by Mathieu Aria, Jeanne Nguyen and Thomas Williams). Let $n \geqslant 3$ and $x_{1}, \ldots, x_{n-1}$ be non-negative integers. We assume:

$$
\begin{aligned}
x_{1}+x_{2}+\cdots+x_{n-1} & =n \\
x_{1}+2 x_{2}+\cdots+(n-1) x_{n-1} & =2 n-2
\end{aligned}
$$

Calculate the minimum value of:

$$
\sum_{k=1}^{n-1} k(2 n-k) x_{k}
$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3n^{2}-3n}
Three towns \(X, Y\), and \(Z\) lie on a plane with coordinates \((0,0)\), \((200,0)\), and \((0,300)\) respectively. There are 100, 200, and 300 students in towns \(X, Y\), and \(Z\) respectively. A school is to be built on a grid point \((x, y)\), where \(x\) and \(y\) are both integers, such that the overall distance travelled by all the students is minimized. Find the value of \(x + y\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{300}
Let f(x) be an even function defined on R. If f(x) is increasing on (-∞, 0), and a = f(ln 1/4), b = f(cos 2), c = f(2^1.2), determine the relationship between a, b, and c using the symbols < or >. Express your answer in the form of a single inequality that includes all variables a, b, and c.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{c < a < b}
Let the complex numbers \( z_{1} = -3 - \sqrt{3} \, \mathrm{i} \), \( z_{2} = \sqrt{3} + \mathrm{i} \), and \( z = \sqrt{3} \sin \theta + \mathrm{i} (\sqrt{3} \cos \theta + 2) \). Find the minimum value of \( \left| z - z_{1} \right| + \left| z - z_{2} \right| \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 + 2\sqrt{3}}
Calculate the sixth partial derivative of $g(x,y)=\frac{1}{1+x^2y^2}$ with respect to $x$ four times and with respect to $y$ two times at the point $(1,1)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Compute $\arctan ( \tan 75^\circ - 2 \tan 30^\circ )$. (Express your answer in degrees as an angle between $0^\circ$ and $180^\circ$.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{75^\circ}
The power function $f(x) = (m^2 - 2m - 2)x^{m + \frac{1}{2}m^2}$ is increasing on the interval $(0, +\infty)$. Find the value of $m$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
There are two equations:  
好 + 好 = 妙, 妙 × 好好 × 真好 = 妙题题妙,  
where each Chinese character represents a digit from 0 to 9, the same character represents the same digit, and different characters represent different digits. What is the number of factors of the four-digit number represented by "妙题题妙"?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{16}
In a regular tetrahedron ABCD, how many points on its surface are equidistant from edge AB and points C and D? Provide your answer as a whole number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
8. Let $a_{1}, a_{2}, a_{3}, a_{4}$ be four distinct numbers from $1, 2, \cdots, 100$, satisfying
$$
\begin{array}{l}
\left(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}\right)\left(a_{2}^{2}+a_{3}^{2}+a_{4}^{2}\right) \\
=\left(a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4}\right)^{2} .
\end{array}
$$

Then the number of such ordered quadruples $\left(a_{1}, a_{2}, a_{3}, a_{4}\right)$ is $\qquad$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{40}
Compute \(\sum_{k=0}^{100}\left\lfloor\frac{2^{100}}{2^{50}+2^{k}}\right\rfloor\). (Here, if \(x\) is a real number, then \(\lfloor x\rfloor\) denotes the largest integer less than or equal to \(x\).)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{101 \cdot 2^{49}-50}
The segment \( K L \) is the diameter of a certain circle. Through its endpoints \( K \) and \( L \), two lines are drawn intersecting the circle at points \( P \) and \( Q \), respectively, which lie on the same side of the line \( K L \). Find the radius of the circle if \( \angle P K L = 60^{\circ} \) and the point of intersection of the lines \( K P \) and \( Q L \) is 1 unit away from points \( P \) and \( Q \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}