inclusionAI/Ring-lite-rl-data huggingface dataset:
Alex is a risk management specialist who helps poker players optimize their winnings and minimize their losses. One of his clients, Jamie, played three rounds of poker. In the first round, Jamie won $120. In the second round, Jamie lost $45. In the third round, Jamie won double the amount he lost in the second round. Alex advised Jamie to save 25% of his total winnings after these three rounds. How much money should Jamie save based on Alex's advice?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{52.5}
一个小镇上共有 2023 位居民，他们成立了一些互不相同的俱乐部 A_1, A_2, \cdots, A_n，每个俱乐部至少一人，每个人可以在任意个不同的俱乐部内. 已知对于每个俱乐部 A_i，存在一个不在其中的居民 b_i，考虑所有 b_i 未加入的俱乐部，它们要么为 A_i，要么和 A_i 没有公共成员. 求该小镇上俱乐部个数的最大值.（程国根）
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2023}
The sum of the number of boys and girls in a school is 1150. If the number of boys is a certain number, then the number of girls becomes that number as a percentage of the total number of students. What is the number of boys in the school?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1058}
[ Angles between angle bisectors $\quad]$ 

In triangle $ABC$, the angle bisectors of the angles at vertices $A$ and $C$ intersect at point $D$. Find the radius of the circumcircle of triangle $ABC$, if the radius of the circumcircle of triangle $ADC$ with center at point $O$ is $R=6$, and $\angle ACO=30^{\circ}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Let \( ABC \) be an isosceles triangle at \( A \) with \( \angle CAB = 20^\circ \). Let \( D \) be a point on the segment \( [AC] \) such that \( AD = BC \). Calculate the angle \( \angle BDC \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30^\circ}
Find the area of the cross-section of a rectangular parallelepiped $ABCDEFG$ by a plane passing through the diagonal $AC_1$, parallel to the base diagonal $BD$, inclined to the base plane at an angle of $30^{\circ}$, and forming an angle of $45^{\circ}$ with the diagonal $A_1C$ if the diagonal of the parallelepiped is $d$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2 \sqrt{5} d^2}{12}}
A year ago, the total cost of buying a lawnmower was 2/5 times less than the cost it goes for now. If the cost was $1800 a year ago, calculate how much it would cost Mr. Lucian to buy 4 such lawnmowers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12000}
Find the sum of all real numbers $x$ for which $$\lfloor\lfloor\cdots\lfloor\lfloor\lfloor x\rfloor+x\rfloor+x\rfloor \cdots\rfloor+x\rfloor=2017 \text { and }\{\{\cdots\{\{\{x\}+x\}+x\} \cdots\}+x\}=\frac{1}{2017}$$ where there are $2017 x$ 's in both equations. ( $\lfloor x\rfloor$ is the integer part of $x$, and $\{x\}$ is the fractional part of $x$.) Express your sum as a mixed number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3025 \frac{1}{2017}}
A person plans to process 408 parts in 15 days. In the first three days, he processes 24 parts each day. Calculate the minimum number of parts he needs to process each day for the remaining days to complete the task ahead of schedule. Express your answer as an integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{29}
Find all prime numbers \( p \) such that there exist integers \( m \) and \( n \) satisfying \( p = m^2 + n^2 \) and \( p \mid (m^3 + n^3 - 4) \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2, 5}
The function $y = f(x)$ is a monotonically decreasing function defined on the interval $[-2, 2]$, and $f(a + 1) < f(2a)$. The range of the real number $a$ is __________.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[-1, 1)}
There are 2023 cups numbered from 1 through 2023. Red, green, and blue balls are placed in the cups according to the following rules.
- If cups $m$ and $n$ both contain a red ball, then $m-n$ is a multiple of 2 .
- If cups $m$ and $n$ both contain a green ball, then $m-n$ is a multiple of 3 .
- If cups $m$ and $n$ both contain a blue ball, then $m-n$ is a multiple of 5 .

What is the smallest possible number of empty cups?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{538}
A train 165 meters long running at the rate of 54 kmph takes 58.9952803775698 seconds to cross a bridge of certain length. How long is the bridge?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{719.93}
A cryptographer devises the following method for encoding positive integers. First, the integer is expressed in base $5$. 
Second, a 1-to-1 correspondence is established between the digits that appear in the expressions in base $5$ and the elements of the set 
$\{V, W, X, Y, Z\}$. Using this correspondence, the cryptographer finds that three consecutive integers in increasing 
order are coded as $VYZ, VYX, VVW$, respectively. What is the base-$10$ expression for the integer coded as $XYZ$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{108}
Given the one-variable quadratic equation in $x$: $x^{2}+\left(2k+3\right)x+k^{2}=0$ has two distinct real roots $x_{1}$ and $x_{2}$. If $\frac{1}{{x}_{1}}+\frac{1}{{x}_{2}}=-1$, then the value of $k$ is ____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
A red long string is folded in half, and then folded in half again, ..., after being folded $m$ times, the bundle obtained is cut in the middle to get some red short strings; a white long string is folded in half, and then folded in half again, ..., after being folded $n$ times, the bundle obtained is cut in the middle to get some white short strings. If the ratio of the number of red short strings to the number of white short strings is an integer greater than 1, please give the smallest possible value of this integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Joe B. is frustrated with chess. He breaks the board, leaving a \(4 \times 4\) board, and throws 3 black knights and 3 white kings at the board. Miraculously, they all land in distinct squares! What is the expected number of checks in the resulting position? (Note that a knight can administer multiple checks and a king can be checked by multiple knights.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{9}{5}}
Given $f(x) = (e^x - 1)^2 + (e^{-x} - 1)^2$, find the minimum value of $f(x)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Of the 6,000 employees of company X, 2/10 are clerical, 3/10 are technical, and 5/10 are managerial. If the clerical staff were to be reduced by 1/4, the technical staff by 1/5, and the managerial staff by 1/10, while 50 clerical employees were promoted to managerial positions and 90 technical employees shifted to clerical roles, what percent of the total number of the remaining employees would then be clerical?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18.65\%}
A thin rectangular slab of potato was cut into two pieces for an osmosis lab. One piece is 50 mm greater than the other. If the original uncut slab is 600 mm, what is the length of the other piece of the potato after it is cut?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{325}
设 a=\underbrace{66\cdots6}_{10\text{个 }6},b=\underbrace{33\cdots3}_{6\text{个 }3}，则 a,b 的最大公约数为__________.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{33}
An Olympic track and field athlete is using a new fitness app to optimize their training sessions. The app tracks their running speed, heart rate, and recovery time. During a training session, the athlete runs 400 meters in 50 seconds, then takes a 2-minute rest before running another 400 meters in 45 seconds. The app calculates the athlete's average speed for the entire session, including the rest time. 

Calculate the athlete's average speed in meters per second for the session, considering the total time spent running and resting.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3.72}
A group of monkeys is divided into three subgroups, with each subgroup having an equal number of monkeys. They go to the orchard to pick peaches. After finishing the picking, they combine all the peaches and distribute them equally among all the monkeys. If each monkey receives 5 peaches, there are 27 peaches left over; if each monkey receives 7 peaches, then at least one monkey receives fewer than 7 peaches. What is the total number of peaches this group of monkeys has picked?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{102}
Given a graph $G$ with vertices representing integers $1,2,\dots,99$, two vertices are connected if their greatest common divisor is at least $3$. Determine the chromatic number of $G$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{33}
$A$ pair of six-sided dice are labeled so that one die has only even numbers (two each of $2, 4$, and $6$), and the other die has only odd numbers (two of each $1, 3$, and $5$). The pair of dice is rolled. Find the probability that the sum of the numbers on the tops of the two dice is $7$. Express your answer in the form \(\frac{k}{m}\) and provide the value of \(k + m\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
How many integer solutions does the equation

$$
\frac{1}{2022}=\frac{1}{x}+\frac{1}{y}
$$

have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{53}
Let $f(x,y)$ be a function defined for all pairs of nonnegative integers $(x, y)$, such that $f(0,k) = f(k,0) = 2^k$ and 
\[ f(a,b) + f(a+1,b+1) = f(a+1,b) + f(a,b+1) \]
for all nonnegative integers $a, b$. Determine the number of positive integers $n \leq 2016$ for which there exist two nonnegative integers $a, b$ such that $f(a,b) = n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{65}
Find the sum of the first eight prime numbers that have a units digit of 3.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{394}
A worker makes an error of some percentage in excess while calculating the edge of a square. As a result, the worker makes a 4.04% error in calculating the area. What is the percentage error in calculating the edge?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2\%}
Given that the ellipse $\frac{x^{2}}{m} + \frac{y^{2}}{n} = 1$ and the hyperbola $\frac{x^{2}}{p} - \frac{y^{2}}{q} = 1$ $(m, n, p, q\in\mathbb{R}^{+})$ share the same foci $F_1$ and $F_2$, and $P$ is an intersection point of the ellipse and the hyperbola, then the product $|PF_1| \cdot |PF_2| = \_\_\_\_\_\_\_\_\_.$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{m - p}
In an acute triangle ABC, let D be a point on [AC] and E be a point on [AB] such that ∠ADB = ∠AEC = 90°. If the perimeter of triangle AED is 9, the circumradius of triangle AED is 9/5, and the perimeter of triangle ABC is 15, calculate the length of BC. Express your answer as a single value.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{24}{5}}
Given the fractional equation $\frac{m}{x-2}+\frac{2x}{x-2}=1$ with a positive root, find the value of $m$. Express your answer as a single numerical value.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-4}
In a tournament with 100 wrestlers, all of different strength, the stronger wrestler always wins against the weaker one. The wrestlers are paired up and have matches. Then, they are paired up differently and have matches again. The winners of both matches receive prizes. What is the minimum possible number of prize winners?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
How many functions $f: \mathbb{Z} \rightarrow \mathbb{R}$ satisfy the following three properties?

(a) $f(1)=1$;

(b) For all $m, n \in \mathbb{Z}, f(m)^{2}-f(n)^{2}=f(m+n) f(m-n)$;

(c) For all $n \in \mathbb{Z}, f(n)=f(n+2013)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1006}
In the plane of square ABCD, how many points P are there such that △PAB, △PBC, △PCD, and △PDA are all isosceles triangles?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
Let $a, b, c, d$ be four real numbers such that $a + b + c + d = 20$ and $ab + bc + cd + da = 16$. Find the maximum possible value of $abc + bcd + cda + dab$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{80}
The base of a triangle is $a$, and the angles adjacent to it measure $45^{\circ}$ and $15^{\circ}$. A circle with a radius equal to the altitude dropped to this base is drawn from the vertex opposite the base. Find the area of the part of the corresponding circle that is contained within the triangle.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\pi a^2 (2 - \sqrt{3})}{18}}
Eight teams compete in a tournament. Each pair of teams plays exactly one game against each other. There are no ties. If the two possible outcomes of each game are equally likely, what is the probability that every team loses at least one game and wins at least one game? Express your answer as a simplified fraction.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{903}{1024}}
Veronica put on five rings: one on her little finger, one on her middle finger, and three on her ring finger. In how many different orders can she take them all off one by one?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and form a geometric sequence with common ratio $r$. Additionally, it is given that $2c - 4a = 0$. Express $\cos B$ in terms of $a$ and $r$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac {3}{4}}
Given an arithmetic-geometric sequence $\{a\_n\}$, the sum of its first $n$ terms is $10$, and the sum of its first $2n$ terms is $30$. Find the sum of its first $3n$ terms.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{70}
Let \( n \) be the product of 3659893456789325678 and 342973489379256. Determine the number of digits of \( n \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{34}
Let $d$ be one of the common tangent lines of externally tangent circles $k_1$ and $k_2$. $d$ touches $k_1$ at $A$. Let $[AB]$ be a diameter of $k_1$. The tangent from $B$ to $k_2$ touches $k_2$ at $C$. If $|AB|=8$ and the diameter of $k_2$ is $7$, then what is the length of $|BC|$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
A club has between 150 and 250 members. Every month, all the members meet up for a group activity that requires the members to be divided into seven distinct groups. If one member is unable to attend, the remaining members can still be evenly divided into the seven groups. Calculate the sum of all possible numbers of members in this club.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2807}
A train 2500 m long can cross an electric pole in 100 sec. What is the speed of the train?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
Given the line $y=a (0 < a < 1)$ and the function $f(x)=\sin \omega x$ intersect at 12 points on the right side of the $y$-axis. These points are denoted as $(x\_1)$, $(x\_2)$, $(x\_3)$, ..., $(x\_{12})$ in order. It is known that $x\_1= \dfrac {\pi}{4}$, $x\_2= \dfrac {3\pi}{4}$, and $x\_3= \dfrac {9\pi}{4}$. Calculate the sum $x\_1+x\_2+x\_3+...+x\_{12}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{66\pi}
In quadrilateral $ABCD$, $AB \parallel CD$ and $BC \perp AB$. Lines $AC$ and $BD$ intersect at $E$. If $AB = 20$, $BC = 2016$, and $CD = 16$, find the area of $\triangle BCE$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8960}
When a circular sector is rotated about one of its boundary radii, it forms a solid whose spherical surface area is equal to the conical surface area. Find the sine of the central angle of the circular sector.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{4}{5}}
Let 
\[ 
S = \left\{ \{a_n\} \mid a_1 = 1, a_{n+1} = 2a_n \text{ or } 4a_n + 1, \; n \in \mathbf{Z}_{+} \right\}.
\]
Let \( T \) be the set of all elements formed by the sequences in \( S \). Consider an arbitrary positive integer \( t \) in the interval \([1, 2021]\). What is the probability that \( t \in T \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{232}{2021}}
Given \( x \in[0, \pi] \), compare the sizes of \( \cos (\sin x) \) and \( \sin (\cos x) \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\cos(\sin x) > \sin(\cos x)}
To walk 4 km, ride a bicycle for 6 km, and drive a car for 40 km, Uncle Vanya takes 2 hours and 12 minutes. If he needs to walk 5 km, ride a bicycle for 8 km, and drive a car for 30 km, he needs 2 hours and 24 minutes. How much time will Uncle Vanya need to walk 8 km, ride a bicycle for 10 km, and drive a car for 160 km?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5 \text{ hours } 48 \text{ minutes}}
Find the smallest natural number $m$ for which there exists a natural number $n$ such that the sets of the last 2014 digits in the decimal representation of the numbers $a=2015^{3 m+1}$ and $b=2015^{6 n+2}$ are identical, with the condition that $a<b$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{671}
Misha and Sasha left city $A$ for city $B$ on bicycles at noon. Simultaneously, Vanya left city $B$ for city $A$. All three travel at constant but different speeds. At 1 PM, Sasha was exactly halfway between Misha and Vanya, and at 1:30 PM, Vanya was halfway between Misha and Sasha. When will Misha be exactly halfway between Sasha and Vanya?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3 \text{ PM}}
A store sells three types of products, A, B, and C, with prices of 2 yuan, 3 yuan, and 5 yuan per item, respectively. A person bought some quantity of these three products, paying a total of 20 yuan. They discovered that they had bought too many of one type of product and returned two items of that product. However, the cashier only had 10 yuan notes and no change, so the person adjusted the quantities of the other two products (while ensuring every product was bought at least once) to keep the total cost the same. What is the quantity of product B that the person finally bought?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Jenny places a total of 20 red Easter eggs in several green baskets and a total of 30 orange Easter eggs in some blue baskets. Each basket contains the same number of eggs and there are at least 5 eggs in each basket. How many eggs did Jenny put in each basket?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Let $f(n) = \sum_{gcd(k,n)=1,1\le k\le n}k^3$ . If the prime factorization of $f(2020)$ can be written as $p^{e_1}_1 p^{e_2}_2 ... p^{e_k}_k$, find $\sum^k_{i=1} p_ie_i$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{818}
Let $L, E, T, M, \text{ and } O$ be digits that satisfy the equation:
\[
LEET + LMT = TOOL
\]
Given that $O = 0$, digits may be repeated, and $L \neq 0$, determine the value of the 4-digit integer $ELMO$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1880}
In the expression 8k8 + k88 - 16t6, k and t represent non-zero digits within the integers. If k and t represent non-zero digits within the integers above, what is the value of t?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Given the sequence $\{a_n\}$ where $a_1 = \frac{1}{2}$ and $a_{n+1} = \frac{1+a_n}{1-a_n}$ for $n \in N^*$, find the smallest value of $n$ such that $a_1+a_2+a_3+…+a_n \geqslant 72$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{238}
Each day, John ate 30% of the chocolates that were in his box at the beginning of that day. At the end of the third day, 28 chocolates remained. How many chocolates were in the box originally?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{82}
A triangle $\bigtriangleup ABC$ has vertices lying on the parabola defined by $y = x^2 + 4$. Vertices $B$ and $C$ are symmetric about the $y$-axis and the line $\overline{BC}$ is parallel to the $x$-axis. The area of $\bigtriangleup ABC$ is $100$. $A$ is the point $(2,8)$. Determine the length of $\overline{BC}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
Irene just bought a new lamp for her bedside table. The old lamp was 1 foot (12 inches) tall, and the new lamp's height is given as 55.56666666666667 centimeters. Irene's friend from Europe wants to know the difference in height between the lamps in meters. How much taller is the new lamp than the old lamp when comparing their heights in meters?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.2508666666666667}
Let f(x) be a function with the domain of R. Proposition p: "∀x > 0, f(x) > 0". What is the negation of proposition p? Express your answer as a logical statement with correct quantifiers and conditions.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{∃x > 0, f(x) ≤ 0}
A container is shaped like a square-based pyramid where the base has side length  $23$  centimeters and the height is  $120$  centimeters. The container is open at the base of the pyramid and stands in an open field with its vertex pointing down. One afternoon  $5$  centimeters of rain falls in the open field partially filling the previously empty container. Find the depth in centimeters of the rainwater in the bottom of the container after the rain.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60}
Given natural numbers \( M \) and \( N \), both greater than ten, consisting of the same number of digits, and such that \( M = 3N \). To obtain the number \( M \), one of the digits in \( N \) is increased by 2, and each of the remaining digits is increased by an odd digit. What digit could the number \( N \) end with? Find all possible answers.

(N. Agahanov)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Let $P_{1}, P_{2}, \ldots, P_{8}$ be 8 distinct points on a circle. Determine the number of possible configurations made by drawing a set of line segments connecting pairs of these 8 points, such that: (1) each $P_{i}$ is the endpoint of at most one segment and (2) two no segments intersect. (The configuration with no edges drawn is allowed.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{323}
A circle of radius 1 is randomly placed in a 15-by-36 rectangle $ABCD$ so that the circle lies completely within the rectangle. Given that the probability that the circle will not touch diagonal $AC$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$817$}