problem stringlengths 71 3.46k | answer stringlengths 0 145 | task stringclasses 6
values | problem_number int64 1 1.3k | set_number int64 1 5 |
|---|---|---|---|---|
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | AIME24 | 1 | 2 |
Eight circles of radius $34$ are sequentially tangent, and two of the circles are tangent to $AB$ and $BC$ of triangle $ABC$, respectively. $2024$ circles of radius $1$ can be arranged in the same manner. The inradius of triangle $ABC$ can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive i... | 197 | AIME24 | 14 | 1 |
Let ABCDEF be a convex equilateral hexagon in which all pairs of opposite sides are parallel. The triangle whose sides are extensions of segments AB, CD, and EF has side lengths 200, 240, and 300. Find the side length of the hexagon. | 080 | AIME24 | 26 | 5 |
The parabola with equation $y = x^2 - 4$ is rotated $60^\circ$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a - \sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime.... | 62 | AIME25 | 39 | 4 |
Let $A$ be the set of positive integer divisors of $2025$. Let $B$ be a randomly selected subset of $A$. The probability that $B$ is a nonempty set with the property that the least common multiple of its element is $2025$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. | 237 | AIME25 | 52 | 3 |
In a table tennis tournament every participant played every other participant exactly once. Although there were twice as many right-handed players as left-handed players, the number of games won by left-handed players was $40\%$ more than the number of games won by right-handed players. (There were no ties and no ambid... | 36 | AMC23 | 65 | 2 |
How many digits are in the base-ten representation of $8^5 \cdot 5^{10} \cdot 15^5$? | 18 | AMC23 | 78 | 1 |
Triangle $ABC$ has side lengths in arithmetic progression, and the smallest side has length $6.$ If the triangle has an angle of $120^\circ,$ Find the area of $ABC$. The final answer can be simplified in the form $m \sqrt{n}$, where $m$ and $n$ are positive integers and $n$ without square factore. What is $m+n$? | 18 | AMC23 | 90 | 5 |
ChIP-seq on a PFA-fixed sample with an antibody to the IKAROS transcription factor in human B cells followed by next-generation sequencing and standard quality control, alignment and peak-calling steps produced ChIP peaks that disappeared when PFA+DSG fixation was used. Where are we most likely to find such disappearin... | At active promoters and enhancers | GPQADiamond | 114 | 1 |
Imagine a point charge q is moving with a trajectory $\vec{s}(t)$, where t is time, with respect to the origin. Let $\vec{r}$ be the field point, where the field is observed, with respect to the origin of the same reference frame, and $\vec{d}$ be the vector from the point where the electromagnetic field was generated... | V(\vec{r},t) = \dfrac{qc}{4\pi\epsilon_o (d c - \vec{d}. \vec{v})}, \vec{A(\vec{r},t)} = \dfrac{\mu_o qc \vec{v}}{4\pi (d c - \vec{d}. \vec{v})} | GPQADiamond | 178 | 1 |
Consider this density matrix
$\rho=\frac{1}{2}\left(\left|0\right\rangle \left\langle 0\right|+\left|1\right\rangle \left\langle 1\right|\right)$
What is its geometrical position in the qubits space? | r=(0,0,0) | GPQADiamond | 242 | 1 |
The set of points $(x,y,z)$ that satisfy
\[2x = 3y = -z\]is a line.
The set of points $(x,y,z)$ that satisfy
\[6x = -y = -4z\]is another line.
Find the angle between these lines, in degrees. | 90^\circ | MATH500 | 306 | 1 |
The binary number $10101001110_{2}$ is equal to what number in base eight? | 2516_8 | MATH500 | 370 | 1 |
How many zeroes are at the end of $42!$ (42 factorial)? (Reminder: The number $n!$ is the product of the integers from 1 to $n$. For example, $5!=5\cdot 4\cdot3\cdot2\cdot 1= 120$.) | 9 | MATH500 | 434 | 1 |
The arithmetic mean of 7, 2, $x$ and 10 is 9. What is the value of $x$? | 17 | MATH500 | 498 | 1 |
In a regular polygon, the measure of an interior angle is 6.5 times the measure of an exterior angle. How many sides does the polygon have? | 15 | MATH500 | 562 | 1 |
Let $P(x)$ be a monic polynomial of degree 3. Suppose that $P(x)$ has remainder $R(x)$ when it is divided by $(x - 1)(x - 4),$ and remainder $2R(x)$ when it is divided by $(x - 2)(x - 3).$ Given that $P(0) = 5,$ find $P(5).$ | 15 | MATH500 | 626 | 1 |
Let $f$ be defined by \[f(x) = \left\{
\begin{array}{cl}
3-x & \text{ if } x \leq 3, \\
-x^3+2x^2+3x & \text{ if } x>3.
\end{array}
\right.\]Calculate $f^{-1}(0)+f^{-1}(6)$. | 0 | MATH500 | 690 | 1 |
In how many ways can 5 students be selected from a group of 6 students? | 6 | MATH500 | 754 | 1 |
Alex is participating in the filming of another video of BrMeast, and BrMeast asked Alex to prepare 250 thousand tons of TNT, but Alex didn't hear him well, so he prepared $n$ boxes and arranged them in a row waiting for trucks. The $i$-th box from the left weighs $a_i$ tons.
All trucks that Alex is going to use hold ... | LiveCodeBench | 805 | 2 | |
You are given two integers, n and k.
An array of distinct positive integers is called a k-avoiding array if there does not exist any pair of distinct elements that sum to k.
Return the minimum possible sum of a k-avoiding array of length n.
Example 1:
Input: n = 5, k = 4
Output: 18
Explanation: Consider the k-avoidi... | LiveCodeBench | 826 | 3 | |
You are given a 0-indexed array nums of n integers and an integer target.
You are initially positioned at index 0. In one step, you can jump from index i to any index j such that:
0 <= i < j < n
-target <= nums[j] - nums[i] <= target
Return the maximum number of jumps you can make to reach index n - 1.
If there is no... | LiveCodeBench | 848 | 1 | |
You are given a 0-indexed array nums and a non-negative integer k.
In one operation, you can do the following:
Choose an index i that hasn't been chosen before from the range [0, nums.length - 1].
Replace nums[i] with any integer from the range [nums[i] - k, nums[i] + k].
The beauty of the array is the length of the ... | LiveCodeBench | 869 | 2 | |
You are given a string moves of length n consisting only of characters 'L', 'R', and '_'. The string represents your movement on a number line starting from the origin 0.
In the i^th move, you can choose one of the following directions:
move to the left if moves[i] = 'L' or moves[i] = '_'
move to the right if moves[i]... | LiveCodeBench | 890 | 3 | |
You have n processors each having 4 cores and n * 4 tasks that need to be executed such that each core should perform only one task.
Given a 0-indexed integer array processorTime representing the time at which each processor becomes available for the first time and a 0-indexed integer array tasks representing the time ... | LiveCodeBench | 912 | 1 | |
You are given a 0-indexed string s having an even length n.
You are also given a 0-indexed 2D integer array, queries, where queries[i] = [a_i, b_i, c_i, d_i].
For each query i, you are allowed to perform the following operations:
Rearrange the characters within the substring s[a_i:b_i], where 0 <= a_i <= b_i < n / 2.
... | LiveCodeBench | 933 | 2 | |
You are given a 0-indexed 2D array variables where variables[i] = [a_i, b_i, c_i, m_i], and an integer target.
An index i is good if the following formula holds:
0 <= i < variables.length
((a_i^bi % 10)^ci) % m_i == target
Return an array consisting of good indices in any order.
Example 1:
Input: variables = [[2,3... | LiveCodeBench | 954 | 3 | |
You are given a 0-indexed string word and an integer k.
At every second, you must perform the following operations:
Remove the first k characters of word.
Add any k characters to the end of word.
Note that you do not necessarily need to add the same characters that you removed. However, you must perform both operatio... | LiveCodeBench | 976 | 1 | |
You are given N strings S_1,S_2,\dots,S_N, each of length M, consisting of lowercase English letter. Here, S_i are pairwise distinct.
Determine if one can rearrange these strings to obtain a new sequence of strings T_1,T_2,\dots,T_N such that:
- for all integers i such that 1 \le i \le N-1, one can alter exactly one ... | LiveCodeBench | 997 | 2 | |
You are given a sequence A=(A_1,A_2,\dots,A_{3N}) of length 3N where each of 1,2,\dots, and N occurs exactly three times.
For i=1,2,\dots,N, let f(i) be the index of the middle occurrence of i in A.
Sort 1,2,\dots,N in ascending order of f(i).
Formally, f(i) is defined as follows.
- Suppose that those j such that A_j ... | LiveCodeBench | 1,018 | 3 | |
There are N sports players.
Among them, there are M incompatible pairs. The i-th incompatible pair (1\leq i\leq M) is the A_i-th and B_i-th players.
You will divide the players into T teams.
Every player must belong to exactly one team, and every team must have one or more players.
Additionally, for each i=1,2,\ldots... | LiveCodeBench | 1,040 | 1 | |
There are N roulette wheels.
The i-th (1\leq i\leq N) wheel has P _ i integers S _ {i,1},S _ {i,2},\ldots,S _ {i,P _ i} written on it, and you can play it once by paying C _ i yen.
When you play the i-th wheel once, an integer j between 1 and P _ i, inclusive, is chosen uniformly at random, and you earn S _ {i,j} point... | LiveCodeBench | 1,061 | 2 | |
There are N people gathered for an event called Flowing Noodles. The people are lined up in a row, numbered 1 to N in order from front to back.
During the event, the following occurrence happens M times:
- At time T_i, a quantity W_i of noodles is flown down. The person at the front of the row gets all of it (if no on... | LiveCodeBench | 1,082 | 3 | |
Keyence has a culture of addressing everyone with the honorific "san," regardless of their role, age, or position.
Even a new employee would call the president "Nakata-san." [Translator's note: this is a bit unusual in Japan.]
You are given a person's surname and first name as strings S and T, respectively.
Print the ... | LiveCodeBench | 1,104 | 1 | |
You are given a string S consisting of uppercase English letters. Separate each character of S with a space and print them one by one in order.
Input
The input is given from Standard Input in the following format:
S
Output
Separate each character of S with a space and print them one by one.
Constraints
- S is a ... | LiveCodeBench | 1,125 | 2 | |
A regular pentagon P is shown in the figure below.
Determine whether the length of the line segment connecting points S_1 and S_2 of P equals the length of the line segment connecting points T_1 and T_2.
Input
The input is given from Standard Input in the following format:
S_1S_2
T_1T_2
Output
If the length of th... | LiveCodeBench | 1,146 | 3 | |
You are given a non-empty string S consisting of uppercase and lowercase English letters. Determine whether the following condition is satisfied:
- The first character of S is uppercase, and all other characters are lowercase.
Input
The input is given from Standard Input in the following format:
S
Output
If the co... | LiveCodeBench | 1,168 | 1 | |
You are given a string S consisting of lowercase English letters. The length of S is between 3 and 100, inclusive.
All characters but one of S are the same.
Find x such that the x-th character of S differs from all other characters.
Input
The input is given from Standard Input in the following format:
S
Output
Prin... | LiveCodeBench | 1,189 | 2 | |
You are given a sequence of positive integers A=(A_1,A_2,\dots,A_N) of length N and a positive integer K.
Find the sum of the integers between 1 and K, inclusive, that do not appear in the sequence A.
Input
The input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answe... | LiveCodeBench | 1,210 | 3 | |
On a coordinate plane, there are N points P_1, P_2, \ldots, P_N, where point P_i has coordinates (X_i, Y_i).
The distance \text{dist}(A, B) between two points A and B is defined as follows:
A rabbit is initially at point A.
A rabbit at position (x, y) can jump to (x+1, y+1), (x+1, y-1), (x-1, y+1), or (x-1, y-1) in on... | LiveCodeBench | 1,232 | 1 | |
There is an N \times N grid, where the cell at the i-th row from the top and the j-th column from the left contains the integer N \times (i-1) + j.
Over T turns, integers will be announced. On Turn i, the integer A_i is announced, and the cell containing A_i is marked. Determine the turn on which Bingo is achieved for ... | LiveCodeBench | 1,253 | 2 | |
You are given a string s representing a 12-hour format time where some of the digits (possibly none) are replaced with a "?".
12-hour times are formatted as "HH:MM", where HH is between 00 and 11, and MM is between 00 and 59. The earliest 12-hour time is 00:00, and the latest is 11:59.
You have to replace all the "?" c... | LiveCodeBench | 1,274 | 3 | |
You are given a 2D boolean matrix grid.
Return an integer that is the number of right triangles that can be made with the 3 elements of grid such that all of them have a value of 1.
Note:
A collection of 3 elements of grid is a right triangle if one of its elements is in the same row with another element and in the sa... | LiveCodeBench | 1,296 | 1 |
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