Circle of Monsters
You are playing another computer game, and now you have to slay $n$ monsters. These monsters are standing in a circle, numbered clockwise from $1$ […]
ACM
Minimum Euler Cycle
You are given a complete directed graph $K_n$ with $n$ vertices: each pair of vertices $u \neq v$ in $K_n$ have both directed edges $(u, v)$ and […]
Divisor Paths
You are given a positive integer $D$. Let’s build the following graph from it: each vertex is a divisor of $D$ (not necessarily prime, $1$ […]
Strange Function
Let’s denote the following function $f$. This function takes an array $a$ of length $n$ and returns an array. Initially the result is an empty […]
Substring Search
You are given a permutation $p$ consisting of exactly $26$ integers from $1$ to $26$ (since it is a permutation, each integer from $1$ to […]
Slime and Biscuits
Slime and his $n$ friends are at a party. Slime has designed a game for his friends to play. At the beginning of the game, […]
Bracket Sequence
A bracket sequence is a string, containing only characters “(“, “)”, “[” and “]”. A correct bracket sequence is a bracket sequence that can be transformed into a correct […]
Dice Tower
A dice is a cube, its faces contain distinct integers from 1 to 6 as black points. The sum of numbers at the opposite dice […]
Unsolvable
Consider the following equation:where sign [a] represents the integer part of number a. Let’s find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase “unsolvable in […]
Well-known Numbers
Numbers k-bonacci ( k is integer, k > 1) are a generalization of Fibonacci numbers and are determined as follows: F(k, n) = 0, for integer n, 1 ≤ n < k; F(k, k) = 1; F(k, n) = F(k, n - 1) + F(k, n - 2) + … + F(k, n - k), for integer n, n > k. Note that we determine […]
Fence Planks
John Doe has a crooked fence, consisting of n rectangular planks, lined up from the left to the right: the plank that goes i-th (1 ≤ i ≤ n) (from left to right) has […]
Merging Two Decks
There are two decks of cards lying on the table in front of you, some cards in these decks lay face up, some of them […]
