New Year and the Sphere Transmission
There are $n$ people sitting in a circle, numbered from $1$ to $n$ in the order in which they are seated. That is, for all […]
Month: May 2020
New Year and the Permutation Concatenation
Let $n$ be an integer. Consider all permutations on integers $1$ to $n$ in lexicographic order, and concatenate them into one big sequence $p$. For […]
New Year and the Acquaintance Estimation
Bob is an active user of the social network Faithbug. On this network, people are able to engage in a mutual friendship. That is, if […]
New Year and the Mallard Expedition
Bob is a duck. He wants to get to Alice’s nest, so that those two can duck! Duck is the ultimate animal! (Image courtesy of […]
New Year and the Factorisation Collaboration
Integer factorisation is hard. The RSA Factoring Challenge offered $$100\,000$ for factoring RSA-$1024$, a $1024$-bit long product of two prime numbers. To this date, nobody […]
New Year and the Tricolore Recreation
Alice and Bob play a game on a grid with $n$ rows and infinitely many columns. In each row, there are three tokens, blue, white […]
Long number
Consider the following grammar: <expression> ::= <term> | <expression> ‘+’ <term> <term> ::= <number> | <number> ‘-‘ <number> | <number> ‘(‘ <expression> ‘)’ <number> ::= […]
Gennady and a Card Game
Gennady owns a small hotel in the countryside where he lives a peaceful life. He loves to take long walks, watch sunsets and play cards […]
Petr and a Combination Lock
Petr has just bought a new car. He’s just arrived at the most known Petersburg’s petrol station to refuel it when he suddenly discovered that […]
Yuhao and a Parenthesis
One day, Yuhao came across a problem about checking if some bracket sequences are correct bracket sequences. A bracket sequence is any non-empty sequence of […]
Makoto and a Blackboard
Makoto has a big blackboard with a positive integer $n$ written on it. He will perform the following action exactly $k$ times: Suppose the number […]
Alex and a TV Show
Alex decided to try his luck in TV shows. He once went to the quiz named “What’s That Word?!“. After perfectly answering the questions “How […]
Egor and an RPG game
One Saturday afternoon Egor was playing his favorite RPG game. While discovering new lands and territories, he came across the following sign: Egor is a […]
Vladislav and a Great Legend
A great legend used to be here, but some troll hacked Codeforces and erased it. Too bad for us, but in the troll society he […]
Mateusz and an Infinite Sequence
A Thue-Morse-Radecki-Mateusz sequence (Thorse-Radewoosh sequence in short) is an infinite sequence constructed from a finite sequence $\mathrm{gen}$ of length $d$ and an integer $m$, obtained in the […]
Flowers and Chocolate
It’s Piegirl’s birthday soon, and Pieguy has decided to buy her a bouquet of flowers and a basket of chocolates. The flower shop has F different types […]
The Child and Binary Tree
Our child likes computer science very much, especially he likes binary trees. Consider the sequence of n distinct positive integers: c 1, c 2, …, c n. The child calls a vertex-weighted rooted binary […]
Epic Convolution
You are given two arrays $a_0, a_1, \ldots, a_{n – 1}$ and $b_0, b_1, \ldots, b_{m-1}$, and an integer $c$. Compute the following sum: $$\sum_{i=0}^{n-1} […]
