Abibbo, Babibbo and Cabibbo compete on the challenges on the training platform. Given a challenge, each of them has a probability p = 1/2 of solving it. They take turns in opening the challenges: if Abibbo solves its challenge, he wins, otherwise it’s Babibbo’s turn; if Babibbo solves its challenge, he wins, otherwise it’s Cabibbo’s turn; if Cabibbo solves its challenge, he wins, otherwise they start again from Abibbo.

Gaspare is writing personalized emails to the ten Team Italy finalists, but he did a mess with the addresses and he doesn’t know to which person every address corresponds.

An array contains the numbers [1, 3, 5, ..., 2047] (the odd integers from 1 to 2047 included). Fixed a positive integer k, a move consists in choosing k elements from the array, applying the bitwise AND between the chosen elements and subtracting this last value from those k integers.

A solid cube of side length 1 is removed from each corner of a solid cube of side length 3.

Alice has two discs with a number written on one of their two sides: disc A has the number 11, while disc B has 9.

300 people will participate in OliCyber.IT, CyberChallenge.IT or both. 1/6 of those who will participate in Olicyber.IT will participate also in CyberChallenge.IT and 1/10 of those who will participate in CyberChallenge.IT will participate also in OliCyber.IT.  

On an island, there are knights, who always tell the truth, and impostors, who always lie. A, B, C and D are the inhabitants of the island and are talking about the number of knights. They say:

Bruno wants to train himself for the finals of CyberChallenge.IT. In order to do so, he solves either two or three challenges each day, tossing a coin. But since solving challenges is difficult, if he solves three challenges in three consecutive days, the next day he does not solve any challenge.   

Lorenzo and Mattia are playing a game at the Team Italy camp. They have a bag with n ping pong balls and, one at a time and starting from Lorenzo, remove some balls from the bag. More specifically, if there are x balls left, they can remove either s(x) or x−s(x) balls, being s(x) the sum of the digits of x. The player who removes the last ball wins.   

Carlo leaked the formula used by the organizers to grade the programming test. It is a function f(x) such that if you solve x problems, you score pow(f(f(f(f(x)))), 2) points. Moreover, it is known that f(f(x)) = sqrt(pow(x, 2) + 15).

Consider a sorted array of 100 integers.