2 player game with 3 dice Puerto Rico Ibero TST 2010.1
Source:
September 16, 2021
combinatorics
Problem Statement
Maria and Luis play the following game: Maria throws three dice and Luis can select some of them (possibly none) and turn them changing their value for the value in the opposite face of each selected die. Prove that Luis can always play in such a way that the sum of the upper faces of the dice after the change is a multiple of . Note: The game is played with normal dice, that is, the sum of opposite faces is .