Problem

Source:

Tags: combinatorics



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 $4$. Note: The game is played with normal dice, that is, the sum of opposite faces is $7$.