Problem

Source: Puerto Rico 2013 TST #1

Tags: combinatorics



Claudia and Adela are betting to see which one of them will ask the boy they like for his telephone number. To decide they roll dice. If none of the dice are a multiple of 3, Claudia will do it. If exactly one die is a multiple of 3, Adela will do it. If 2 or more of the dice are a multiple of 3 neither one of them will do it. How many dice should be rolled so that the risk is the same for both Claudia and Adela?