6 positive integers one at each side of a cube
Source: XIII May Olympiad (Olimpiada de Mayo) 2007 L1 P3
September 22, 2022
number theory
Problem Statement
Jorge chooses different positive integers and writes one on each face of a cube. He threw his bucket three times.
The first time his cube showed the number facing up and also the sum of the numbers on the faces sides was . The second time his cube showed the number facing up and also the sum of the numbers on the faces sides was . The third time his cube showed the number up, plus all the numbers on the side faces. They turned out to be primes. What are the numbers that Jorge chose and how did he distribute them on the faces of the cube? Analyze all odds.Remember that is not prime.