Question 14
Jorge chooses 6 distinct positive integers and writes one on each face of a cube. He rolls his cube three times.
The first time his cube showed the number $5$ on top and, moreover, the sum of the numbers on the lateral faces was $20$.
The second time his cube showed the number $7$ on top and, moreover, the sum of the numbers on the lateral faces was $17$.
The third time his cube showed the number $4$ on top and, moreover, all the numbers on the lateral faces turned out to be prime.
Which numbers did Jorge choose and how did he distribute them on the faces of the cube? Analyse all the possibilities.
The first time his cube showed the number $5$ on top and, moreover, the sum of the numbers on the lateral faces was $20$.
The second time his cube showed the number $7$ on top and, moreover, the sum of the numbers on the lateral faces was $17$.
The third time his cube showed the number $4$ on top and, moreover, all the numbers on the lateral faces turned out to be prime.
Which numbers did Jorge choose and how did he distribute them on the faces of the cube? Analyse all the possibilities.