Quentin L. Meunier

Problem 1005

Ruben wants to cut with a saw a large wooden cube into 64 small dice of the same size. The saw cuts according to a plan, and Ruben can change the arrangement of the pieces after each cut.

1A. How many cuts will it take, at least, to get the 64 dice?

After cutting, Ruben paints each side of each die in blue, yellow, red, or black. He does this so that, by assembling all the dice, he can reconstruct, according to his desire, a large blue cube, or a yellow, red, or black one.

2A. Knowing that exactly 40 dice have the four colors on their faces, how many two-colored dice did Ruben paint?

For this problem, I made a program for the second question which simply checks the conditions of the problem statement given 64 defined dice.

The code of the program can be found here.

1A: The minimum number of cuts is 6.
1B : There are 8 two-colored dice.