64 dice in 8x8 fomation, wanted is all face 1 on top
Source: 1985 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p1
November 21, 2022
combinatoricsgamegame strategy
Problem Statement
Sixty-four dice with the numbers ”one” to ”six” are placed on one table and formed into a square with eight horizontal and eight vertical rows of cubes pushed together. By rotating the dice, while maintaining their place, we want to finally have all sixty-four dice the "one" points upwards. Each dice however, may not be turned individually, but only every eight dice in a horizontal or vertical row together by to the longitudinal axis of this row may turn. Prove that it is always possible to solve the dice by repeatedly applying the permitted type of rotation to the required end position.