2006 BAMO p5 k switces in a row, 4 directions each
Source:
August 27, 2019
combinatorics
Problem Statement
We have switches arranged in a row, and each switch points up, down, left, or right. Whenever three successive switches all point in different directions, all three may be simultaneously turned so as to point in the fourth direction. Prove that this operation cannot be repeated infinitely many times.