IMO 2024 Shortlist C8
Let n be a positive integer. Given an nˆn board, the unit cell in the top left corner is initially coloured black, and t...
Category: Combinatorics
Problem
Let n be a positive integer. Given an nˆn board, the unit cell in the top left corner is initially coloured black, and the other cells are coloured white. We then apply a series of colouring operations to the board. In each operation, we choose a 2 ˆ 2 square with exactly one cell coloured black and we colour the remaining three cells of that 2 ˆ 2 square black. Determine all values of n such that we can colour the whole board black. (Peru) Shortlisted problems 7