Problem

Source: 2020 RMM Shortlist C1

Tags: combinatorics, grid, RMM, RMM 2020, RMM Shortlist



Bethan is playing a game on an $n\times n$ grid consisting of $n^2$ cells. A move consists of placing a counter in an unoccupied cell $C$ where the $2n-2$ other cells in the same row or column as $C$ contain an even number of counters. After making $M$ moves Bethan realises she cannot make any more moves. Determine the minimum value of $M$. United Kingdom, Sam Bealing