Problem #WSP-5660

Problems Combinatorics

Problem

A \(5\times5\) grid is given with \(25\) counters, each red on one side and white on the other. Counters are placed on the grid one at a time. When a counter is placed, any counters on neighbouring squares are flipped. Two squares are neighbours if they share a side (not just a corner). The aim is to finish with all counters showing red. During the process counters may flip several times. How many flips occur in total?