Welcome back from the summer holidays! We hope you’re rested and ready for an exciting year of problems. Today we’re going to dive right into our first topic with a fun game called “Lights Out."
Imagine a board of little square buttons, and each square has a light that can be either on or off. When you press on a square, that square’s light flips (from on to off, or off to on), but so do the lights of all its neighbours: the squares directly above, below, to the left, and to the right of it. In the pictures of today’s problem sheet, we’ll use dark blue to mean that a light is on, and light blue to mean that the light is off. An interactive version of this game can be freely found by searching ’Lights Out (game)’ on Wikipedia. It may be useful if you want to try some of the harder problems at home.
Let’s see what kind of games we can play with these boards: