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 grid of square buttons. Each square has a light that can be ON or OFF. When you press a square, that light flips, and so do the lights directly above, below, left, and right. In today’s pictures, dark blue means OFF and light blue means ON. If you want to try it at home, search “Lights Out (game)” on Wikipedia for an interactive version.
Before we start, let’s write three key words. After we see the examples, their meaning will be much clearer:
A light pattern is just which lights are ON or OFF on the board.
A plan is the collection of buttons you choose to press to make a pattern
A quiet plan is a plan that is not empty (it has at least one button on it) and when pressed, leaves the board looking exactly like it was before. For example: if the board starts all OFF and a quiet plan is pressed, then the board will still be all OFF.