Today we will learn a really useful strategy for solving a certain kind of problems. This strategy is called the invariance principle, and after working through this sheet you’ll be able to recognise easily when we need to use an invariant to solve a problem. This strategy is applicable to kinds of problems where some task is repeatedly performed, and we wish to see if it is possible to transform our “initial state" into some given “final state". The key is to ask yourself:
What stays the same?