Invariants & Parity

What never changes?

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• An invariant is a quantity that no move can change.
• If the start and goal differ in an invariant, the goal is impossible.
• Parity and colourings are the classic invariants.

Steps

1. The mutilated chessboard
2. Count the colours
3. Handshakes
4. The blackboard game
5. Sam Loyd’s puzzle
6. Flipping cups