Nim & Strategy Games
Math · Intermediate · Lesson 1 of 7

Winning & Losing Positions

Work backwards from the end

An interactive lesson with 5 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

  • W positions have a move to an L position. L positions only lead to W positions.
  • Work backwards from the end to classify positions.
  • Winning means always moving to an L position.

Steps

  1. Two kinds of position
  2. Take one or two
  3. Who should go first?
  4. Twenty-one
  5. The general rule