Fibonacci Nim

A game solved by Zeckendorf

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

• Each move takes at most twice the previous move.
• Every number is a unique sum of non-consecutive Fibonacci numbers (Zeckendorf).
• Fibonacci piles lose; otherwise take the smallest Zeckendorf term.

Steps

1. Take up to twice as many
2. Write it in Fibonacci
3. Winning moves
4. Why the smallest term?
5. A hundred stones
6. Losing piles