Fibonacci Nim
A pile contains 76 stones. Two players alternate. The first player may remove any number of stones except the whole pile (at least 1, at most 75). After that, each player removes at least one stone and at most twice the number of stones the opponent just removed. The player who takes the last stone wins. The first player has exactly one winning first move. How many stones does it remove? Give an integer.
Related problems & prerequisites
Worth solving first
- Take Away a Perfect Square 5.0/10
- Wythoff's Losing Pairs up to Fifty 5.0/10
Source: Fibonacci Nim (Michael Whinihan, 1963), a classic Zeckendorf-representation game. Statement written for AxiomIQ.