Losing Nim Triples
A game of Nim is played with three piles, each containing between 1 and 15 stones inclusive; there are 15³ = 3375 ordered starting triples (a, b, c). Players alternate removing any positive number of stones from one pile, and whoever takes the last stone wins. For how many ordered triples does the second player win with optimal play? Give an integer.
Related problems & prerequisites
Worth solving first
- Nim 3-4-5 6.0/10
Source: Bouton's theorem on Nim (1901). Statement written for AxiomIQ.