Nim Where You May Split a Pile
Four piles contain 7, 10, 12 and 13 stones. Two players alternate; a move is either (a) to remove any positive number of stones from one pile, or (b) to split one pile into two non-empty piles without removing any stones. The player who cannot move loses. The first player has exactly one winning first move, and it is of type (a). How many stones does it remove? Give an integer.
Related problems & prerequisites
Worth solving first
- Nim 3-4-5 6.0/10
Source: Lasker's Nim (Emanuel Lasker, 1931), analysed in Winning Ways. Statement written for AxiomIQ.