Cram on a Four-by-Four Board
Two players alternately place a 1×2 domino, horizontally or vertically, on a 4×4 board so that it covers exactly two empty squares. Dominoes may not overlap. The player who cannot place a domino loses. Which player wins with optimal play? Answer 'the first player' or 'the second player'.
Related problems & prerequisites
Worth solving first
- Maker and Breaker on a Grid 4.0/10
- Race to 100 3.0/10
Source: Cram is a standard impartial domino-placing game; the symmetry argument is classical. Statement written for AxiomIQ.