Multi Knight: Strategy
Determining Winning and Losing States
To determine the winning and losing states for Multi Knight, we will have to use the Sprague-Grundy theorem and calculate the Grundy values for the positions we care about.
Observation of Independent Games
The key observation in Multi Knight is that each knight is independent of the others and is its own game. Each of these games is actually a game of Lone Knight. There are only 64 positions in Lone Knight, so we can calculate the Grundy values for all of them. Try to calculate the Grundy values for the positions on your own before looking at the solution. Hint: Start with the positions that have no valid moves.