Token Game

What this combinatorial game theory interview question tests

This is a medium-difficulty puzzle that probes your ability to analyze impartial games using symmetry and strategy-stealing arguments. It requires you to think beyond brute-force game trees and instead identify structural properties that determine winning and losing positions.

To solve problems like this, candidates typically look for invariants or symmetric strategies that allow one player to mirror or neutralize the opponent's moves. The key is recognizing which game states are truly equivalent, and whether the initial position favors the player who moves first or second. Interviewers value clear reasoning about why a strategy works, not just a guess at the answer.

• Impartial games and the Sprague–Grundy theorem
• Symmetry and strategy-stealing strategies
• Winning and losing positions
• Parity and invariant analysis