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Beyond brute force
The DP reveals a pattern: you win if . Can we prove this directly? From : any move (1, 2, or 3) leaves . Opponent wins. From : take stones. Leave . Opponent loses.
This is the power of game theory DP: compute the pattern with DP, then prove and simplify to . This pattern appears in many game theory problems. Look for cyclic structures in the win/lose sequence.
