No reachable chess position with more than 218 moves
7 hours ago
- #chess
- #mathematics
- #optimization
- Nenad Petrović's 1964 chess composition with 218 moves for White remains unbeaten.
- Computer-assisted proof confirms no reachable chess position exceeds 218 moves.
- Mathematical optimization techniques were used to explore possible chess positions.
- Key observations include the uselessness of most black pieces and the impact of checks on move counts.
- Simplified chess rules were applied to reduce computational complexity.
- Optimal fractional solutions provided upper bounds but no positions exceeded 218 moves.
- Confirmed optimality of existing records: 144 moves without promotions and 288 moves in illegal positions.
- Future challenges include finding positions with most captures, stalemates, checks, etc.