A set of four chess-inspired puzzles is presented. One puzzle considers a chess tournament where not all players face each other and some play more games than others, requiring a proof that the number of players who played an odd number of games is even. Another puzzle asks whether a knight can traverse an 8×8 board exactly once starting at the bottom-right square and finishing at the top-left square. A third puzzle asks for the minimum number of moves for a pawn to leave its starting square, reach promotion, and return to its original square under cooperative play. A final puzzle involves swapping two pairs of knights on a nonstandard grid, solved by thinking abstractly rather than physically.
"A chess tournament is taking place with several participants. Not every player played against every other player, and some players may have played many more games than others. Some of the players played an odd number of games. Prove that the number of such players must be even."
"Starting in the bottom right corner of a regular 88 chessboard, is it possible for a knight to visit every square on the chessboard exactly once and end up in the top left corner?"
"Take a chessboard with the standard initial setup of pieces. What's the fewest number of moves needed for a pawn to leave its initial place, get promoted/queened, and then return to its original position? (Assuming the two players are collaborating to achieve this, not that the one is scuppering the other)."
"Show how to swap the two pairs of knights on the following strangely-shaped grid. The knights make one move at a time. You're trying to get the black nights to where the white knights are, and the white knights to where the black knights are. If you try to solve this problem using knights on a physical grid, you will get very confused. Try to think abstractly. With one simple(ish) insight, the problem is quickly solvable."
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