This set of four puzzles draws inspiration from chess. 1. Oddities: In a chess tournament involving multiple players where not all face each other and some compete more often, several participants play an odd number of games. Prove that the count of such players must be even. 2. L of a trip: A knight moves in an L-shape, advancing two squares one way and one perpendicular. From the bottom right of an 8×8 board, can it reach every square once and finish at the top left? 3. Pawn return: On a standard chessboard setup, what is the minimum moves for a pawn to depart its start, promote to queen, and return home, with both sides cooperating? 4. Four knights: On an irregular grid, swap positions of two black and two white knights through successive moves. Think conceptually rather than using physical pieces for clarity. Solutions appear later. The puzzles originate from We Solve Problems, a charity offering free math sessions for secondary students in various UK cities. Sessions run from September to May and are led by graduate students. The column has featured puzzles biweekly since 2015.
