Puzzles
Checkers jump toward a target row. Can they ever reach the fifth row up?
Pegs sit on every square of an infinite checkerboard below a horizontal line. Each move takes one peg and jumps it over an adjacent peg in a straight line, removing the peg that was jumped, exactly like in checkers or peg solitaire. Starting only from below the line, can you ever get a peg to land five rows above it?
Reveal the answer
No — it's provably impossible, no matter how cleverly you play. John Conway proved it in 1961 by assigning each square a weight based on powers of the golden ratio and showing the total weight of all pegs can never grow enough to reach row five, however many moves you make. Row four, just one short, is reachable.