Puzzles
Clear the board to one peg, but never the centre, why not?
In classic English peg solitaire, you start with every hole filled except the centre, and jump pegs over each other to remove them, aiming to finish with a single peg. You can finish with one peg, but never, starting from that setup, in the centre hole. Why is the centre provably unreachable?
Reveal the answer
A colouring argument, often attributed to mathematician John Conway, assigns pegs to classes based on position modulo 3 and shows each legal jump changes the count in a way that rules out ending on the centre from a centre-start. The game is first documented in a 1697 French engraving of the Princess de Soubise, and Gottfried Leibniz wrote about it in 1710.
— Wikipedia contributors, Peg solitaire — earliest reference 1697; Leibniz's account 1710