A model of backward causation in which the future affects the past could help unite quantum mechanics and general relativity – and satisfy a challenge thrown down almost a century ago by Arthur Eddington.
Can you move a knight on a chessboard so that it visits every square exactly once? Euler was one of the first to analyse this problem systematically, but some questions about it are still open today.
Can you find a path through on this city map that crosses every bridge exactly once? Euler's answer to this problem started off the filed of graph theory.