Games, because they follow well-defined rules, represent good laboratories for testing our predictive skills. They help us to a better understanding of randomness and uncertainty and provide insight about how we might forge information into knowledge [Nate Silver,

Hex: John Nash proved in 1952 that a game of Hex cannot end in a tie, and that for a symmetric board there exists a winning strategy for the player who makes the first move (by the strategy-stealing argument). However, the argument is non-constructive: it only shows the existence of a winning strategy, without describing it explicitly. Finding an explicit strategy has been the main subject of research since then.

Knight's: 3x3 middle square, circuits and 3x4, 4x4 and graph theory (start at P, never get back, start elsewhere to go through P then stuck at A (or miss it)), 6x6 Knights

Tower of Hanoi The minimum number of moves required to solve a Tower of Hanoi puzzle is 2^n - 1, where n is the number of disks.