Hex has the interesting distinction of having been invented by two different distinguished mathematicians. Piet Hein was first, in 1942, and John Nash independently 're-invented' it in 1948 while at Princeton. Not just a game, but the progenitor of a new class of games - "connector games", Hex has several interesting properties. Games cannot be drawn, and though it has been shown that there is a winning strategy, no one knows what it is.
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