Hex Connection

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Two players take turns claiming hexagons on an 11 × 11 rhombus board. Red must build an unbroken chain from the top edge to the bottom; Blue must connect the left edge to the right. Click any empty hex to claim it. Toggle hints to see which moves would win immediately.

Hex Connection was invented independently in the 1940s by the Danish mathematician Piet Hein and the American John Nash — the same Nash later famous for game theory and the Nash equilibrium. On any board size, the game can never end in a draw: one player must eventually form a complete chain while blocking the other. Nash proved something even stronger using the strategy-stealing argument: the first player always has a theoretical winning strategy, though finding the actual moves on an 11 × 11 board remains computationally intractable. The game is a natural introduction to topology — the study of properties preserved under continuous deformation — and connects to Nash’s use of the Brouwer fixed-point theorem in his doctoral work at Princeton.