ヘックス
Join your own two sides of the board with an unbroken chain. A draw is impossible.
Found twice: by Piet Hein in Copenhagen in 1942, and again by John Nash at Princeton in 1948, who is said to have proved that the first player wins with perfect play without anyone finding out how. The proof that it cannot end in a draw is the same argument.
別名はNash, John, Con-tac-tix, Polygon。
目的
- Join your own two sides of the board with an unbroken chain of your stones: Black the top and bottom, White the left and right.
- A full board always has exactly one winner, so a draw is impossible — that is a fact about the shape of the board, not a rule anybody wrote.
盤
- A square board of 11, 13, 19 lines; 11×11 by default.
- A rhombus ruled as a triangular lattice, eleven points a side by default, with the stones on the crossings. Black owns the top and bottom edges, marked dark; White owns the left and right, marked pale. The two corners between a dark edge and a pale one belong to both.
手順
- Players take turns placing one stone on any empty point. Nothing ever moves and nothing is ever taken.
- Three families of lines cross at every point, so each one touches six others: two along its row, two along its slanted column, and two along the board's short diagonal.
- The game ends the moment one colour's chain reaches from one of their sides to the other.
細則
- Either colour may open, or the first stone may be drawn by lot.
- Openings on offer: Free, Swap.
- The threat reading, hints and the chance-of-winning bar are switched off: there are no lines here, only whether your two sides are joined.
- 11×11 is the usual size, and the one the world championship uses; 13×13 and 19×19 are played too. The corners belong to both of their sides.