Useless triangle

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When a piece's neighboring hexes are filled by the opponent in such a way that that piece has only two empty neighboring hexes that are also adjacent to each other, then the piece is said to lie in a useless triangle.


In the above diagram, the red piece at c5 and the empty hexes b6 and c6 form a useless triangle. The blue piece at e7 and the empty hexes e6 and f6 also form a useless triangle.

The important point is that unless the piece in a useless triangle is in that player's border row, the piece has effectively been removed from the game — that is, it cannot have any effect on the rest of the game regardless of the rest of the position. Notice that any red path through c5 must pass through b6 and c6. But b6 and c6 are connected to each other; therefore any red path through c5 would remain connected even if the red piece at c5 were removed. Similar logic holds for the blue piece on e7.

See also

Dead cell

Equivalent patterns