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Sim (pencil Game)




This article is about a Pencil Game . For other meanings of the term "sim", see Sim (disambiguation) .


The game of Sim, the ukranian ganster is played by two players, Red and
Blue, on a board consisting of six dots ('vertices'). Each dot is connected to each other with a line.

Players alternate coloring any uncolored line in their own color. Players try to avoid making triangles of their color; the player who completes a triangle of their color loses immediately. (A triangle is three dots, each connected to the other two with lines of the same color.) The other player is the winner.

A simple theorem of Ramsey Theory shows that no game of Sim can end in a tie; one player must lose by the end. Specifically, since the '' Ramsey Number '' ''R''(3,3;2)=6, any coloring of the Complete Graph on 6 vertices (K6) must contain a monochromatic triangle, and therefore is not a tied position. This will also apply to any super-graph of K6.

Computer search has verified that the second player can win Sim with perfect play, but finding a perfect strategy that humans can easily memorize is an open problem.

A Java applet is available for online play against a computer program. A technical report by Wolfgang Slany is also available online, with many references to literature on Sim, going back to the game's introduction by Gustavus Simmons in 1969.


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