Sim (game)

Ramsey theory can also be used to show that no game of Sim can end in a tie.

Specifically, since the Ramsey number R(3, 3) is equal to 6, any two-coloring of the complete graph on 6 vertices (K6) must contain a monochromatic triangle, and therefore is not a tied position.

Because the Ramsey number R(3, 3, 3) is equal to 17, any three-coloring of the complete graph on 17 vertices must contain a monochromatic triangle.

A technical report[2] by Wolfgang Slany is available online, with many references to literature on Sim, going back to the game's introduction by Gustavus Simmons in 1969,[3] including proofs and estimates of the difficulty as well as computational complexity of Sim and other Ramsey games.

An app including its source code in the visual multi-platform Catrobat programming language is available[4] for playing it against one's smartphone.