Encyclopedia > Sim

  Article Content

Sim

The game of Sim 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 R(3,3;2)=6, any coloring of the complete graph on 6 vertices must contain a monochromatic triangle, and therefore is not a tied position.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
East Marion, New York

... size is 2.30 and the average family size is 2.79. In the town the population is spread out with 18.5% under the age of 18, 4.4% from 18 to 24, 20.6% from 25 to 44, ...

 
 
 
This page was created in 27.4 ms