Sim (pencil game)
Sim is a game for two people. The game board consists of six points, each of which is connected to each other by a line. Each player is assigned a color and alternating colors each player a line with his color. Who produces a triangle in your color, loses immediately.
The Ramsey theory shows that no sim game can end with a draw. This is especially true because the Ramsey number R (3,3) = 6. Each 2 - coloring of the complete graph with 6 nodes () must contain a monochromatic triangle. This also applies to each of the upper graph. The reason for this is very simple to understand: One chooses an arbitrary point. Let's call this P1. This is connected to the other five points. Of these five lines must be at least three in a color we call this color F1. Let us now look at the three points that are reached by these three same-colored lines. Either the lines between these three points are all in one color, then, these three points, a triangle of the same color or at least two of the three points are connected with a line color in F1, then, these two points P1 with a same colored triangle.
Means complete enumeration with the computer, it has been found that the second player always wins in error-free game. Finding a perfect game strategy that can also people remember is not so far been successful.
Sim is an example of a Ramsey - game. Other Ramsey games are possible. Thus, for example, must according to the Ramsey also every 3 - coloring of a complete graph with 17 nodes contain a monochromatic triangle. In the corresponding Ramsey game, the two players use any of three colors. It is still unknown who wins it.