Sim

Sim was invented in 1969 by a mathematician named Gustavus J Simmons.

The game is started on a hexagon with only the vertices drawn.
In turn, players put a line of their colour that connects 2 vertices.
The player who first completes a triangle of their colour loses, but only when the corners of the triangle are 3 vertices of the hexagon.

Altough it was already solved, there even exist (quite complicated) winning strategies, I solved it again.

With perfect play, the second player wins in 15 moves, 15 lines is the maximum number of lines that can be drawn.

I've demonstrated this by creating a program which plays perfect.

Here's a screenshot



To download, press here (351 kb)


In fact, the game can't be drawn. This can be shown, using the pigeonhole principle.

From every vertice, 5 lines can be drawn. Using 2 colours, say red and white, there must be at least 3 lines of the same colour, shown below.



From that vertice, those 3 lines connect 3 vertices which form a triangle.
If any of the lines in that triangle would be red, there would be a red triangle.

If none of the lines in that triangle would be red, that triangle itself would be white.



Move on to Shove Off

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