ABSTRACT
This chapter discusses the game of SIM which is played by two persons on the six vertices of a regular hexagon using two colored pencils. Each player in turn fills in one of the 15 possible lines connecting a pair of the points. The player who is first to form a complete triangle of his color, loses. The object of the game is not to form such a triangle ourselves and to force our opponent to do so. Unlike NIM, the game is not trivial; and unlike TIC-TAC- TOE, a drawn game is impossible. Since five lines originate there, at least three must be of the same color — say blue. No one of the three lines joining the endpoints of these lines can be blue if the player is not to form a blue triangle, but then the three interconnecting lines form a red triangle. Hence, at least one chromatic triangle must exist, and a drawn game is impossible.
