Six Dots, Two Colors, No Triangle Allowed
Draw six dots and connect every pair with a line. Two players take turns coloring in one uncolored line at a time, each using their own color. The first player to complete a triangle in their own color loses. Can you find a way to never lose — or even guarantee a win?
Reveal the answer
No game of Sim can end in a tie: with six points, Ramsey's theorem (R(3,3)=6) guarantees any two-coloring of all 15 lines must contain a monochromatic triangle, so someone always loses. Later computer analysis showed the second player can always force a win. Sim was invented by cryptographer Gustavus Simmons in 1969 and introduced to a wide audience by Martin Gardner in his 'Mathematical Games' column, Scientific American, February 1973.