How to Play Sim
Sim was invented by Gustavus Simmons in 1969: a pencil-and-paper game built on a theorem, with a bite in its tail. Every line you draw is a trap you set for yourself.
The rules
- Six dots in a hexagon, with all fifteen lines between them available.
- Players take turns colouring one uncoloured line in their colour.
- Whoever completes a triangle whose three sides are their colour (corners on the dots) loses. Mixed-colour triangles don't count.
- There are no draws: by the fifteenth line someone has lost.
Playing on kawu
Tap a line to colour it. Lines that would complete a triangle of your colour are dashed as a warning. The count of safe lines left for each player is shown under the board. Play red or blue against the computer, or two players on one device. Hint shows the computer's choice.
Next, read the Sim strategy.
Frequently asked questions
Why can't Sim end in a draw?
Ramsey's theorem: however you colour the fifteen lines between six dots with two colours, some triangle ends up all one colour. So by the last line one player has completed one and lost.
Who wins with perfect play?
The second player, as computer searches have shown. The winning strategy is far too complicated to memorise, which is why the game stays interesting between people.
Last updated 2026-10-20