Sim

Six dots sit in a hexagon with all fifteen connecting edges drawn faintly. Players take turns claiming one uncoloured edge in their own colour. The trap: complete a triangle of three dots all in YOUR colour and you lose.

• Each turn you must colour exactly one previously uncoloured edge.
• A triangle counts only when all three of its edges are your colour.
• Whoever first closes such a same-colour triangle loses the game instantly.
• There is no draw, the edges always run out in someone's favour.

• Desktop: click in the gap between two dots to colour that edge.
• Phone & tablet: tap between two dots to claim the nearest open edge.

• Solo vs CPU at Easy, Medium or Hard.
• Choose to play Red or Blue, and pick which colour moves first.
• 2-player hotseat, or online via invite, code or quick-match.

• Don't build two edges of a triangle in your own colour unless you can force your opponent to fill the third elsewhere first.
• Watch for double threats, a single forced move that would complete one of two triangles is how most games are lost.

Sim is a paper-and-pencil game that exists mainly because of a theorem. Six dots are drawn and every pair is joined, giving fifteen lines; two players take turns colouring a line in their own colour, and whoever completes a triangle of their colour loses.

The theorem is what makes it interesting. Ramsey theory proves that any two-colouring of those fifteen edges must contain a monochromatic triangle — so a drawn game is not merely rare, it is impossible. Someone always loses.

That converts the whole game into an exercise in delay. Neither player can aim to survive; each can only try to force the other into having no safe line left, which usually happens abruptly and several moves after the position was already decided.

Sim is a classic public-domain graph-colouring game proven to always have a winner. This is an original, free browser version with three CPU strengths plus hotseat and online play.

A free, original browser game on PlayPendium. No download, no install.