Avoid a triangle: rules and printable materials

Claim one edge per turn and avoid completing a triangle made entirely of your own edges.

Suggested group

2

Plan for

10–18 minutes

Bring

Six-vertex board and two distinguishable pens

Identify the board

Use six numbered dots around a hexagon. Each pair of dots is connected by one faint guide edge, fifteen edges in total. Crossings in the middle are not additional dots. Choose two distinct colours, or agree that one player uses a solid line and the other a dashed line; keep a written owner list if colours are hard to distinguish. The faint guides have no owner at the start.

Take a legal turn

On your turn, choose exactly one still-unclaimed guide edge and mark it as yours. An edge is identified by its two endpoint numbers, such as 1–4. You cannot erase ownership, recolour an opponent’s edge, draw a new connection or skip a turn. After marking, inspect whether that new edge completes any triangle using only your own three edges. If it does, you lose immediately.

Worked triangle

Suppose you already own 1–2 and 2–3. Claiming 1–3 would create your triangle 1–2–3, so you would lose on that move. If 1–3 belongs to the other player, those three lines are mixed ownership and do not make you lose. Any three numbered dots can form a triangle; it need not be one of the small visible regions bounded by crossing guides.

Check after every edge

Announce endpoints before marking so both players can find the same edge. Check the two endpoints against each of the other four dots: if both connecting edges to a third dot are already yours, the newly claimed edge completes a losing triangle. The host ledger lists all fifteen pairs and their owners. Resolve an unclear mark from that ledger before another move, not after a later result is known.

Finish and restart fairly

Stop as soon as a player completes their own triangle, then circle the three endpoint labels for verification. Never reverse the goal midway and reward a completed triangle. Play two games, swapping the first player in game two. If two players each win once, record a shared result rather than inventing a surprise tie-breaker. Use a clean board for every game. One person may announce an edge while a helper marks it, preserving the same decision rules without requiring a steady hand. This is a paper strategy game; the page does not provide computer opposition or automatic legality checks.

Printable materials

Preview before printing at 100% scale; turn off browser headers and footers. Keep host answers separate. This is a manual tabletop kit, not computer opposition or an automatic judge.