Trigon Puzzles

How to solve a Trigon

It takes about three minutes to learn and a lifetime to get tired of. Watch the video, or read the rules underneath — they cover the same ground.

Trigon Explainer Video — 7 minutes 39 seconds. Plays right here; you don't have to go anywhere. Prefer YouTube? Watch it there.

The rules, in writing

  1. The shape is made of triangles

    Triangular dominoes are fitted together into a shape. Every triangle has a number on each of its three sides, and a number in the centre. The centre number is always the sum of the three side numbers.

  2. You get the centres. You work out the sides.

    Every centre number is printed for you. None of the side numbers are. That is the puzzle: reasoning backwards from each total to the three numbers that made it.

  3. Where two triangles meet, the number is shared

    Neighbouring triangles share a side, and that side carries the same number for both. To save writing it twice, the number is written once and a gap is left. This sharing is what links the whole grid together — solve one triangle and you have handed yourself a clue about its neighbour.

  4. Start with the zero

    A centre of 0 can only be 0+0+0. There is no other possibility. Fill it in, cross it off the key, and work outwards from there. At the other end, the largest total works the same way: in a 666 puzzle a centre of 18 can only be 6+6+6.

  5. Use the key, and cross things off

    Every puzzle comes with a key listing all the number combinations for each total — a centre of 4 can be 004, 013, 022 or 112, and nothing else. Strike each combination out as you use it. As the key empties, the remaining choices narrow, and the route reveals itself.

  6. Never guess

    This is the whole game, and it is what makes a Trigon different from most number puzzles. There is exactly one route through, and it never requires a leap.

Dax's rule: "Never put in a number because it will fit. Only put in a number because nothing else will fit."

A few practical notes

Use a pencil

And a rubber. Everyone makes mistakes, including the people who made these. Working in pencil is part of how the puzzle is meant to be played.

Sizes and difficulty

The 333 series is a coffee break. The 444, 555 and 666 series get progressively larger and longer. Each puzzle also carries its own rating, from Easy through to Extreme — and Extreme means what it says.

Stuck?

Go back to the last thing you were certain of and check it. A Trigon is never unsolvable, but one wrong number early on will quietly poison everything after it.

Now try one

Today's puzzle is free and takes a few minutes. Or take a free book away with you and solve it with a pencil, the way they were made to be solved.

Play today's puzzle Get a free book