How to play Number Triangles

Each side number is the sum of the two corners next to it — find the hidden corners and sides. Also known as Arithmagons.

The rules

Choose a shape (triangle, square or pentagon) and a difficulty, then press New Puzzle.
The number on each side is the sum of the two corners at its ends.
Tap a circle and type a number. Find every missing corner and side.
Hint shows the next number you can work out, and the sum that gives it.

A triangle has sides 9, 12 and 13, and no corners shown. All the sides add to 34, and each corner is counted twice, so the corners add to 17.

The side of 9 joins two corners; the third corner is opposite it, so it is 17 − 9 = 8. Now the other corners follow: 12 − 8 = 4 and 13 − 8 = 5.

Subtract along a side. If a side is 15 and one of its corners is 6, the other corner is 15 − 6 = 9.
Add two corners. Two known corners give the side between them straight away.
The halving trick. In a triangle (or pentagon) with only the sides shown, add all the sides and halve it: that is the total of all the corners. Take away the opposite side to find a corner.
Work round the shape. Each number you find usually unlocks the next one along.

Adding a side to a corner instead of subtracting.
Using the halving trick on a square — with an even number of sides it does not work.

Arithmagons are a classic classroom puzzle used to teach addition and algebraic thinking.

Why doesn’t the square have the halving trick?

In a square, the sides cannot tell you the corners on their own — so square puzzles always show at least one corner.

Are negative numbers used?

No — all the numbers are whole numbers of at least 1.

Is there always one answer?

Yes — every puzzle is checked to have exactly one answer.