How the maths behind honeycombs can help you work a jigsaw puzzle

What do bathroom walls, honeycombs and jigsaw puzzles have in common? Obviously, the answer is math.

If you’re trying to cover a surface with copies of a shape — for example, you’re tiling a bathroom — you’ll ideally want a shape like a square or rectangle. They will cover the entire surface without any gaps, which is why these boring shapes are often used as wall tiles.

But if your looks don’t quite match, you can still try to get the best coverage by arranging them effectively.

Imagine trying to…