Free logic puzzle

Bridges (Hashi)

Also known as Hashi or Hashiwokakero

Join the islands with bridges. Each number tells you how many bridges that island needs.

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How to play

Join the islands with straight bridges. The number on an island says how many bridges touch it.
Bridges run up, down, left or right. They never cross, and at most two join the same pair.
Tap an island, then a neighbour, to build a bridge. Tap again for a double. Every island must end up connected.

First moves

Islands that need everything

Count an island's neighbours: the islands it can see in a straight line, up to four. Each neighbour takes at most two bridges. An island showing 8 needs double bridges to all four; a 6 with three neighbours or a 4 with two neighbours needs doubles all round too. Draw those first.

One short of full

When an island's number is one less than twice its neighbours, every neighbour gets at least one bridge. A 7 with four neighbours, a 5 with three or a 3 with two: there is not enough room to leave any neighbour out, so draw a single bridge to each and come back later.

Islands with one neighbour

An island with only one neighbour has no choice: all its bridges go to that neighbour. A 1 next to a single island gets one bridge, a 2 gets a double. As the board fills up, more islands end up with one neighbour left, because bridges block the lines they cross.

Keep everything connected

All islands must end up as one connected group. So two 1s never join each other, and two 2s never take a double bridge between them: either would close off a little group that can never reach the rest. Rule those links out and the remaining options often leave only one choice.

Origin

Hashiwokakero is a puzzle from the Japanese publisher Nikoli. It first appeared in Puzzle Communication Nikoli, issue 31, in September 1990, after an earlier form in issue 28 in December 1989.

The name means “build bridges!” in Japanese. In English it has also been published as Bridges and as Chopsticks, a mix-up between two Japanese words that both read hashi. The Times prints it as Hashi, and in the Netherlands, Belgium, France and Denmark it is published as Ai-Ki-Ai.

Sources: Wikipedia: Hashiwokakero

Why play it here

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Questions

Is Bridges the same as Hashi?

Yes. Bridges is our name for Hashiwokakero, or Hashi for short: the same rules, with islands, numbers and at most two bridges between any pair.

Does every Bridges puzzle have one solution?

Yes. Every puzzle has exactly one solution, and you can reach it by logic alone. A hint shows the next bridge and, where it can, why it has to be there.

Can bridges run diagonally or cross?

No. Bridges run straight up, down, left or right, and they never cross another bridge.

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