Hashiwokakero, usually shortened to hashi and also sold as Bridges, is a logic puzzle published by the Japanese company Nikoli. The grid holds numbered circles called islands, and you connect them with bridges so that each island has exactly as many bridges as its number. It looks simple, but a handful of counting techniques solve almost every square without guessing. This guide sets out the rules, then the techniques in the order you will use them, with examples you can try on our free hashi puzzle.
Bridges run in straight horizontal or vertical lines between two islands.
Bridges may not cross each other or pass over another island.
At most two bridges join any pair of islands.
The number on each island is the total number of bridges touching it.
When finished, every island must be connected into one group.
Each island has at most four neighbours (up, down, left and right) and at most two bridges to each, so the largest possible number is 8.
If an island's number equals twice its number of neighbours, every connection is a double bridge. An 8 with four neighbours, a 6 with three (for example on an edge) and a 4 with two (for example in a corner) are all completely solved straight away.
If an island's number is more than twice the number of its other neighbours, each neighbour must get at least one bridge. The general rule: with k neighbours and number n, each neighbour gets at least n − 2(k − 1) bridges.
Apply it again whenever a neighbour becomes unreachable, because a blocked direction lowers k and can make the rule bite.
| Neighbours | Number | Certain bridges to each neighbour |
|---|---|---|
| 2 | 3 | At least 1 each |
| 2 | 4 | 2 each (full) |
| 3 | 5 | At least 1 each |
| 3 | 6 | 2 each (full) |
| 4 | 7 | At least 1 each |
| 4 | 8 | 2 each (full) |
An island that can only reach one other island must send all its bridges there. A 1 or 2 with a single possible neighbour is solved immediately. Look for these along edges and behind existing bridges, which can cut off directions.
Because all islands must end up connected, you cannot close off a small group. Two 1s next to each other cannot be joined: that would use up both and leave them cut off from the rest. Likewise two 2s cannot be joined by a double bridge. So a 1 whose only neighbours are another 1 and one other island must connect to the other island.
As you place bridges, track how many each island still needs. A 5 that already has three bridges needs two more; if only one neighbour still has space, both go there. Our game marks islands that already have all their bridges and counts them in the Islands total above the grid.
Every bridge you draw blocks any other bridge that would cross it. After placing a long vertical bridge, check islands on either side: a 3 that could previously reach three neighbours may now reach only two, which the capacity rule then turns into certain bridges.
Near the end you will often see two options that both satisfy the numbers. Choose the one that keeps every island joined into one network. If one choice would leave a group of islands with no unused capacity and no link to the rest, it is wrong.
If you enjoy this style of reasoning, Akari (Light Up), Shikaku and the nonogram use similar counting logic. Our how to solve logic puzzles guide covers the general habits that make all of them faster.
It is Japanese for "build bridges!". The puzzle is also called hashi or Bridges.
8, because an island has at most four neighbours and can take at most two bridges to each.
No. Bridges cannot cross each other or pass over islands, and they must run straight horizontally or vertically.
Yes. The finished puzzle must form one connected network, which is the rule behind the isolation technique.
Easy grids are solved with the full-island and capacity rules alone. Harder grids rely on isolation and connectivity, but none should need guessing.
Solve the full islands first, apply the capacity rule everywhere, then use isolation and connectivity to finish. Re-check after each bridge, since every new line blocks crossings. Put it into practice on easy, medium and hard grids in our free hashi puzzle.