Hashi (Bridges): Rules and Solving Techniques

Hashiwokakero, usually shortened to Hashi, means building bridges. You are given islands marked with numbers and you connect them until every island has exactly the number of bridge ends it asks for. There is no arithmetic beyond counting to eight, and yet a hard grid can stall an experienced solver for twenty minutes. The reason is that one of the four rules does not look like a constraint until the very end.

The rules

1. Bridges run horizontally or vertically between two islands, never diagonally.
2. Each island's number is exact. An island marked 5 must end with five bridge ends touching it, no more and no fewer.
3. At most two bridges may connect the same pair of islands, drawn as a double line.
4. Bridges may not cross each other, and may not pass through an island.
5. Everything must connect. When the puzzle is finished, you must be able to travel from any island to any other by bridges.

That last rule is the one that catches people. You can satisfy every number perfectly and still have an invalid solution, because your bridges formed two separate islands of islands.

The opening: find the forced islands

Before deducing anything, place the bridges that have no alternative. Given that each pair allows at most two bridges, an island's number sets a ceiling on how many neighbours it needs.

• An 8 must send two bridges in all four directions. Always. It is the single most useful island on the board.
• A 6 with three neighbours must send two to each.
• A 4 with two neighbours must send two to each.
• A 3 with two neighbours must send at least one to each, because two to one neighbour leaves only one for the other.
• A 1 in a corner with one neighbour sends its single bridge there.
• Any island whose number equals twice its neighbour count is fully determined. Fill it immediately.

Every bridge you place removes possibilities elsewhere, because it blocks crossings. On a dense grid the opening moves alone often cascade through a third of the puzzle.

Place what is forced before you deduce anything. Half of a Hashi grid usually solves itself if you look for ceilings first.

The middle: partial deductions

After the forced islands, progress comes from weaker statements that still eliminate options.

• At least one bridge. If an island's number is high enough that it cannot reach its total without using a particular neighbour, draw one bridge there even if you cannot yet tell whether it is a double.
• Blocked lines. A bridge already drawn blocks every crossing route. Scan for neighbours that are now unreachable and reduce their options accordingly.
• Saturated islands. Once an island has all its bridges, mark it as closed. No further bridge may touch it, which often forces its remaining neighbours.
• The last connection. When an island needs one more bridge and has only one open neighbour left, that bridge is forced regardless of what else is unresolved.

The ending: the isolation rule

The connection rule becomes a solving technique in the final third. Suppose two islands marked 1 sit next to each other, and joining them would satisfy both. If the rest of the grid is not yet connected to that pair, that bridge is illegal: it would seal a closed two island network that can never reach the rest. So the bridge must go elsewhere.

Generalised: never complete a group that is separated from the remaining islands. Whenever a move would close off a self contained cluster before the whole board is joined, that move is wrong. On hard grids this rule is often the only thing that resolves the last few bridges, and it is the technique most beginners never learn.

Common mistakes

• Drawing doubles too early. A double bridge is a strong commitment that blocks a whole line. Place singles where you know at least one is needed, and upgrade later.
• Forgetting to mark saturated islands. An island at its number is as informative as a wall. If you do not mark it, you keep reconsidering it.
• Solving the numbers and ignoring the network. Check connectivity as you go, not only at the end, or you will unwind ten correct bridges to fix one.
• Guessing. A proper Hashi has a unique solution reachable by deduction. Every impasse is a technique you have not applied.

Where it fits

Hashi comes from the same Japanese puzzle tradition as Sudoku and Kakuro, published by Nikoli, and it is the most spatial of the three. Where Sudoku is elimination and Kakuro is combination, Hashi is about connection and blocking, which makes it a good change of gear when number puzzles start to feel repetitive. The history is in the Nikoli puzzle tradition.

Its natural companion is Nurikabe, which uses the same connection logic in reverse: there the wall must be connected and the islands must not touch. Our combined guide is MyRin Hashi and Nurikabe, and if you prefer arithmetic, compare Kakuro and Sudoku.

MyRin includes Hashi with 600 levels across easy, medium and hard, alongside 32 other games, free on iOS and Android.

FAQ

What are the rules of Hashi?

Connect numbered islands with horizontal or vertical bridges. Each island must have exactly as many bridge ends as its number. At most two bridges may join the same pair of islands. Bridges cannot cross each other or pass through an island. When finished, every island must be reachable from every other.

What is the first move in Hashi?

Look for islands whose number forces their bridges. A 4 with only two neighbours must send two bridges to each. An 8 always sends two in all four directions. A 3 with two neighbours must send at least one to each. These are free moves that need no deduction.

Why is my Hashi solution rejected when all the numbers match?

Because of the connection rule. Every island must belong to one single network. If your bridges form two separate closed groups, the puzzle is unsolved even though every island has the right count.

Is Hashi the same as Hashiwokakero?

Yes. Hashiwokakero means building bridges in Japanese, and the puzzle is often shortened to Hashi. It was popularised by the Japanese publisher Nikoli, the same house behind the modern form of Sudoku.