How to Solve Bridges (Hashi): 7 Techniques from Basic to Expert

Bridges, known in Japan as Hashiwokakero ("build bridges"), or Hashi for short, is a connection puzzle first published by Nikoli in 1990. The rules fit in three lines: connect islands with horizontal or vertical bridges so that every island's number equals the bridge ends touching it, no more than two bridges run between any pair, bridges never cross or pass through another island, and the whole network ends up connected. Every Daily Grid Bridges puzzle has one intended solution. These seven techniques will take you from your first grid to expert boards.

1. Saturated corners and edges

Start with islands whose number equals the maximum bridges they could possibly have. An island with two visible neighbors and a clue of 4 must have exactly two bridges to each, so place all four immediately. The same logic applies to a 6 with exactly three available neighbors and an 8 with four. Count visible neighbors rather than relying only on whether an island sits near a geometric corner, because other islands and completed bridges can change what is available.

2. The one-neighbor rule

If an island has only one available neighbor, all of its remaining bridge demand must go there. A 1 with one neighbor gets one bridge; a 2 with one neighbor gets a double bridge. Neighbors become unavailable as they reach their clues or as another bridge blocks a crossing route, so re-scan for this rule constantly. An island that had three options early can drop to one option mid-solve.

3. Near-saturation (the N-1 argument)

This is the most-used technique in Hashi. If an island's number is one less than its theoretical maximum, every available neighbor must receive at least one bridge. A 3 with two neighbors can distribute its bridges only as 1 and 2, so one bridge is guaranteed in both directions. A 5 with three neighbors guarantees one toward each, and a 7 with four neighbors does the same. These guaranteed singles carve the board into readable regions.

4. Capacity counting

Sometimes an island's demand can only be met by adding up capacities. If a 5 has three neighbors but one of them can accept at most one more bridge, the other two directions must supply at least four. That forces doubles if each can accept two. Whenever remaining demand equals total remaining capacity exactly, every one of those bridges is forced. This is the workhorse rule on medium boards.

5. The isolation rule

The connectivity requirement is a solving tool. No group of islands may become sealed off from the rest of the board. The classic case is a pair of adjacent 1 islands: joining them would satisfy both and create a closed component, so that bridge is forbidden. The same goes for satisfying a small group internally when it would have no remaining route to the rest of the board. On expert boards, eliminating one isolating bridge often forces the correct alternative.

6. Blocking and lines of sight

Every bridge you place also blocks any perpendicular bridge from crossing its path. Expert solvers read this proactively. If an island can meet its clue only through a particular corridor, any perpendicular bridge that would cut that corridor is impossible. Before placing an optional-looking bridge, check which future connections it removes. Hashi endgames are often decided by corridor ownership.

7. Track the connected components

Local clue counts can all look valid while the islands still form two separate networks. As the solve develops, identify each connected component and ask how it can still join the others. If a component has only one possible outward connection, that connection is mandatory. If an optional bridge would use up the final capacity of its endpoint and leave another component stranded, reject it. In the endgame, this global check often distinguishes two locally legal choices.

Use the three-tap cycle carefully

In Daily Grid, tapping two aligned islands once adds a single bridge, tapping again makes it a double, and a third tap removes the connection. Before cycling a tentative bridge, recheck both endpoint totals. It is easy to turn a correct single into an accidental double while concentrating on only one island.

A useful rhythm is to place forced singles first, pause to update remaining demand at both ends, and add the second bridge only when capacity reasoning proves it. That keeps the board readable and makes an incorrect count easier to trace.

Putting it together

• Open with saturated and near-saturated islands (techniques 1 and 3); they never require lookahead.
• After every placement, re-scan for islands reduced to one neighbor (technique 2).
• When stuck, switch from single islands to counting across two or three (technique 4).
• Use isolation and corridors (techniques 5 and 6) instead of guessing.

The best way to internalize these is repetition: a fresh Bridges puzzle drops on Daily Grid every day at midnight Pacific Time, free in your browser, and there are unlimited practice puzzles when one a day isn't enough.