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 bridges touching it, no more than two bridges run between any pair, bridges never cross, and the whole network ends up connected. Every well-made Hashi puzzle, including the daily Bridges puzzle on Daily Grid, has exactly one solution reachable by logic alone. 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. A corner island touches at most two neighbors, so a corner "4" must have exactly two bridges to each — place all four immediately. The same logic applies to an edge island marked 6 (three neighbors, two bridges each) and any island marked 8 (all four directions, doubled). These moves are 100% forced and usually unlock the rest of the board.

2. The one-neighbor rule

If an island has only one available neighbor, all of its bridges must go there. A "1" with one neighbor gets one bridge; a "2" with one neighbor gets a double bridge. Neighbors get "used up" as bridges elsewhere block lines of sight, so re-scan for this rule constantly — an island that had three neighbors early can drop to one neighbor mid-solve.

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

The most-used technique in Hashi. If an island's number is one less than its theoretical maximum, then every neighbor must receive at least one bridge. A corner "3" (max 4) must send at least one bridge to each of its two neighbors — you can place one bridge each way and only the second bridge's position remains open. An edge "5" (max 6) sends at least one bridge in all three directions. A center "7" (max 8) sends at least one everywhere. Placing these guaranteed single bridges early carves 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 is a "1", that neighbor can absorb at most one bridge — so the other two directions must supply at least four, which forces double bridges if those neighbors allow only two each. Whenever remaining demand equals 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 not decoration — it is a solving tool. No group of islands may become sealed off from the rest of the board. The classic case: two "1" islands adjacent to each other can never be joined, because that bridge would form a closed island pair. The same goes for a "2"–"2" pair connected by a double bridge when neither has other neighbors. On expert boards, watch for larger pockets: if placing a bridge would satisfy every island in a small cluster while cutting it off from everything else, that bridge is wrong — and its elimination often forces the correct one.

6. Blocking and lines of sight

Every bridge you place is also a wall: it blocks any perpendicular bridge from crossing its path. Expert solvers read this proactively. If an island on the far side of the board can only reach its required count through a corridor, any bridge that would seal that corridor is impossible. Before placing an optional-looking bridge, check what it cuts off — Hashi endgames are usually decided by who controls the corridors.

7. Parity and endgame counting

On the hardest boards, count globally. The sum of all island numbers is twice the number of bridges, so the total is always even — and regional sums must balance too. If a region of the board connects to the rest through a single corridor, the bridges through that corridor must carry exactly the imbalance between the region's internal demand and supply. When you're down to two candidate placements and both satisfy local numbers, the connectivity requirement (rule 5) breaks the tie: exactly one keeps the network whole.

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 — a well-formed Hashi never needs trial and error.

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.