How to Solve Hashi (Bridges) Puzzles: Rules & Techniques
Hashi — short for Hashiwokakero, "build bridges" — is the puzzle that turns arithmetic into an archipelago. Numbered islands must be joined by horizontal and vertical bridges: at most two per pair, no crossings, every island's number met exactly, and the whole map connected into one network. It's pure counting logic, and every board on our free Hashi is verified to fall to the techniques below — no guessing required.
The rules in thirty seconds
- Bridges run straight between two islands with a clear line of sight — horizontal or vertical only.
- At most two bridges between the same pair of islands.
- Bridges may never cross other bridges or pass through islands.
- Each island's number = exactly how many bridges touch it (1–8).
- Everything must end up in one connected network.
1. Start where capacity is maxed
Some islands are forced before you draw a single line. Count an island's neighbors and remember each can take at most 2 bridges:
- A corner island can see at most 2 neighbors — so a corner 4 is two doubles, done.
- An edge island sees at most 3 — an edge 6 is three doubles.
- An interior 8 is four doubles, all directions.
Slightly weaker but just as useful: a corner 3 must have at least one bridge in each direction (2+2 capacity minus the 3 leaves no direction empty). This "half forced" reasoning fills boards fast.
2. The all-but-one rule (the workhorse)
For any island: if skipping one neighbor leaves the others' combined capacity short of the island's number, at least one bridge to that neighbor is forced. Formally: needed − (total capacity − this neighbor's capacity) > 0 ⇒ that many bridges are guaranteed. It sounds abstract; in play it's "this 5 has neighbors worth 2+2+1 — drop the 1 and I only reach 4, so the 1 gets a bridge." Our in-game hint system spells out exactly this count when you ask.
3. Every bridge changes the map
Bridges block sight lines. The moment you draw one, islands that used to see each other across that corridor no longer do — which shrinks capacities — and neighbors that reached their number drop out of everyone's counts. After every placement, recount the islands around it; forced moves cascade in chains of three and four.
4. Don't strand a pocket
The connectivity rule has a sharp local edge: joining two 1-islands to each other seals them off from the world — illegal. Same for a pair of 2s taking a double bridge between them (unless they're the entire puzzle). Generalized: never complete a small group's numbers if it would close the group off; some link must stay open to the rest of the map. This rule mostly removes options, which in Hashi is exactly what a deduction is.
5. Endgame: connectivity finishes the job
Late boards often reach "all numbers satisfied except two islands with one bridge missing each". If connecting them directly is legal, that's your answer; if not, some earlier double should have been a single along a different route — undo locally and re-route. On our boards the counting rules alone always suffice, but reading the network's shape gets you there faster.
Common mistakes
- Treating numbers as minimums. They're exact — an island with too many bridges is broken, and our board will outline it in red.
- Forgetting bridges block sight. The pair you're counting on may no longer see each other after that last placement.
- Ignoring the doubles limit. Two per pair, full stop — an 8 can't take three from one side.
- Leaving connectivity for "later". The isolation rule is a live constraint from move one, not an endgame check.
Play free unlimited Hashi — three board sizes, a shared daily with streaks, teaching hints and the no-guess guarantee. Enjoy connection puzzles? Pipes has you rotating a plumbing network into one leak-free tree, and Akari lights rooms with the same flavor of counting.