How to solve Hashi

How to solve Hashi: techniques that work

Count neighbours before anything else. An island's number is spread across at most two bridges per neighbour, so an island showing 2k with exactly k neighbours must run a double bridge to every one of them: a corner 4 with two neighbours is fully forced, as is an edge 6 with three. These "saturated" islands are free moves — play them all first.

One step weaker but just as useful: an island whose number is 2k−1 with k neighbours must connect at least once to every neighbour. That single guaranteed bridge is often enough to block a crossing elsewhere and cascade into the next deduction.

Keep the network connected. All islands must end up in one web, so a bridge that would seal off a finished sub-network — say, a 1—1 pair on the edge linking only to each other — is illegal even if the numbers allow it. Late in a board, connectivity is usually the argument that decides the last few bridges.

Common mistakes

Forgetting that bridges block each other: a bridge is a wall for every perpendicular route. Players plan two bridges that cross and only notice when the second refuses to draw.

Overloading a pair. However large the numbers, two islands can share at most two bridges — an 8 next to an 8 still exchanges only a double bridge and needs other neighbours for the rest.

From easy to hard

More islands mean longer chains between forced moves. On hard boards alternate systematically: saturate the full islands, then run the connectivity check, then look for almost-saturated ones. Hashi (Hashiwokakero, "build bridges") rarely needs more than these three ideas.