How to play Hashi (Bridges)

The rules

Hashi (short for Hashiwokakero, and also known as Bridges) is played on a grid of numbered islands. Join them with bridges so that:

• each island has exactly as many bridges as its number;
• bridges run in straight lines across or down, between two islands;
• at most two bridges join the same pair of islands;
• bridges never cross each other or pass over an island;
• when you finish, every island is connected into one group.

1. Islands with no choice

Count how many neighbours an island can reach, and remember each can take at most two bridges. A 4 in a corner can only reach two islands, so it needs a double bridge to each. An 8 needs double bridges in all four directions.

2. At least one bridge each way

The same counting gives partial answers. A 3 with only two neighbours can't put all three bridges to one of them (the limit is two), so it must have at least one bridge to each. Draw those single bridges in now. A 5 with three neighbours, or a 7 with four, works the same way.

3. Don't cut anyone off

Because everything must end up connected, some bridges are impossible. Two 1s can never join each other: they would form a closed pair with nowhere else to go. Likewise two 2s can never be joined by a double bridge.

4. Use crossings

Once a bridge is drawn, no other bridge can cross it. That often leaves a nearby island with fewer neighbours than before, and the counting in step 1 kicks in again.

A good routine

1. Draw the bridges forced by counting (corners, edges, 8s, 7s).
2. Add the “at least one” singles.
3. Cross out bridges that would isolate islands or cross existing ones.
4. Repeat: each bridge you add changes what the neighbours can do.