Daily Hashi

Island counts are necessary but not sufficient

The number inside an island is its final degree: a 3 needs exactly three bridges in total. A pair of aligned islands may carry one or two bridges, but bridges cannot run diagonally or cross another line.

The interface helps with local arithmetic. A satisfied island turns green and an overfilled one turns red. Those colors do not prove the whole puzzle is valid, because several green islands can still form a closed group disconnected from the rest of the board.

Start with capacity constraints

An island near an edge or corner has fewer available neighbors. Compare its required count with the maximum bridges those neighbors can accept. A high number with only two possible neighbors often forces at least one double bridge; a 1 can eliminate every alternative once one connection is fixed.

Before completing a small cluster, check whether it still has a route to the remaining islands. Connectivity is easiest to preserve early and difficult to repair after nearby counts have already been saturated.

A practical network-first method

1. Mark islands whose bridge count nearly equals their available capacity.
2. Add forced single or double bridges without crossing existing lines.
3. Recalculate the remaining count for both endpoints after every connection.
4. Avoid sealing a subgroup unless it already includes every island.
5. Use undo when a later island has no legal route, rather than overfilling a neighbor.

Bridges is the closest alternative because it uses the same Hashiwokakero rules with unlimited boards. Daily Akari keeps the low-language grid deduction but replaces network construction with a light-placement coverage problem.