How to solve Hashi

This guide starts with the rules, then shows the moves that are always safe, and works up to the tricks that crack Hard and Expert puzzles. There is no guessing needed in solving any of these puzzles!

In the pictures, blue bridges are the ones the tip lets you place, a blue ring marks the island to look at, and ✕ marks a gap that can't take a bridge. A grid that fades out means the board goes on that way.

The rules

Circles are called islands. Its number says how many bridges it needs.
Bridges run straight across or down, between two islands with nothing in between.
There can be 1 or 2 bridges between islands.
Bridges never cross each other or pass over an island.
When you're done, every island has exactly its number, and all of them are joined into one group.

A solved puzzle. Every island has its number, crossed out when full, and you can walk from any island to any other.

The first moves

Only one way to go

An island with a single neighbour left gets all its remaining bridges from it. Look for these along the edges and next to finished islands.

Nowhere else to go.

Only one way to fill all bridges

An island can take at most two bridges from each neighbour. When its a 4 in a corner, a 6 on an edge, an 8 anywhere there is only one way to fill.

One short of everything

When the number is one less than that, it still needs at least one bridge to every neighbour: with one missing anywhere, the others couldn't make up the difference. That's a 3 in a corner, a 5 on an edge and a 7 in the open.

A 3 in a corner must connect to both neighbors. Usually this is a good way of starting an easy puzzle.

A 5 on an edge needs all 3 neighbors.

Keeping everything connected

The last rule, one group, is the source of some of the best tricks.

Two 1s never join

A bridge between two 1s would finish both, cutting them off from the rest of the board. The same goes for a double bridge between two 2s.

Not to the other 1, so down.

At most one to the other 2, so at least one down.

Don't close off a group

The same idea works for bigger groups. Before finishing a set of islands, check that something in it still reaches the rest of the board.

Joining the 3 to the 1 would finish all three and cut them off, so its last bridge goes right.

When you're stuck

Try it and see

When no simple move is left, pick a gap and ask what if it had a bridge. Follow the sure moves from there. If you reach an island that can't be satisfied, or a group that gets cut off, the guess was wrong: that gap takes no bridge, and you've learned something for sure.

The hardest puzzles need this more than once. Bookmark the position before you try, so you can come back to it.

General habits

Start with the big numbers and the corners and edges: they have the fewest choices.
After every bridge, look again at its two islands and their neighbours. One move usually leads to the next.
Late in the puzzle, think about connections: which groups still need to reach each other, and through which gaps.