Bridges – a daily Hashi logic puzzle

Bridges is a daily logic puzzle, the Japanese Hashi (Hashiwokakero): numbered islands sit on a grid, and you connect them with bridges. Each number tells you how many bridges leave that island.

Every day you get three boards: an easy one (7×7), a medium one (9×9) and a hard one (12×12). Each has exactly one solution, and each can be solved by pure logic, without guessing.

How to play

1. Drag from an island to a neighbour in the same row or column, or tap the two islands one after the other. The first move builds one bridge, the second a second one, the third removes them.
2. Tapping the water between two islands cycles the bridges too.
3. Two islands share at most two bridges, bridges run only horizontally or vertically, and they may never cross.
4. An island turns green when it has exactly as many bridges as its number, and red when it has more. The board is done when every number fits and all islands form one connected network.

Tips

• Start with the big numbers: an 8 needs two bridges in all four directions, and a 4 in a corner needs two in both.
• Never join a 1 to another 1: the pair would shut itself off and never reach the others.
• If an island has only one neighbour left, all its missing bridges go there.

Strategy

• Count the room an island has. A 3 with only two neighbours could fit four bridges at most, so at least one bridge goes to each of them. A 5 with three neighbours also gets at least one bridge in every direction.
• Watch the crossings. As soon as a bridge is built, every route that would cross it is gone, and the options of the nearby islands suddenly shrink.
• Think about the network. If a second bridge between two islands would close off a small group whose numbers are all complete but which is cut off from the rest, that second bridge cannot exist.
• On the hard board, when you are stuck, pick a doubtful bridge and think through what would happen if you built it. If the consequences lead to a contradiction, for example an island running out of room, you can be sure there is no bridge there.

A worked example

An invented example: a 4 sits in the top-left corner with one neighbour to the right and one below. Four bridges in two directions means two each way, so the 4 gets two double bridges and is already done.

The neighbour below is a 2: its two bridges are now used up, so nothing else can leave it. If a 1 stood to its right, that 1 has to find another neighbour, and that is the key to the next step.

History of the game

Hashiwokakero means "build bridges!" in Japanese. The puzzle was made popular in the early 1990s by the Japanese publisher Nikoli, the same publisher that made the name Sudoku famous worldwide. In English it spread as Bridges or simply Hashi.

The beauty of the game is how two kinds of thinking work together: the numbers call for local counting, but in the end the whole network must hang together, so sometimes a distant island decides what happens on the other side of the board.

Frequently asked questions

Is there always a solution?

Yes, exactly one. Every board is checked by a solver before it goes live.

Do I ever have to guess?

No. We only publish boards that can be solved with logic. The hard level includes steps where you have to think through what a bridge would lead to.

Why can't I build a bridge between two islands?

Most likely it would cross another bridge. Remove that one first, or find another route.

Every number fits, but it isn't solved. Why?

Not all islands are in one network: a group has been cut off somewhere. Find it and connect it to the rest.

What if I get stuck?

The Solution button (two taps) shows the answer. The level then ends, but it does not count as solved.