How to play Bridges

Bridges is a logic puzzle about building a network. Islands are scattered on a grid of water, each with a number. You draw bridges between them so that every island has exactly as many bridges as its number says, no bridges cross, and in the end every island can be reached from every other. The puzzle is sometimes called Hashi.

Every puzzle here is generated fresh by the game when you start it, has exactly one solution, and can be solved by reasoning alone. You never need to guess. The four levels grow from about ten islands on Easy to more than thirty on Crazy, and each level asks for deeper reasoning than the one before.

How to play on skill.games

When you open the game, the settings popup appears. Choose a level under DIFFICULTY, choose how mistakes are treated under MISTAKES, and press PLAY. A new puzzle is generated in a moment.

• The board shows the islands as round discs with their numbers, over a sea marked with faint dots where islands could stand. On a screen that is wider than it is tall, the board is turned a quarter to make it bigger.
• Building a bridge: drag from an island towards one of its neighbours and let go. You can also tap the water between two islands, or tap one island and then its neighbour. Each time you do this for the same pair, it goes from no bridge to one bridge, to two bridges, and back to none.
• Choosing an island: a tap on an island highlights it and shows dotted guides to the neighbours it can reach. Tap a neighbour to add a bridge (tap it again for a second one), or tap the highlighted island again to let go.
• Crossings: a bridge can't cross another bridge. If one is in the way, the game refuses and the blocked path flashes red.
• UNDO (under the board, or beside it on a wide screen) takes back your last change, all the way back to the start. Undo is free and unlimited.
• Finished islands turn green when they have exactly their number of bridges. An island with too many turns red, with its number underlined. A group of finished islands that is cut off from the rest gets a dashed red ring, because it can never join the others.

The game waits a moment before it checks a change, so cycling through two bridges to clear a pair never counts against you. A change is checked as soon as you work on a different pair, or about a second after your last tap on it.

The top line shows the clock, the level, the board size and your mistakes. The clock runs only while you play: it stops when the menu or a popup is open. The menu button in the top-left corner pauses the game, starts a new puzzle or switches the sound on or off. On a computer, Z undoes and Escape lets go of a highlighted island. The game is saved after every move, so if you close the page you can press CONTINUE later and carry on with the same bridges, clock and undo history.

When the last bridge is in place, the islands light up and the results screen shows your time, your best time at that level (a star marks a new record), your mistakes, the board size and the puzzle's code, together with your wins, losses, win rate and streaks.

Rules

Bridges. A bridge runs straight along a row or a column between two islands, over open water. It can't pass over another island, and it can't bend.

One or two. Two islands can be joined by a single bridge or a double bridge, never more.

Numbers. Every island ends up with exactly as many bridges as its number. A double bridge counts as two.

No crossings. Bridges never cross each other.

All connected. When the puzzle is finished, every island must be reachable from every other one along bridges.

Mistakes - Unlimited (the default). When a change leaves an island with more bridges than its number, or closes off a finished group from the rest, it is drawn in red and the mistakes counter goes up by one. Nothing else is checked, so nothing about the solution is revealed. Because the solution is unique, a board where every island is green and everything is joined is always the right one.

Mistakes - 3 lives. Every change is checked against the solution once it settles. A bridge that shouldn't be there costs a life: the pair is set to the right number of bridges, drawn in red and locked (a red cross on the water if there should be no bridge at all). The third mistake ends the game and counts as a loss.

Abandoned puzzles. Starting a new puzzle before finishing the current one counts as a loss in your statistics for that level.

Solving techniques

These are the methods the game's own solver uses to grade every puzzle, from the simplest up.

• Filling up: compare an island's number with what its neighbours can take. A 4 in a corner with two neighbours needs two double bridges; a 3 with only two neighbours needs at least one bridge to each; an 8 is joined to all four neighbours by doubles. A finished island takes no more bridges.
• Blocking: once a bridge is certain, no bridge can cross it, so the islands on either side lose that direction.
• Isolation of pairs: two 1s next to each other can't be joined - they would form a little group of two that could never reach the rest. Likewise two 2s can't be joined by a double bridge.
• Connectivity: more generally, no bridge may finish off a whole group of islands while others are still outside it. And a group of joined islands with only one way out must use that way.
• Island analysis: list every way to finish one island and test each against its neighbours (can they still reach their numbers?), the bridges it would block, and the groups it would close off. Whatever all the surviving ways have in common is settled.

Strategy tips

• Start with the big numbers and the corners. An island whose number is twice its number of neighbours is completely decided at once.
• Look for islands with one neighbour. A 1 or a 2 with a single neighbour has nowhere else to go.
• Count what's left. As bridges go in, recompute what each island still needs and what its open directions can still give.
• Think about the whole network. Before finishing a small cluster, check that it still connects to the rest. The isolation rule decides many puzzles.
• Use the blockers. A long bridge across the middle cuts the board in two and removes options on both sides.
• Don't guess. Every puzzle here can be solved by logic. If you feel stuck, pick an island and list the ways it could still be finished.

Difficulty levels

The game generates every puzzle on the spot and grades it with a solver that works the way a person does, always using the easiest step available. A puzzle is given to you only if its hardest required step matches the level you chose.

• Easy: a board up to 7x7 with about ten islands; filling up and blocking are all you need.
• Normal: a board up to 8x10 with about seventeen islands; at least one step needs the isolation of pairs.
• Hard: a board up to 9x12 with about two dozen islands; at least one step needs connectivity.
• Crazy: a board up to 10x14 with more than thirty islands; at least one step needs island analysis.

Statistics and best times are kept separately for each level. If Bridges is new to you, start on Easy and move up once the corners and the big numbers start solving themselves.