Why critter islands?

In most bridges puzzles the islands are plain circles with numbers. You join them up, the last bridge goes down, and that’s it. We like the puzzle a lot, but we wanted a reason to care about each island along the way.

So every island here has a small critter on it: a turtle, a crab, a penguin, an otter and a dozen more. The number is how many bridges that critter is waiting for. When an island has exactly the right count, its critter waves. When every island is joined, a little ferry sets off along your bridges and visits each one in turn, and the critters wave again as it passes. On a big map, the waving also shows at a glance which islands are done.

A bit of real bridges puzzle history

The bridges puzzle comes from Nikoli, the Japanese puzzle publisher. Its Japanese name is Hashiwokakero, which means “build bridges!” It first appeared in Nikoli’s magazine, Puzzle Communication Nikoli, in issue 31 in September 1990. An earlier version had run in issue 28, in December 1989.

The idea came from a reader, not the staff. Japanese sources credit a contributor who sent it in under a pen name. The same person also created nurikabe, another Nikoli favorite, which first ran in 1991.

In English the puzzle is usually called Bridges or Hashi, and The Times in Britain has printed it as Hashi. It is sometimes called Chopsticks too, from a mix-up: hashi written with one character means bridge, and written with another it means chopsticks. In 2009 a computer scientist, Daniel Andersson, proved that deciding whether a bridges puzzle can be solved is NP-complete. In plain words, nobody knows a method that stays fast on every board as the boards get very large.

Three seas

• Lagoon, 7×7: 15 small maps with 5 to 14 islands. Puzzle 1 has just five.
• Harbor, 10×10: 15 maps with 13 to 23 islands.
• Open Sea, 13×13: 15 big maps with 24 to 42 islands. The last few ask you to think a few moves ahead.

A small program made every map from a numbered seed. A solver then checked that each one has exactly one answer and measured how much work it takes, and the maps run from least work to most.

How to play

• Each island’s number is how many bridges must touch it.
• Drag from an island to its neighbor to build a bridge. Drag again for a double bridge, and once more to take it away.
• You can also tap one island, then the other, or tap the water between them. On a keyboard, the arrows move between islands and Shift with an arrow builds.
• Bridges go straight across or straight up and down. They can’t cross each other, and two islands share at most two bridges.
• All the islands must end up joined in one group, so the ferry can reach every one.
• Undo takes back your last move. Check shows wrong bridges but costs a star. No checks earns 3 stars, and you never get fewer than 1.
• Solve a puzzle to open the next two. Your stars save on this device.
• Sound is on to start. Tap 🔊 to mute, or 🎵 for music.
• Earn 3 stickers in this game for your QuickBOP sticker book.

Tips

Start with the full islands. A 4 in a corner has only two neighbors, so it needs a double bridge to both. A 6 with three neighbors, or an 8 with four, works the same way.

Count what’s left. A 3 with only two neighbors must get at least one bridge to each, because two bridges to one side are not enough.

Don’t close off a group. Two islands marked 1 can never join each other, because that pair would be cut off from everyone else. The same goes for two 2s joined by a double bridge.

Use Undo freely. Try an idea, and if it goes wrong, step back. Undo costs nothing, and Check is there when you’re stuck.

Your turn

Five islands are waiting in the first lagoon. Build your first bridge and see who waves.