Bridges, known more verbosely as Hashiwokakero, is a logic puzzle. Like many great logic puzzles, it was invented by Nikoli and published in Nikoli magazine (another similarity being the long, unpronounceable name).
Circles represent cities and lines represent bridges. The task here is simple: bridge all cities together so that no bridges overlap, and so that there are no separate groups. All cities must be connected and part of the same network.
The catch is those numbers inside the circles. Each number indicates how many bridges must connect to that particular city. For instance, a circle containing the number one would only have a single bridge leading out of it, connecting it to one other city. A circle with the number two would have two bridges, and so forth.
Since bridges must be straight lines, there could be up to four other cities to connect, depending on the direction the bridge is going, and whether there is even another city in that direction. A circle with a number four is simple to solve; it has four bridges connecting it to each of the nearest cities in every direction (north, south, east, and west).
Where it gets a bit tricky is when you realize that the numbers go above four. Here’s the kicker: double bridges are possible, and often required in the correct solution, especially for harder puzzles. These are simply wider bridges that count as two bridges, but still only connect the same two cities as a single bridge would.
The best way to solve Bridges puzzles is to start with the easy deductions, and work outward from those. If a city marked two (having only two bridges) only has two cities it can connect to, then connect those first. Keep in mind it might only have a double-bridge to one of those cities, rather than two single bridges, one to each city.
The first round of these easier connections may block off others and help you solve some of the more difficult ones. Remember, bridges cannot cross each other, and they must always be straight lines.
In the Simon Tatham version of this puzzle, you can simply click on one city and drag in one of the four directions to create a bridge. Do it again, and it will create a double bridge. A third attempt will create a third bridge. Drag across once more, and all the bridges will disappear, if something needed changed or redone.
It is also available on BrainBashers. Enjoy bridging the gaps in this fascinating puzzle!