Bridges

"In Hashiwokakero you are the king of the islands, and your job is to connect the islands."

This is a genuine Japanese puzzle, it appeared for the first time in a Japanese publication, in 1980. The Japanese name for this puzzle is Hashi o kakero, literally 'build bridges'. The puzzle is a rectangle containing islands (these are circles with numbers from 1-8). The objective is to connect all of the islands in a single connected group with bridges. The number of bridges connected to each island must correspond with the number on that island. Bridges must travel in a straight line between different islands; they must not cross any other bridges or islands. A maximum of two bridges can connect any pair of islands.

A few hints can be offered to solvers. It is important to remember that the objective is to create a single network of bridges; islands cannot be joined if, in doing so, a short circuit is created. (So, two islands containing a 1 cannot be joined, since if they are, no other bridges can be joined to them.) A island positioned in the corner with a 4, or along the border containing a 6, or anywhere containing an 8, will have two bridges from it in each direction. Determining the position of any bridge will eliminate other possible places for bridges. As options are narrowed, additional tips can be applied: for example, an island containing a 3 that can only be travelled from in a vertical direction must have at least one bridge in each direction, up and down. If the quota of bridges for an island has been met, it is a good idea to shade in the island, which effectively takes it out of consideration.