Hashi

Hashi Instructions:
Here's how to play Hashi:
Hashi, also known as bridges, is a puzzle type that requires one to make connections.

The puzzle is presented as a series of numbers in circles... these represent islands. One must create bridges (straight lines that are either horizontal or vertical) between pairs of islands in such a way that each island ends up with the number of bridges into/out of it as the number inside it.

Thus a '2' island must have two bridges in/out. There cannot be more than two bridges between any 2 islands. Additionally bridges cannot cross over each other. Once complete, there must be a route from any island to any other island in the puzzle by means of walking over the bridges.

Building Bridges, One By One

Hashi is a Japanese logic puzzle, and the full name for it is hashiwokakero.

In the West it is often published under the name of bridges, although by 'often' one must not assume it is commonly seen, because it tends only to be published in puzzle magazines and does not appear in too many other places.

As outlined in the instructions, the aim is simply to connect all the islands together in such a way as to satisfy the number of bridges between each island, whilst within the constraints that there are no more than two bridges between islands, that bridges must be horizontal or vertical and that no bridges can cross over other bridges.

A lot of the interest for this puzzle type comes from the fact that it must be possible to walk from any island to any other island in the finished puzzle by means of the bridges. This introduces isolation logic, and it is often this that will help one to solve the puzzle.

For instance, it may be that the final bridge for an island could go to two other islands. At times however one can use isolation to work out which: if the bridge went to option a then that might create a closed set of islands away from the main group, and in that instance you will know it must connect the other way.

Hashi puzzles have only one solution that can be reached by logic alone. There are various solving rules that can be used. The most common way to get started is to find islands that must have certain bridges no matter what their final configuration.

The easiest to place would be an '8' which is the maximum bridges an island can have: two in each of the four allowed directions, so these can be marked in straight away. Similarly with 4's at the corners or 6's along the edges. The isolation rule is useful with islands that only have one bridge: clearly two 1 islands can't connect to each other since if they did they would be an isolated pair of islands.

It is useful to cross-off an island once you have placed all the bridges for it whilst solving the hashi puzzle to stop oneself from accidentally connecting more bridges to it further along the solve path.

Hashi puzzles come at a range of grid sizes, and size to some extent determines the difficulty of the puzzle, though other constraints such as whether the solver must take into account isolation also come into play.

Related puzzles

Fillomino, Hidoku, Kakuro, Nonogram

Last updated: 17 Feb 2012

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Sample solution:
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