Hashi, short for hashi o kakero (“build bridges”) is another logic puzzle invented by the Japanese puzzle company Nikoli. It first appeared in Nikoli’s magazine in December of 1989.  Like Sudoku, it is simple in construct, but can be very difficult to solve. There is no standard size for hashi, but typically the larger the puzzle, the trickier it is. The puzzle starts out with just the “islands” – numbers from 1 to 8 enclosed in little circles. The objective of hashi is to draw bridges to connect all the islands to one another following five rules:

1. A bridge is a straight line which connects two islands, and must emanate horizontally or vertically from an island (no diagonal lines allowed).

2. The number of bridges connected to an island must match the number on the island.

3. A pair of islands can be connected by one or two bridges, but not more. This is why the maximum number for an island is 8: there are four possible ports, which can each host two bridges.

4. Bridges cannot cross other bridges or islands.

5. All the islands have to be connected to each other in the end, through some series of bridges.

This may seem overwhelming, but considering the rules there are a few techniques that immediately present themselves as good starting places when doing this puzzle.

First, look for islands whose bridge placement possibilities are limited by their quantity of neighbors. For example, if an island only has one other island it can possibly connect to (see Figure 1), all of its bridges must connect to that island. Another instance might be if an island with 4 bridges is in the corner of the puzzle; then it must have two neighbors, with two bridges connecting it to each neighbor (Figure 2).  Finally, you might have a case where an island with 3 bridges has two neighbors (Figure 3).  In all the possibilities for bridge placement, you must have at least one bridge between the 3 island and each of its neighbors.

 

 

 

 

 

 

Next, look for cases which might violate the rule that all the islands must be connected.  For instance, if two 1 islands are next to one another, they cannot be connected without cutting them off from the rest of islands (Figure 4).  This can help cut down on bridge placement options.  In Figure 4, the 1 island must connect to island A since that’s its only other neighbor.

 

 

 

 

 

These are the basics to solving hashi puzzles.  They can be tricky to get the hang of, but with a little practice, one can start picking out the patterns pretty quickly.  I first learned of hashi puzzles through Games magazine, which was a monthly puzzle magazine.  Some of the puzzles cycled in and out of the magazine, but hashi appeared in almost every issue, and I was quickly addicted.  There is a great sense of completion in connecting the scattered islands, which, at first glance, seem patternless.  Below is a link to a website with free printable hashi puzzles.  Happy puzzling!

http://www.websudoku.com/?hashi

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Sources:

http://www.conceptispuzzles.com/index.aspx?uri=puzzle/hashi/rules