## Hashi (Bridges)

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In the game Hashi or Hashiwokakero (Bridges/Chopsticks or Let’s Build Bridges!), you are given islands and you have to build bridges north-south or east-west between them. You are told the total number of bridges attached to each island, and you can build at most two bridges between any pair of islands. The bridges can’t cross, and it must be possible at the end to go from any island to any other island via some combination of bridges.

In other words, you are given the vertices of a graph and you have to construct vertical or horizontal edges. You are told the degree of each vertex, and you can have up to two edges between each pair of vertices. The final graph is planar and connected. Sound like fun? Then try it out here!

There are several mathematical questions you can ask:  What is the greatest number of bridges emanating from a single island?  What are the greatest/fewest number of bridges you could have for a given number or configuration of islands?  A quick search didn’t reveal nearly as much published on the mathematics of Hashi compared to, say, Sudoku, so this might be a fruitful area for some fun research!

The photograph of the bridge over the Struma River in Bulgaria is copyrighted © Nikola Gruev and is published on Wikipedia Commons under the terms of the GNU Free Documentation License.

### 2 Responses to “Hashi (Bridges)”

1. Batman Says:

There are 10 online puzzles here (some of them are the same as the site listed above). For solving techniques, try the Indigo Puzzles help page. I’m completely hooked now – thanks!

2. Batman Says:

Even better: Vegard Hanssen’s page has thousands of puzzles of various sizes and difficulties.