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Single Combination

The most basic technique in Hashi is the "Single Combination" technique. In Hashi, the number of bridges leaving each island must be the same as the number written on the island, and there can be at most two bridges in each direction. The single combination technique states that if there is only one way in which an island can have the number of bridges stated, then this must be the way the island is linked to its neighbours. An example is given below:

In the above example, the '2' island highlighted in orange can only bridge to the '5' island, highlighted in red, as shown. There is therefore only one way the these bridges can be placed, as shown in blue. This is the simplest example of a Single Combination. The example below is somewhat less obvious:

In this case the '3' island, highlighted in orange, must bridge once to the '2' island below and twice to the '3' island left of it, as shown. The orange island can bridge to the '2' below it, and to the '3' to the left. Normally, it would be possible to bridge to the '2' island twice, but here the '2' island already has one bridge. So we can have at most one bridge from the '2' island. Because there is a maximum of 2 bridges in each direction, this means that the orange '3' island must have bridges placed as shown.

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