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Forbidden Combinations

To recap, the rules of hashi are that each island must have the number of bridges written on it, there can be at most 2 in any direction, and all islands must be interlinked in the solution. The techniques we've looked at so far use the first part of this, but there is another type of technique based on the second part: all islands must be interlinked. The forbidden combinations technique is an easy-to-spot special case. Obviously, if all islands must be linked, then we can't create a self-contained group of completed islands (a continent). There are certain combinations of bridges between islands which will create such a continent that are easy to spot. For example, a '1' cannot bridge to a '1', because they would then form a disconnected continent. Similarly, a '2' can't bridge twice to a '2'. Here is an example:

The orange '2' must bridge to the '2's highlighted in red, either side of it, as shown. This is because the other options would lead to a forbidden combination, in this case 2==2. Here is another example:

Here, the orange '3' must bridge to both of the red '2's. If it didn't, then it would have to double bridge to one or the other of them, creating a continent. Here is a list of some common forbidden combinations ('--' represents a single link, '==' represents a double link):

• 1--1
• 2==2
• 1--2--1
• 1--3==2
• 2==4==2

Copyright © Adam A. Brown, 2006. www.sudokutiger.com