Help for Naked Sets

Naked Sets

A naked set is a group of 2, 3, 4, or 5 cells that occur in the same unit (row, column or box), which contain the same number of candidates. A naked triple, for example, has three cells having 3 candidates between them. If these contained, say, 123, 123, 123, then in the solved puzzle they could be one of 6 combinations: 123, 132, 213, 231, 312, 321, whereas if they contained 12, 13, 23 then there would be only two possibilities: 132, 213. When each of the possible combinations is used to initiate a forcing net, and those combination(s) causing a contradiction removed, then the remaining combinations can be re-combined. The resulting cells may have a reduced number of candidates.

In order to improve the power of the method, an extension is implemented which involves identifying all instances of two numbers in a row , column or box. Each number of the pair in turn is added to the naked set combination and as above, the forcing net generated. If a contradiction occurs in each case, and since one of the pair of numbers must be true, then the combination can be eliminated as above. The Easter Monster puzzle can be solved using this method following the SK loop eliminations.