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Sunday, March 6, 2011

KenKen - A non-trivial case

Solving one of my CleverClever puzzles, I encountered the following configuration:

Suppose that the 112x cage is solved by the combination [8 7 2 1]. Then, the 8 must be in (7,5), because there is already an 8 in either (3,6) or (4,6). But if that is the case, then the remaining three cells of the cage, all in column 6, must contain 7, 2, and 1. This leads to a contradiction, because it would force us to remove the 1s in (2,6) and (8,6), thereby leaving both cells with a 9 as the only possible candidate. Therefore, the 112x cage must be solved with [7 4 2 2] (which, incidentally, means that (7,5) must contain a 2).

I don’t have a name for this strategy, but it is a nice example of a technique that does not (and cannot) occur in Sudoku.

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