I use this blog as a soap box to preach (ahem... to talk :-) about subjects that interest me.

Monday, March 7, 2011

KenKen - One more case

Here is one more interesting strategy I discovered when solving one of my CleverClever puzzles.

The four-cell cage on the right shows all possible candidates of each cell. We can discard the 1 of (5,8) because the sum must be even and the three other cells only have even candidates. Then, as the 1 of row 5 can only be in (5,1), we can remove all other candidates from that cell and the corresponding candidates in the other cell of the cage.

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.

Saturday, March 5, 2011

KenKen Strategies

Most of the strategies used to solve Sudoku rely on the interplay of boxes and lines. Therefore, it is not surprising that they are not transferable to KenKen® (registered trademark of Nextoy LLC).