DonM wrote:Hi Luke- for the benefit of those who may not be familiar with URs, can you expound a bit on the UR exclusion.
Potential unique rectangles with bivalues catch my attention because if a strong link is involved, something good always happens. To cite
Havard from
HERE:With a Unique Rectangle with the numbers [ab] that has two cells with "extra candidates" ([xabx]), and these cells are on a diagonal from each other, and you have a strong link between any two of the cells in the Rectangle for candidate [a], then you can eliminate candidate [a] from the cell with extra candidates that is not part of the strong link.
In this case, there's a strong link on (1) in r3c24, and the "cell with extra candidates that is not part of the strong link" is r1c2.
Incidentally, if there are two strong links:
If a potential UR has bivalues on the diagonals and two strong links meeting in an "elbow' in one of the bivalue cells, after applying the above rule the strong candidate can be placed in the elbow.
If there are four strong links (x-wing):
If a potential UR has bivalues on the diagonals and one of the components forms an x-wing, then to quote Keith, "The diagonal pairs must have the x-wing component."
As for the other ones:
The x-wing overlay on 2 in r12c29 takes out the same candidate.
The x-wing overlay on 9 in r59c78 takes out the 4 in r9c8.
If there's an x-wing on one of the candidates and only one bivalue cell is involved, then the non-x-wing component on the diagonal of the bivalue cell can be eliminated. How's that for a mouthful.