In Logic of Sudoku, Andrew Stuart describes a unique rectangle with only one bv corner. The tell-tale naked pair is not there. Stuart calls this formation a hidden UR, with good reason. You have to find the bv candidates in the three other corners. Once found, you then look for a slink pattern that guarantees that a deadly rectangle cannot appear.
With apologies for using yet another from The Logic of Sudoku, here is Andrew’s example:
As you complete your bv scan, you notice four cells in a rectangle in two boxes that contain numbers 6 and 9, but only one corner cell at the upper right is a bv. You then verify that the opposing corner cell at lower left is flanked by two slinks of a bv number, in this case, 6.
Now you can invoke Andrew’s hidden UR rule. Just remove the other bv number 9 from the opposing cell! Were this candidate to be true, as shown at left, the slinks force a deadly rectangle in the solution!
To this, I can add that Andrew’s rule is not the only way to find removals or confirmations in the hidden UR. The explicit marking of slinks makes the verification easy in this case, but, along with standard UR, hidden UR is actually a more general application of forcing chains. I recommend a quick trial on an extra presentation slide, followed by an accounting on the original slide, via a combination of slink, ER, or forcing chain. I will have more examples later.
In the next post, we will shamelessly plunder another topic in Logic, the avoidable UR, to close this series of posts on the unique rectangle.
Another mission coming up a series about Sudoku writers and their ideas. I’m starting with Tom Sheldon and his Sudoku Master Class, published in 2006, which became an accessible inspiration for me in 2009.
Your next UR lesson will be from his Apprentice section, #3. Tom tells his apprentices what to look for. In this case, it’s a unique rectangle.
Let’s start with box marking for the next post.
Oh, one more thing. We were working on a Tom Sheldon puzzle, weren’t we!? Did you
find the your way out of the deadly rectangle in Sudoku Master Class # 110? Its yet another UR possibility. The 2 in r5c5 is the only one in r5 and outside of the rectangle. If it goes away, the deadly rectangle will be forced via boxline! This candidate therefore has the leverage to demand promotion to clue, and when we grant it, #110 comes crashing down.
Yep, call it the Boxline UR.