dailysudoku.com

[keith]

This is not new. It came up about five years ago, then disappeared. Here is the original discussion:

http://forum.enjoysudoku.com/type-3-unique-rectangles-hidden-subsets-t4088.html

We are probably all familiar with Unique Rectangles. Types 1 and 2 involve only cells in the UR, and are pretty straightforward. Type 5 (never seen in a useful way, in my book) is a diagonal Type 1. (Like the Loch Ness monster, some claim to have seen it.)

Types 4 and 6 involve not only the four cells in the UR, but also conjugate constraints on the deadly pattern candidates. Let's put those aside.

Which leaves the Type 3 UR:

[Asellus]

The elimination is easy to see if the inferences are made explicit:
(1=3)r5c4 - UR[(3)r4c5=(4)r6c5]; r6c5<>1

As ones list of memorized pattern types becomes longer, I believe that at some point it becomes easier to work directly with the induced inferences. It is also more powerful since useful cases are not constrained to recognized patterns.

For those with such pattern-based arsenals it is a good one, especially if the reason for the elimination is not otherwise readily obvious.

[daj95376]

In the EnjoySudoku forum, the topic of Mike Barker's UR types was very recently revived. (here)

In fact, ronk opened the new discussions with MB's UR+2kx -- which your pattern falls under. Since I'm not always successful in deciphering MB's type descriptions, I'm not suggesting that we use them here.

I agree with Asellus' statement, "I believe that at some point it becomes easier to work directly with the induced inferences".

I've programmed my solver for the standard UR Types 1-6 and added an expanded capability to handle some eliminations based on specific strong links being present. I've even considered expanding that logic to include ALS/Subsets.

The elimination using an ALS/Subset in conjunction with the UR constaint:

(1)r6c5 - (13)r5c4,r4c5 = UR[(2)r4c5 - (2=1)r4c2 - (1=2)r6c2 - (1)r6c5]

Note: if you move <13> from r5c4 to any of r6c46, then you can eliminate <12> from r6c5.

[keith]

[ronk]

[keith]