I checked this to see if my solver would find it.
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+------------+---------------+------------------+
| 8 23 23 | 4569 456 69 | 56 7 1 |
| 4 6 5 | 1 3 7 | 2 9 8 |
| 9 7 1 | 256 256 8 | 356 4 35 |
+------------+---------------+------------------+
| 6 123 234 | 7 8 39 | 13459 135 23459 |
| 13 8 9 | 456 1456 2 | 7 16 34 |
| 7 5 234 | 469 146 369 | 8 136 2349 |
+------------+---------------+------------------+
| 5 13 8 | 26 267 4 | 19 23 79 |
| 12 9 6 | 3 27 15 | 145 8 457 |
| 23 4 7 | 8 9 15 | 135 1235 6 |
+------------+---------------+------------------+
Possible eliminations:
Unique Rectangle UR+2/1SL (type 4 variant 1): (23)r14c23, bilocal digit 2 (row 1) => -3r4c3
Unique Rectangle UR+3/3SL Subtype K: (69)r16c46 => -6r1c4
Unique Rectangle UR+3/3SL Subtype K: (26)r37c45 => -6r3c4
Unique Rectangle UR+3/2SL Subtype B: (16)r56c58 => -6r6c5
Unique Rectangle UR+3/3SL Subtype F: (16)r56c58 => -6r56c5
My solver finds it as a both a subtype B or F (UR +3 extra candidate cells with 3 strong links)
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ab abX
|
a| UR+3/2SL Subtype B: eliminate b from lower right cell
a |
abY-----abZ
ab-----abX
a |
b| UR+3/3SL Subtype F: eliminate a from lower left and lower right cells
b |
abY-----abZ
The subtype designation letters used here are non standard, but I added them to the solver in order to keep track of the different variations. They run from A to T.
There's discussion of various other types of UR's here:
post26448.html#p26448post28313.html#p28313---------------------------------------------
Edit:
Looking at Andrews Hidden Rectangle page, it appears that he hasn't covered all possible types. In addition to the references I posted above, I overlooked an important one by David P. Bird:
unique-rectangles-gallery-t33752.htmlIn going through all of these resources, I ended up compiling my own list of conjugate link patterns for UR+3 and UR+4 types and worked my way through the logic in order to understand the eliminations. Excluding rotations and reflections, the following patterns are what I came up with (nCL notation refers to number of conjugate links):
UR+3 patterns:
UR+3/1CL - 2 distinct patterns, none of which yield direct eliminations in UR cells;
UR+3/2CL - 8 distinct patterns, 5 of which yield direct eliminations in UR cells;
UR+3/3CL - 8 distinct patterns, all of which yield direct eliminations in UR cells;
UR+3/4CL - 5 distinct patterns*, 5 of which of which yield direct eliminations in UR cells .
* There is a 6th UR+3/4CL pattern which can never occur because all options are contradictory.
UR+4 patterns:
UR+4/1CL - 1 distinct pattern which yields no direct eliminations in UR cells;
UR+4/2CL - 2 distinct patterns, neither of which yield direct eliminations in UR cells;
UR+4/3CL - 3 distinct patterns, 2 of which yield direct eliminations in UR cells;
UR+4/4CL - 4 distinct patterns, 2 of which yield direct eliminations in UR cells.
Note that some of the patterns may yield eliminations in external cells or may yield eliminations in the UR cells when applied in combination with external strong links. I haven't checked for those cases.
BTW, here's a rather interesting superimposed (double?) UR+4 that my solver caught in a recent puzzle by Mith:
the-descent-t38214.html000800000009076000001000540020000003030450020400032010056000100000780000000009008
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+-------------------+-----------------+-------------------+
| 23567 467 23457 | 8 1249 1345 | 23679 3679 12679 |
| 2358 48 9 | 1235 7 6 | 238 38 12 |
| 23678 678 1 | 239 29 3 | 5 4 2679 |
+-------------------+-----------------+-------------------+
| 156789 2 578 | 169 169 178 | 46789 56789 3 |
| 16789 3 78 | 4 5 178 | 6789 2 679 |
| 4 6789 578 | 69 3 2 | 6789 1 5679 |
+-------------------+-----------------+-------------------+
| 23789 5 6 | 23 24 34 | 1 379 2479 |
| 1239 149 234 | 7 8 1345 | 23469 3569 24569 |
| 1237 147 2347 | 12356 1246 9 | 23467 3567 8 |
+-------------------+-----------------+-------------------+
Superimposed Unique Rectangles (17|18)r45c16:
(17)r45c16 UR+4/3CL Subtype B (aab-) => -7r5c1
(18)r45c16 UR+4/3CL Subtype B (aab-) => -8r5c1