The New Sudoku Players' Forum

[kurbads]

I've got this rectangle with 5s and 8s and a 5 outside which must be 5 to avoid deadly pattern (multiple solutions), have I?



1..|.23|.97
.6.|.1.|...
...|..8|...
---+---+---
89.|...|5..
57.|...|.69
..2|...|.48
---+---+---
...|6..|...
...|.3.|.8.
71.|58.|..6

Also because after this R7C23 must be 2 or 3, and R7C1 is 2 or 3 only, it makes hidden naked pair and makes the R7C9 - 5!

[Leren]

Yes, that's correct. Its called a Unique Rectangle type 3. Alternatively you can make life a bit easier as follows.

Code: Select all

*--------------------------------------*
| 1    *58   *58  | 4  2 3 | 6  9  7   |
| 2349  6    #379 | 79 1 5 | 8  23 34  |
| 2349  24   #379 | 79 6 8 | 12 5  134 |
|-----------------+--------+-----------|
| 8     9     4   | 3  7 6 | 5  1  2   |
| 5     7     1   | 8  4 2 | 3  6  9   |
| 6     3     2   | 1  5 9 | 7  4  8   |
|-----------------+--------+-----------|
| 23   *2-58 *58-3| 6  9 1 | 4  7  35  |
| 49    45    6   | 2  3 7 | 19 8  15  |
| 7     1    #39  | 5  8 4 | 29 23 6   |
*--------------------------------------*

You can first remove the 3 from r7c3 via the naked triple 379 in r239c3. You are then left with a Unique Rectangle Type 1 in the 4 cells marked * and remove 58 from r7c2. For brevity I've shown both moves in the same PM.

Leren

[RSW]

The unique rectangle is of multiple types, and gives a number of different eliminations:

Code: Select all

 +-----------------+--------+----------------+
 | 1    58    58   | 4  2 3 | 6   9    7     |
 | 2349 6     379  | 79 1 5 | 8   23   234   |
 | 2349 245   3579 | 79 6 8 | 124 1235 12345 |
 +-----------------+--------+----------------+
 | 8    9     4    | 3  7 6 | 5   12   12    |
 | 5    7     1    | 8  4 2 | 3   6    9     |
 | 6    3     2    | 1  5 9 | 7   4    8     |
 +-----------------+--------+----------------+
 | 234  248-5 38-5 | 6  9 1 | 24  7    5-234 |
 | 49   5-4   6    | 2  3 7 | 149 8    145   |
 | 7    1     39   | 5  8 4 | 29  23   6     |
 +-----------------+--------+----------------+


One of the peculiarities of UR's is that they tend to disappear as you make eliminations. So, it's often beneficial to analyze all possibilities before making any eliminations. Doing this, we get:
1. Unique Rectangle (5/8)r17c23 UR+2≠ (type 3) with UR+ in rows forms a locked set with 234r7c17 => -234r7c9
2. Unique Rectangle (5/8)r17c23 UR+2≠ (type 3) with UR+ in common block forms a locked set with (2349)b7p149 => -4r8c2
3. Unique Rectangle (5/8)r17c23 UR+2/1CL (type 4): bilocal digit 8 (row 7) => -5r7c23
4. Unique Rectangle (5/8)r17c23 UR+2/1CL (type 4 variant 1): bilocal digit 8 (column 2) => -5r7c3

Some of the above eliminations may be redundant. For example, the elimination from No. 4 is already taken care of by No. 3.
In total there are 6 eliminations from this UR.

Edit: Should also mention that there are two other UR's in this puzzle that give eliminations:
(7/9)r23c34 => -3r9c3 -5r3c2 -9r23c3
(1/2)r34c89 => -2r3c9