## Unique Rectangle rule does not work (my mistake)

Post the puzzle or solving technique that's causing you trouble and someone will help

### Unique Rectangle rule does not work (my mistake)

Today's Brain Bashers "super hard" sudoku APPEARS (at first) to be invalid. I get to the following point (see export below), where there appears to be a unique rectangle at R2C3, R2C5, R4C3, & R4C5. By the rule of the Unique Rectangle, R4C5 should be "3" but it is not (to be proven later). This leaves the four squares above to all contain the values 1&2, which leaves two possible solutions to the puzzle.
However, the puzzle DOES only have one solution, due to the XY wing created by R6C5, R2C5, & R5C6, which eliminates the "1" from R4C5 (and solves the puzzle).
So, although the puzzle is valid, the rule of the unique rectangle is WRONG in this case.

Here is my export:
Style 1
-------
.935.6.2.47.3.9586..6...9..94.8.5.67......8.93689.7.15.....8...63.4.2158.8.1.3.9.

Style 2
-------
.935.6.2.
47.3.9586
..6...9..
94.8.5.67
......8.9
3689.7.15
.....8...
63.4.2158
.8.1.3.9.

Style 3
-------
. 9 3 | 5 . 6 | . 2 .
4 7 . | 3 . 9 | 5 8 6
. . 6 | . . . | 9 . .
-------+-------+------
9 4 . | 8 . 5 | . 6 7
. . . | . . . | 8 . 9
3 6 8 | 9 . 7 | . 1 5
-------+-------+------
. . . | . . 8 | . . .
6 3 . | 4 . 2 | 1 5 8
. 8 . | 1 . 3 | . 9 .
Last edited by Jaremy on Wed May 10, 2006 10:29 am, edited 1 time in total.
Jaremy

Posts: 2
Joined: 10 May 2006

Jaremy wrote:unique rectangle at R2C3, R2C5, R4C3, & R4C5

In a unique rectangle the four cells must appear in only in 2 rows, 2 columns and 2 boxes. Your rectangle is not a UR, because it's spread over 4 boxes.

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

RW wrote:
Jaremy wrote:unique rectangle at R2C3, R2C5, R4C3, & R4C5

In a unique rectangle the four cells must appear in only in 2 rows, 2 columns and 2 boxes. Your rectangle is not a UR, because it's spread over 4 boxes.

RW

Wow, I find it amazing that this is the first time I've bumped into that technicality. Thanks for pointing that out to me.
Jaremy

Posts: 2
Joined: 10 May 2006