The New Sudoku Players' Forum

[Jaremy]

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 .

[RW]

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

[Jaremy]

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.