The New Sudoku Players' Forum

[bcbhatta]

I have independently found the following rule which I have named as the Rule of Corners:

If a number appears at four corners of a square or rectangle of any size (from 2X2 to 9X9), and if the pair of columns or the pair of rows forming that rectangle do not contain that number at any other cell, then that number cannot be at any other cell of the conjugate pair of rows or columns of the rectangle as well. In other words, that number can be only at the four corners of the rectangle.

The following partially solved problem illustrates this rule:

(279) (67) 3 5 8 (279) 4 (26) 1
1 8 4 (29) 6 (2379) (79) (235) (35)
(279) 5 (69) 1 (37) 4 (79) (236) 8
3 (67) (68) (28) 5 (267) 1 4 9
(579) 2 1 4 (37) (379) 6 8 (35)
(59) 4 (689) (89) 1 (369) 2 (35) 7
6 3 2 7 9 5 8 1 4
4 1 7 3 2 8 5 9 6
8 9 5 6 4 1 3 7 2

In the above example, the remaining solution can be found only by using the above rule, and only one such combination exists. I invite the readers to spot this combination.

I also request the readers to inform me if any other person has found or published this rule before me. Please use the poll option.

B C Bhattacharya

[Carcul]

bcbhatta,

First, I want to congratulate you for having discovered this rule for your own. I think no matter if something is already known or not, is always very important to discover that by our own. Second, I am sorry to say that your Rule of Corners is already known for sometime as "X-Wing".
In your example, the Rule of Corners aplies to number 9 in cells 1 and 6 of rows 1 and 5.

Regards, Carcul

[bcbhatta]

Thanks Sir, for a prompt response and a gentle manner of correcting my illusion.

BC Bhatta