The New Sudoku Players' Forum

[KevinR7]

I am relatively new to advanced Sudoku solving techniques and I would be grateful if someone could explain the logic behind the following.

I have a puzzle with a series of 6s in it as follows:

R1 @ C1, C2, C6, C8 & C9
R2 @ C2, C6, C7 & C8
R3 @ C2, C6, C7 & C8
R4 - 6 as solution in C5
R5 @ C7 & C8
R6 - 6 as solution in C3
R7 @ C4, C7 & C8
R8 @ C2 & C4
R9 @ C1, C4, C8 & C9

The matrix formed by the 49 squares inside the outermost columns and rows contains between 2 and 5 6s in each row or column (except where 6 has been found as the solution in a row or column).

The 6s lying outside the inner matrix, but sharing a column with it i.e. in R1C2, R1C6, R1C8, R9C4 & R9C8 are deemed not to be candidates and can be removed, but the 6s not seen by any of the rows or columns of the inner matrix i.e. in R1C1, R1C9, R9C1 & R9C9 remain.

Help!

Kevin

[Sped]

Code: Select all

 
 *--------------------------------------------------------------------------------------------------------*
 | 123456789  123456789  12345789   | 12345789   12345789   123456789  | 12345789   123456789  123456789  |
 | 12345789   123456789  12345789   | 12345789   12345789   123456789  | 123456789  123456789  12345789   |
 | 12345789   123456789  12345789   | 12345789   12345789   123456789  | 123456789  123456789  12345789   |
 |----------------------------------+----------------------------------+----------------------------------|
 | 12345789   12345789   12345789   | 12345789   6          12345789   | 12345789   12345789   12345789   |
 | 12345789   12345789   12345789   | 12345789   12345789   12345789   | 123456789  123456789  12345789   |
 | 12345789   12345789   6          | 12345789   12345789   12345789   | 12345789   12345789   12345789   |
 |----------------------------------+----------------------------------+----------------------------------|
 | 12345789   12345789   12345789   | 123456789  12345789   12345789   | 123456789  123456789  12345789   |
 | 12345789   123456789  12345789   | 123456789  12345789   12345789   | 12345789   12345789   12345789   |
 | 123456789  12345789   12345789   | 123456789  12345789   12345789   | 12345789   123456789  123456789  |
 *--------------------------------------------------------------------------------------------------------*


r1c1, r1c9, r9c1, and r9c9 form a classic X wing. r1c1 and r9c1 are the only 6s in column 1 and r1c9 and r9c9 are the only 6s in column 9.

If r1c1 is a 6 then r1c9 can't be, so r9c9 has to be a 6. If r9c1 is a 6 then r9c9 can't be, so r1c9 must be a 6.

In either case, rows 1 and 9 will have 6s in them so all cells in rows 1 and 9 (besides the cells forming the X Wing) can have their 6s removed.

[Ruud]

Hi Kevin

Here is a graph of your digit 6 situation:



It shows an x-wing in columns 1 & 9. The green cells form the x-wing, the red cells can be eliminated.

An explanation of x-wings can be found here: http://www.sadmansoftware.com/sudoku/technique6.htm

I see Sped has already answered your question, but I keep the post.

Ruud.

[KevinR7]

Sped & Ruud

Thanks very much for your explanations and directions to the further details. I can now understand the logic behind what was previously causing me a headache.

Kevin