The New Sudoku Players' Forum

[NormanvD]

Hello, I'm new here and new to sudoku in general, and I'm stuck with this one. Could someone tell me what I can cross off and why so?

image.jpg (205.66 KiB) Viewed 1121 times

[JasonLion]

I see a unique rectangle (type 2) and then singles to the end.

[NormanvD]

Could you point it out to me? I can't seem to find it

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 9     1     8      | 2467  247   26     | 47    3     5      |
| 3     47    2      | 1     9     5      | 8     47    6      |
| 47    6     5      | 3     8     47     | 1     2     9      |
|--------------------+--------------------+--------------------|
| 6     5     1      | 27    27    9      | 3     8     4      |
| 8     47    47     | 5     1     3      | 9     6     2      |
| 2     9     3      |*48    6    *48     | 5     1     7      |
|--------------------+--------------------+--------------------|
| 147   3     47     | 9     24-7  126    | 26    5     8      |
| 5     2     6      |*48+7  3    *48+7   | 4-7   9     1      |
| 147   8     9      | 246-7 5     126    | 26    47    3      |
*--------------------------------------------------------------*

To explain the Unique Rectangle that Jason mentioned, look at the cells I've marked *. They all contain 48 except for the lower two that contain 48+7.

If neither of these lower two cells were to contain 7 then all 4 cells would contain only 48. This is an impossible arrangement.

The puzzle would have either 0 solutions, or 2 solutions by interchanging the 4's and 8's in the 4 cells. Since most published puzzles are supposed to have exactly one solution the 4 exposed 48's would probably correspond to a 0 solution state.

Either way, one of the 7''s in the lower two * cells must be 7. This means that you can remove 7 from all cells that can see both of these cells. There are 3 of them that I've marked with -7 in the diagram.

You don't say whether you are familiar with Unique Rectangle arguments or just overlooked this one. If not, here are links to two excellent teaching sites that discuss this topic, and a whole lot of other solving techniques.

http://hodoku.sourceforge.net/en/techniques.php

http://www.sudokuwiki.org/Strategy_Families

Leren

[NormanvD]

Thank you very much for your in depth explanation! I'll was familiar with the unique rectangle but I overlooked this one completely, thanks alot!

[denis_berthier]

No need to suppose uniqueness:

finned-x-wing-in-columns: n4{c7 c5}{r1 r8} ==> r8c6 ≠ 4, r8c4 ≠ 4
singles to the end