The New Sudoku Players' Forum

[Guest]

Picked up an abandoned sudoku and progressed it to here but just can't see the next step - any hints gratefully received



*5* | 9*3 | ***
2** | *** | **5
**7 | *2* | 8*9
------------------
675 | 382 | 491
*2* | *** | 367
*43 | 76* | 528
------------------
**1 | *5* | 9**
5** | *** | **3
*** | 134 | *5*

[Sue De Coq]

The key is to consider the cell r8c2, which has three legal candidates values - 6, 8 and 9. Now consider Row 9, which must, or course, contain each of a 6, 8 and 9 somewhere along its length. Think about the possible positions that each of these three values could occupy - and that should tell you which value belongs in r8c2.

[Guest]

Thanks, that was quick!

As ever, it's obvious once someone's pointed it out to you!

[Guest]

Hello Sue,

You say:

The key is to consider the cell r8c2, which has three legal candidates values - 6, 8 and 9. Now consider Row 9, which must, or course, contain each of a 6, 8 and 9 somewhere along its length. Think about the possible positions that each of these three values could occupy - and that should tell you which value belongs in r8c2.

But I cannot see how this will uniquely determine cell r862.

It seems to me that the full list of possibilities for row 9 are:

789 - 689 - 2689 - 1 - 3 - 4 - 267 - 5 - 26

(adjacent cells are separated by hyphens to make reading easier)

This expands to the followling exhaustive list of cases for row 9:

7 - 89 - 89 - 1 - 3 - 4 - 26 - 5 - 26
89 - 89 - 26 - 1 - 3 - 4 - 7 - 5 - 26
89 - 6 - 89 - 1 - 3 - 4 - 7 - 5 - 2

In the first 2 cases, cell r8c2 can still be either of 69 or 68, depending on whether cell r9c2 is 8 or 9, whilst in the last case cell r8c2 will be 89. But this still does not uniquely determine the value to go in cell r8c2.
Is my logic correct? If not, where is my error?

[Sue De Coq]

The critical point is that the values 8 and 9 in Row 9 have to go into the first box (because the second box is fully occupied and Columns 7 and 9 already contain 8s and 9s), which means that they can't go into r8c2. This leaves 6 as the sole candidate for r8c2.

[Guest]

Hello Sue,

Yes, I understand now. Thank you for the explanation.