The New Sudoku Players' Forum

[captain51]

THSI IS FROM 2ND DEGREE BLACK BELT SUDOKU BY FRANK LONGO. QUITE A FEW OF THE PUZZLES WIND UP LIKE THIS AND I DON'T UNDERSTAND HOW TO FINISH IT. R3C5 HAS TO BE A 7. BUT WHY?
ANY HELP WOULD BE APPRECIATED.

THANKS


- 9 8|- 4 1|7 - -|
- 4 3|- 8 2|9 - 1|
- 1 5|9 - -|- - 4 |
--------------------
4 7 9|1 - -|- - - |
3 5 6|2 9 8|4 1 7|
1 8 2|4 5 7|6 9 3|
---------------------
9 6 1|- - 4|- 2 -|
8 3 4|6 2 5|1 7 9|
5 2 7|8 1 9|3 4 6|

[wintder]

Here is the position that you posted.

Code: Select all

.98.417..
.43.829.1
.159....4
4791.....
356298417
182457693
961..4.2.
834625179
527819346

Here is an invalid markup of what would be the case of r3c5 NOT being a 7. (It is invalid because, in this case, the puzzle is incorrectly "solved".)

Code: Select all

.---------------.---------------.---------------.
| 26   9    8   | 35   4    1   | 7    356  25  |
| 67   4    3   | 57   8    2   | 9    56   1   |
| 27   1    5   | 9    36   36  | 28   8    4   |
:---------------+---------------+---------------:
| 4    7    9   | 1    36   36  | 258  58   258 |
| 3    5    6   | 2    9    8   | 4    1    7   |
| 1    8    2   | 4    5    7   | 6    9    3   |
:---------------+---------------+---------------:
| 9    6    1   | 7    7    4   | 58   2    58  |
| 8    3    4   | 6    2    5   | 1    7    9   |
| 5    2    7   | 8    1    9   | 3    4    6   |
'---------------'---------------'---------------'

Assuming that the rest could be completed you would be left with r3c56 and r4c56 being arbitrary, that is the puzzle would be done whether you set r3c5 to 3 or 6. That is two solutions that are equally valid.

A suduko must have only one solution or it is not a valid puzzle.
We take advantage of knowing that fact to set r3c5 to 7 back here.

Code: Select all

.---------------.---------------.---------------.
| 26   9    8   | 35   4    1   | 7    356  25  |
| 67   4    3   | 57   8    2   | 9    56   1   |
| 267  1    5   | 9    36*7 36  | 28   368  4   |
:---------------+---------------+---------------:
| 4    7    9   | 1    36   36  | 258  58   258 |
| 3    5    6   | 2    9    8   | 4    1    7   |
| 1    8    2   | 4    5    7   | 6    9    3   |
:---------------+---------------+---------------:
| 9    6    1   | 37   37   4   | 58   2    58  |
| 8    3    4   | 6    2    5   | 1    7    9   |
| 5    2    7   | 8    1    9   | 3    4    6   |
'---------------'---------------'---------------'

This technique only works reliably on valid 9X9 sudokus and is not accepted by all.

A place for better study is here:
http://forum.enjoysudoku.com/viewtopic.php?t=2000