Stuck on a really hard sudoku!

[jkmyoung]

Hey, are there any sudoku experts out there? Can anyone tell me the next step in solving this sudoku and explain it properly? I've used all the rules I can think of but am now stuck.

51--263--
7264-35-8
93-5-76--
395278461
86--54--9
47--698-5
-59-41-83
-43--2-5-
-87-35-4-
 

[JosAH]

A stupid brute force solver solves this one in 0ms.

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

kind regards,

Jos

[jkmyoung]

Thanks to your help I've found that there are at least 2 other solutions.

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

[JosAH]

@jkmyoung
Yup, and that's exactly why trying to compute a solution fails: sometimes you can not compute a single value for a cell, only two or more values are possible. e.g. see an empty sudoku board. A (more or less) brute force approach simply tries a possiblity and when it fails it tries another possibility.

Let's continue this discussion in the original thread in the algorithms section.

kind regards,

Jos