## mtrying to cash in on this Psycho-Sudoku.com grid...no luck!

Advanced methods and approaches for solving Sudoku puzzles

### mtrying to cash in on this Psycho-Sudoku.com grid...no luck!

I have been trying to solve this grid on www.psycho-sudoku.com, their daily Sudoku challenge (they dont tell you which level of difficulty it is but there is only one on the dialy page) pays GBP 10 to the 1st correct solution- I tried some of the advanced looping techniques in the forum but I reach a dead end at every loop :(

I give up if anyone solves it please could you post the steps. :D
SudokuKing

Posts: 4
Joined: 16 March 2006

Hi,

This daily challenge:

Code: Select all
`4 . .|. . .|. 6 .. . 3|. . .|5 . .. . 2|7 . .|. . .-----+-----+-----6 . .|. . 3|. . .. . 5|. . .|2 . .. . .|. . 4|. . 8-----+-----+-----. . .|. . 5|7 . .7 . 6|. 9 .|4 . .. 8 .|. . .|. . .`

Has more than 100,000 solutions and belongs in the Sudoku Hall of Shame.

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

do you know how I can come up with a one feasible solution?

Thanks
SudokuKing

Posts: 4
Joined: 16 March 2006

SudokuKing wrote:do you know how I can come up with a one feasible solution?

Your puzzle has 131,076 solutions, so some guessing is needed to find any of them. Here's one of the ways that <rubylips' solver> finds one of the solutions:
START
1. The value 8 in Box [1,3] must lie in Column 7.
- The moves (2,8):=8 and (3,8):=8 have been eliminated.
The cell (5,6) is one of 2 candidates for the value 7 in Column 6.
2. The cell (9,5) is the only candidate for the value 7 in Row 9.
3. The value 9 in Box [1,2] must lie in Column 6.
- The moves (1,4):=9 and (2,4):=9 have been eliminated.
The cell (1,3) is one of 2 candidates for the value 8 in Column 3.
4. The cell (5,1) is the only candidate for the value 8 in Column 1.
5. The cell (3,7) is the only candidate for the value 8 in Column 7.
6. The value 7 in Box [2,1] must lie in Column 3.
- The moves (4,2):=7 and (6,2):=7 have been eliminated.
The cell (8,2) is one of 2 candidates for the value 5 in Box [3,1].
7. The cell (3,1) is the only candidate for the value 5 in Column 1.
8. The cell (4,9) is one of 2 candidates for the value 5 in Column 9.
9. The cell (9,8) is the only candidate for the value 5 in Row 9.
10. The value 7 in Box [1,3] must lie in Column 9.
- The move (2,8):=7 has been eliminated.
The cell (9,7) is one of 2 candidates for the value 6 in Column 7.
11. The cell (5,9) is the only candidate for the value 6 in Column 9.
12. The value 1 is the only candidate for the cell (5,5).
13. The value 9 is the only candidate for the cell (5,4).
14. The value 4 in Box [1,3] must lie in Column 9.
- The moves (2,8):=4 and (3,8):=4 have been eliminated.
The value 6 in Box [1,2] must lie in Column 6.
- The moves (2,4):=6, (2,5):=6 and (3,5):=6 have been eliminated.
The values 1, 4, 7 and 9 occupy the cells (4,2), (4,3), (4,7) and (4,8) in some order.
- The move (4,2):=2 has been eliminated.
The value 2 in Box [2,2] must lie in Row 4.
- The moves (6,4):=2 and (6,5):=2 have been eliminated.
The cell (7,2) is one of 2 candidates for the value 2 in Column 2.
15. The cell (6,1) is the only candidate for the value 2 in Row 6.
16. The value 4 in Box [2,1] must lie in Column 2.
- The move (4,3):=4 has been eliminated.
The cell (2,8) is one of 2 candidates for the value 2 in Column 8.
17. The 14 permutations of Row 2 and 12 permutations of Row 3 combine legally in 19 different ways.
Row 2:
1-6-3-4-8-9-5-2-7
1-7-3-4-8-6-5-2-9
1-9-3-4-8-6-5-2-7
1-6-3-8-4-9-5-2-7
1-7-3-8-4-6-5-2-9
1-9-3-8-4-6-5-2-7
9-1-3-4-8-6-5-2-7
9-1-3-8-4-6-5-2-7
9-6-3-1-4-8-5-2-7
9-7-3-1-8-6-5-2-4
9-6-3-4-8-1-5-2-7
9-6-3-8-4-1-5-2-7
9-7-3-4-8-6-5-2-1
9-7-3-8-4-6-5-2-1
Row 3:
5-1-2-7-3-6-8-9-4
5-1-2-7-4-6-8-3-9
5-1-2-7-4-6-8-9-3
5-6-2-7-3-1-8-9-4
5-6-2-7-4-1-8-3-9
5-6-2-7-4-1-8-9-3
5-6-2-7-3-9-8-1-4
5-9-2-7-3-6-8-1-4
5-6-2-7-4-9-8-1-3
5-9-2-7-4-6-8-1-3
5-6-2-7-4-9-8-3-1
5-9-2-7-4-6-8-3-1
No combination has the value 9 as a candidate for the cell (3,9).
- The move (3,9):=9 has been eliminated.
The cell (5,8) is one of 2 candidates for the value 3 in Row 5.
18. The value 4 is the only candidate for the cell (5,2).
19. The cell (1,7) is the only candidate for the value 3 in Column 7.
20. The cell (3,5) is the only candidate for the value 3 in Row 3.
21. The cell (3,9) is the only candidate for the value 4 in Row 3.
22. The cell (6,2) is the only candidate for the value 3 in Row 6.
23. The cell (4,8) is the only candidate for the value 4 in Row 4.
24. The cell (4,3) is the only candidate for the value 7 in Row 4.
25. The cell (6,8) is the only candidate for the value 7 in Row 6.
26. The 7 permutations of Row 8 and 12 permutations of Row 9 combine legally in 16 different ways.
Row 8:
7-5-6-1-9-2-4-8-3
7-5-6-2-9-1-4-8-3
7-5-6-3-9-1-4-8-2
7-5-6-2-9-8-4-1-3
7-5-6-8-9-2-4-1-3
7-5-6-3-9-8-4-1-2
7-5-6-3-9-2-4-8-1
Row 9:
1-8-4-3-7-2-6-5-9
1-8-9-4-7-2-6-5-3
3-8-1-4-7-2-6-5-9
9-8-1-4-7-2-6-5-3
3-8-4-1-7-2-6-5-9
9-8-4-1-7-2-6-5-3
3-8-4-2-7-1-6-5-9
9-8-4-2-7-1-6-5-3
3-8-9-4-7-1-6-5-2
9-8-4-3-7-1-6-5-2
3-8-9-4-7-2-6-5-1
9-8-4-3-7-2-6-5-1
No combination has the value 1 as a candidate for the cell (8,4).
- The move (8,4):=1 has been eliminated.
The 8 permutations of Column 6 and 3 permutations of Column 8 combine legally in 9 different ways.
Column 6:
1-6-9-3-7-4-5-8-2
1-9-6-3-7-4-5-8-2
9-1-6-3-7-4-5-8-2
9-6-1-3-7-4-5-8-2
9-8-6-3-7-4-5-1-2
2-6-9-3-7-4-5-8-1
2-9-6-3-7-4-5-8-1
9-8-6-3-7-4-5-2-1
Column 8:
6-2-1-4-3-7-9-8-5
6-2-9-4-3-7-1-8-5
6-2-9-4-3-7-8-1-5
No combination has the value 9 as a candidate for the cell (3,6).
- The move (3,6):=9 has been eliminated.
The 13 permutations of Row 2 and 3 permutations of Row 3 combine legally in 11 different ways.
Row 2:
1-6-3-4-8-9-5-2-7
1-7-3-4-8-6-5-2-9
1-9-3-4-8-6-5-2-7
1-6-3-8-4-9-5-2-7
1-7-3-8-4-6-5-2-9
1-9-3-8-4-6-5-2-7
9-1-3-4-8-6-5-2-7
9-1-3-8-4-6-5-2-7
9-6-3-1-4-8-5-2-7
9-6-3-4-8-1-5-2-7
9-6-3-8-4-1-5-2-7
9-7-3-4-8-6-5-2-1
9-7-3-8-4-6-5-2-1
Row 3:
5-1-2-7-3-6-8-9-4
5-6-2-7-3-1-8-9-4
5-9-2-7-3-6-8-1-4
In each combination, the value 9 in Box [1,1] appears in Row 2 or Row 3.
No combination has the value 9 as a candidate for the cell (2,9).
- The moves (1,2):=9 and (2,9):=9 have been eliminated.
The cell (4,2) is one of 2 candidates for the value 1 in Row 4.
27. The value 9 is the only candidate for the cell (6,3).
28. The value 7 is the only candidate for the cell (1,2).
29. The value 9 is the only candidate for the cell (4,7).
30. The value 1 is the only candidate for the cell (6,7).
31. The cell (2,1) is the only candidate for the value 1 in Box [1,1].
32. The value 7 is the only candidate for the cell (2,9).
33. The values 6 and 9 occupy the cells (2,2) and (2,6) in some order.
- The move (2,6):=8 has been eliminated.
The cell (8,6) is the only candidate for the value 8 in Column 6.
34. The value 1 is the only candidate for the cell (8,8).
35. The value 9 is the only candidate for the cell (3,8).
36. The value 1 is the only candidate for the cell (1,9).
37. The value 6 is the only candidate for the cell (3,2).
38. The value 9 is the only candidate for the cell (2,2).
39. The value 1 is the only candidate for the cell (3,6).
40. The value 2 is the only candidate for the cell (9,6).
41. The value 3 is the only candidate for the cell (8,4).
42. The value 9 is the only candidate for the cell (1,6).
43. The value 6 is the only candidate for the cell (2,6).
44. The value 8 is the only candidate for the cell (7,8).
45. The value 2 is the only candidate for the cell (8,9).
46. The cell (9,4) is one of 2 candidates for the value 4 in Row 9.
47. The value 8 is the only candidate for the cell (2,4).
48. The value 2 is the only candidate for the cell (4,4).
49. The value 5 is the only candidate for the cell (1,4).
50. The value 6 is the only candidate for the cell (6,4).
51. The value 1 is the only candidate for the cell (7,4).
52. The value 2 is the only candidate for the cell (1,5).
53. The value 4 is the only candidate for the cell (2,5).
54. The value 8 is the only candidate for the cell (4,5).
55. The value 5 is the only candidate for the cell (6,5).
56. The value 4 is the only candidate for the cell (7,3).
57. The value 6 is the only candidate for the cell (7,5).
58. The value 1 is the only candidate for the cell (9,3).
59. The cell (7,1) is one of 2 candidates for the value 3 in Row 7.
60. The value 9 is the only candidate for the cell (7,9).
61. The value 9 is the only candidate for the cell (9,1).
62. The value 3 is the only candidate for the cell (9,9).

Code: Select all
` 4 7 8 | 5 2 9 | 3 6 1  1 9 3 | 8 4 6 | 5 2 7  5 6 2 | 7 3 1 | 8 9 4 -------+-------+------  6 1 7 | 2 8 3 | 9 4 5  8 4 5 | 9 1 7 | 2 3 6  2 3 9 | 6 5 4 | 1 7 8 -------+-------+------  3 2 4 | 1 6 5 | 7 8 9  7 5 6 | 3 9 8 | 4 1 2  9 8 1 | 4 7 2 | 6 5 3`
r.e.s.

Posts: 337
Joined: 31 August 2005

SudokuKing wrote:do you know how I can come up with a one feasible solution?

This is another one of the solutions:

Code: Select all
`+-------+-------+-------+| 4 7 8 | 3 5 2 | 9 6 1 | | 1 6 3 | 8 4 9 | 5 7 2 | | 9 5 2 | 7 6 1 | 8 3 4 | +-------+-------+-------+| 6 2 9 | 5 8 3 | 1 4 7 | | 8 4 5 | 6 1 7 | 2 9 3 | | 3 1 7 | 9 2 4 | 6 5 8 | +-------+-------+-------+| 2 9 4 | 1 3 5 | 7 8 6 | | 7 3 6 | 2 9 8 | 4 1 5 | | 5 8 1 | 4 7 6 | 3 2 9 | +-------+-------+-------+`

Good luck with it!

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

Dude I got an e-mail saying I won, :) I used this grid:

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

it's only GB10 if you want e-mail me your paypal ad and I'll send you half when I get it.
SudokuKing

Posts: 4
Joined: 16 March 2006