Yet another sudoku property wanted

Everything about Sudoku that doesn't fit in one of the other sections

Postby Mauricio » Wed Nov 14, 2007 10:34 am

gsf wrote:...it produced
Code: Select all
...5..2.3.....9.68.42..8....1.....5..79.8.....3.7..6.4.......7..27.6........3.94. # 1 25 50 6

which has 6 non-backdoor empty cells

I thought that too (puzzles with low count of non backdoor cells), but I was not patient enough to look for them for a day, the best I found was something like 12 non backdoor cells.
Last edited by Mauricio on Wed Nov 14, 2007 3:15 pm, edited 2 times in total.
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Postby gsf » Wed Nov 14, 2007 5:05 pm

Mauricio wrote:I thought that too (puzzles with low count of backdoor cells), but I was not patient enough to look for them for a day

low count of non-backdoor cells
those are tough to off/on refine -- ~1-2 more backdoors per added clue
but if you've got cycles to burn let the computer(s) worry about patience
gsf
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Postby Mauricio » Mon Nov 19, 2007 6:46 am

Small improvement:
Code: Select all
# 28 clues
+-------+-------+-------+
| . . . | . . . | . . 1 |
| . . 2 | . 1 3 | 4 5 . |
| . 6 . | 7 8 . | . . 9 |
+-------+-------+-------+
| . . . | . 4 9 | 6 . . |
| . 4 7 | . . . | . 8 3 |
| 2 . . | 1 . . | . . 4 |
+-------+-------+-------+
| . . 5 | . . . | . . 2 |
| 3 2 . | . . . | . . . |
| 4 8 . | . 2 6 | . . . |
+-------+-------+-------+
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Postby Mauricio » Mon Nov 19, 2007 12:39 pm

Code: Select all
#27 clues
+-------+-------+-------+
| . . . | . . . | . . 1 |
| . . . | . . 2 | . 3 . |
| . . . | 4 5 . | 2 6 . |
+-------+-------+-------+
| . . . | . . 7 | 4 . . |
| . . 5 | 2 3 . | . . . |
| . 1 6 | . . . | . 2 8 |
+-------+-------+-------+
| . 7 8 | . . 9 | . . . |
| 1 . 3 | 6 . 8 | . 5 . |
| 2 . . | 7 1 . | . . . |
+-------+-------+-------+
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Postby Mauricio » Mon Nov 19, 2007 9:49 pm

Code: Select all
#25 clues
+-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | . . 2 | . 3 4 |
| . 5 . | . 6 7 | 8 . . |
+-------+-------+-------+
| . . . | . 3 8 | . . 6 |
| . 4 9 | . . . | . . 5 |
| 7 . . | 2 . . | . . . |
+-------+-------+-------+
| . . 7 | . . . | . . . |
| 2 6 . | 9 . 5 | 1 4 . |
| 9 . . | 1 . . | . . . |
+-------+-------+-------+
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Postby Mauricio » Tue Nov 20, 2007 3:28 am

Code: Select all
#24 clues
+-------+-------+-------+
| . . . | . . . | . . 1 |
| . . . | . . 2 | . 3 . |
| . 4 5 | . 6 . | 7 . . |
+-------+-------+-------+
| . . . | . 3 . | 1 2 . |
| . 8 9 | . 4 . | . . . |
| 7 . . | . . . | . . 5 |
+-------+-------+-------+
| . . 2 | 5 . . | . . 6 |
| . 3 . | 8 . . | . . 9 |
| 1 . . | . . 7 | 4 . . |
+-------+-------+-------+

I never thought this low could be possible, I am now almost convinced of the existence of a 22, at least.


A sudoku with 23 clues and just 1 non backdoor cell (singles), which of course leads to another 24:
Code: Select all
+-------+-------+-------+
| . . . | . . . | . . 1 |
| . . . | . . . | 2 3 . |
| . 1 4 | . 5 6 | . . . |
+-------+-------+-------+
| . . . | . . 7 | . 8 9 |
| . . 6 | 4 . . | . . . |
| 5 7 . | . . 2 | . . . |
+-------+-------+-------+
| . . . | 1 . . | 7 . 4 |
| . . 5 | . 9 . | . . . |
| . . 8 | . 3 . | 6 . . |
+-------+-------+-------+


And then it came, a minimal sudoku with the property I asked for:
Code: Select all
#23 clues
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . 1 | . . 2 |
| . 3 4 | . . . | . 5 . |
+-------+-------+-------+
| . . 2 | . . 3 | . 4 . |
| . . 6 | . 5 . | . . 7 |
| 1 . . | 8 . . | 6 . . |
+-------+-------+-------+
| . 5 . | 2 . 4 | . 1 . |
| . 9 . | . . . | . 3 . |
| 8 . . | . 7 6 | . . . |
+-------+-------+-------+
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Postby Mauricio » Tue Nov 20, 2007 8:30 am

Indeed, here it is:
Code: Select all
#22 clues, minimal
+-------+-------+-------+
| . . . | . . . | . . 1 |
| . . . | . . 2 | . . 3 |
| . 4 5 | . 6 . | . 7 . |
+-------+-------+-------+
| . . . | . . 7 | . . . |
| . . 2 | 1 8 . | . . . |
| 9 . . | . . . | 5 . 4 |
+-------+-------+-------+
| . . . | 3 9 . | . 8 . |
| . 1 . | . . . | 6 . . |
| 7 . . | 4 . . | 2 . . |
+-------+-------+-------+

I am sure there is at least a 21 out there, but it is beyond my current capabilities.
Last edited by Mauricio on Tue Nov 20, 2007 5:02 am, edited 1 time in total.
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Postby gsf » Tue Nov 20, 2007 9:01 am

Mauricio wrote:
Code: Select all
#22 clues, minimal

great result
gsf
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