Ask for some patterns that they don't have puzzles.

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

Postby udosuk » Wed Sep 26, 2007 4:43 pm

RW wrote:
Eioru wrote:I try to add another one empty box.
Code: Select all
*********   *********
*********   *********
...***...   ...***...
...*.*...   ....*....
...*.*...   ....*....
...*.*...   ....*....
...***...   ...***...
*********   *********
*********   *********

Your second pattern is impossible because of the same reasons as Mauricios pattern above (assume uniqueness, one clue in column 5 may be removed as hidden single, then row swapping tells you that the puzzle with an empty band would have 6 solutions=impossible).

Could you explain a little more please RW, I take it you're saying that one of r456c5 can be removed, but then there are still 2 left and I don't see how an empty band should pop out?:?:
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Postby RW » Wed Sep 26, 2007 4:56 pm

udosuk wrote:Could you explain a little more please RW, I take it you're saying that one of r456c5 can be removed, but then there are still 2 left and I don't see how an empty band should pop out?:?:

I was refering my previous proof in this thread, see here. You can do exactly the same thing with this pattern.

Short summary: If you remove the three digits in r456c5, you get three empty cells with exactly three possibilities each (the remaining 6 digits are already present in the column). You may lay down the three digits in 3!=6 different ways. If one of these gives an unique puzzle, then all of them must give an unique puzzle (same as the original puzzle, but rows swapped) -> The puzzle with all of r456 empty would have exactly 6 solutions, which has been proved impossible by JPF and Red Ed.

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Postby Eioru » Thu Sep 27, 2007 1:51 pm

I'm curious about three pattern I didn't find, too.

Code: Select all
....*....   *.......*   *...A...*
.*.*.*.*.   .*.*.*.*.   .*.*.*.*.
.........   .........   .........
.*.*.*.*.   .*.*.*.*.   .*.....*.
*.......*   .........   A.......B
.*.*.*.*.   .*.*.*.*.   .*.....*.
.........   .........   .........
.*.*.*.*.   .*.*.*.*.   .*.*.*.*.
....*....   *.......*   *...B...*


They are all 20-clue pattern.
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Postby JPF » Thu Sep 27, 2007 2:46 pm

The two first patterns are fully symmetric.

If you look at this thread, you will see their code.

pattern 1 :
Code: Select all
0-1-6-2 0-10-1-2 1-0-6-2 1-10-0-2  18-0-1-2  18-1-0-2

pattern 2 :
Code: Select all
0-8-6-2  0-10-4-2  16-0-6-2 16-10-0-2  18-0-4-2  18-8-0-2


For these patterns, no puzzles posted so far.

but I posted #36, isomorphic to this one :
Code: Select all
 1 . . | . . . | . . 2
 . 3 . | 4 . 5 | . 6 .
 . . . | . . . | . . .
-------+-------+-------
 . 4 . | 1 . 3 | . 5 .
 . . . | . 7 . | . . .
 . 6 . | 5 . 8 | . 3 .
-------+-------+-------
 . . . | . . . | . . .
 . 5 . | 3 . 4 | . 9 .
 9 . . | . . . | . . 1


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Postby coloin » Fri May 09, 2008 6:55 pm

From above, this pattern apparently doest have any valid puzzles.
Code: Select all
+---+---+---+                                                                   
|***|***|***|                                                                         
|***|***|***|                                                                         
|...|***|...|                                                                         
+---+---+---+                                                                         
|...|*.*|...|                                                                         
|...|*.*|...|                                                                         
|...|*.*|...|                                                                         
+---+---+---+                                                                         
|...|***|...|                                                                         
|***|***|***|                                                                         
|***|***|***|                                                                         
+---+---+---+

This means that in every grid there is always an unavoidable set in these
33 clues.

I believe neither does this one.

Code: Select all
+---+---+---+         
|*..|*.*|..*|         
|...|*.*|...|       
|...|*.*|...|         
+---+---+---+         
|***|***|***|         
|...|***|...|         
|***|***|***|         
+---+---+---+         
|...|*.*|...|       
|...|*.*|...|         
|*..|*.*|..*|         
+---+---+---+  !


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