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

Everything about Sudoku that doesn't fit in one of the other sections
RW wrote:
Eioru wrote:I try to add another one empty box.
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`*********   ******************   *********...***...   ...***......*.*...   ....*.......*.*...   ....*.......*.*...   ....*.......***...   ...***...*********   ******************   *********`

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?
udosuk

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Joined: 17 July 2005

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.

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

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`....*....   *.......*   *...A...*.*.*.*.*.   .*.*.*.*.   .*.*.*.*..........   .........   ..........*.*.*.*.   .*.*.*.*.   .*.....*.*.......*   .........   A.......B.*.*.*.*.   .*.*.*.*.   .*.....*..........   .........   ..........*.*.*.*.   .*.*.*.*.   .*.*.*.*.....*....   *.......*   *...B...*`

They are all 20-clue pattern.
Eioru

Posts: 182
Joined: 16 August 2006

The two first patterns are fully symmetric.

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

pattern 1 :
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`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 :
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`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 :
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` 1 . . | . . . | . . 2 . 3 . | 4 . 5 | . 6 . . . . | . . . | . . .-------+-------+------- . 4 . | 1 . 3 | . 5 . . . . | . 7 . | . . . . 6 . | 5 . 8 | . 3 .-------+-------+------- . . . | . . . | . . . . 5 . | 3 . 4 | . 9 . 9 . . | . . . | . . 1`

JPF
JPF
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Location: Paris, France

From above, this pattern apparently doest have any valid puzzles.
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`+---+---+---+                                                                   |***|***|***|                                                                         |***|***|***|                                                                         |...|***|...|                                                                         +---+---+---+                                                                         |...|*.*|...|                                                                         |...|*.*|...|                                                                         |...|*.*|...|                                                                         +---+---+---+                                                                         |...|***|...|                                                                         |***|***|***|                                                                         |***|***|***|                                                                         +---+---+---+`

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

I believe neither does this one.

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`+---+---+---+         |*..|*.*|..*|         |...|*.*|...|        |...|*.*|...|         +---+---+---+         |***|***|***|         |...|***|...|         |***|***|***|         +---+---+---+         |...|*.*|...|        |...|*.*|...|         |*..|*.*|..*|         +---+---+---+  !`

C
coloin

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