Two equal boxes

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Two equal boxes

Postby GouinJP » Sat Oct 29, 2022 1:00 pm

Hello
In a sudoku, two rows or two columns can't be equal but I am asking if in a 17 clue sudoku, two boxes can be equal?
Thank you
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Re: Two equal boxes

Postby m_b_metcalf » Sat Oct 29, 2022 3:04 pm

GouinJP wrote:In a sudoku, two rows or two columns can't be equal but I am asking if in a 17 clue sudoku, two boxes can be equal?
Thank you

Why not? About 5% have this property, even without looking at isomorphs:
Code: Select all
 . . . . . . . 1 2
 4 . . . 9 . . . .
 . . . . . . . 5 .
 . 7 . 2 . . . . .
 6 . . . . . 4 . .
 . . . 1 . 8 . . .
 . 1 8 . . . . . .
 . . . . 3 . 7 . .
 5 . 2 . . . . . .   See boxes 1 and 6
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Re: Two equal boxes

Postby m_b_metcalf » Sun Oct 30, 2022 10:11 am

Of course, in general, it's possible to construct valid puzzles in which three boxes each repeat three times. Here's a (non-minimal) example:
Code: Select all
 . 6 8 4 . . . . .
 . 2 7 . 5 . . . .
 . . 3 . . . . . 9
 4 . . . . . . 6 8
 . 5 . . . . . 2 7
 . . . . . 9 . . 3
 . . . . 6 8 4 . .
 . . . . 2 7 . 5 .
 . . 9 . . 3 . . .
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Re: Two equal boxes

Postby coloin » Sun Oct 30, 2022 10:59 am

Code: Select all
+---+---+---+
|12.|..3|...|
|3..|5..|..8|
|...|...|...|
+---+---+---+
|6..|12.|...|
|...|3..|...|
|...|...|..7|
+---+---+---+
|..7|.9.|12.|
|...|.6.|3..|
|..5|8..|...|
+---+---+---+  19C with 3 similar boxes
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Re: Two equal boxes

Postby m_b_metcalf » Sun Oct 30, 2022 1:05 pm

Code: Select all
 2 . . 1 . . . . 6
 . . . 7 . . . 3 .
 . . . . . . . 4 5
 . . . 2 . . 8 . .
 6 3 . . . . . . .
 . 5 . . . . . . .
 1 . . . . . 2 . .
 . . . 4 3 . . . .
 . . . . . 5 . . .   17C, with 3 identical boxes

 2 . . 7 . . . . 6
 . . . 1 . . . 3 .
 . . . . . . . 4 5
 . . . 2 . . 8 . .
 6 3 . . . . . . .
 . 5 . . . . . . .
 1 . . . . . 2 . .
 . . . 4 3 . . . .
 . . . . . 5 . . .   17C, with 3 identical boxes

 3 . . 4 . 5 . . .
 . . . . . . 9 . 1
 . . . 8 . . 2 . .
 4 . . 3 . . . 5 .
 . 9 . . . . . 1 .
 . 2 . . . . . . .
 6 . . . . . 3 . .
 . . . . 8 . . . .
 . . . . 9 . . . .   17C, with 3 identical boxes
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Re: Two equal boxes

Postby dobrichev » Sun Oct 30, 2022 1:38 pm

Likely the empty boxes are considered equal.
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Re: Two equal boxes

Postby m_b_metcalf » Sun Oct 30, 2022 4:23 pm

dobrichev wrote:Likely the empty boxes are considered equal.

If you mean two identical boxes in the 17-clue file, that makes for only 71 out of 2592.

Mike
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Re: Two equal boxes

Postby coloin » Sun Oct 30, 2022 4:37 pm

Code: Select all
+---+---+---+
|12.|...|...|
|3..|5..|..8|
|...|...|.6.|
+---+---+---+
|6..|12.|4..|
|...|3..|...|
|...|...|..9|
+---+---+---+
|...|...|12.|
|...|..9|3..|
|..5|..8|...|
+---+---+---+  18C with 3 similar clues in 3 boxes
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Re: Two equal boxes

Postby coloin » Sun Oct 30, 2022 5:00 pm

Code: Select all
+---+---+---+
|12.|3..|...|
|...|..5|..8|
|...|...|.7.|
+---+---+---+
|...|12.|4..|
|.39|...|...|
|8..|...|...|
+---+---+---+
|.6.|...|12.|
|...|...|...|
|..5|4.8|...|
+---+---+---+   18C with 2 clues the same in 3 boxes

:::more:::

Hidden Text: Show
Code: Select all
12.3..........5..8.......7....12.4...39......8.........6....12............54.8...
12.3...4......5..8............12.....39......8.......9.6....12.7..........5..8...
12.7...3......5..8............12.4....9......8.......9.6....12.7..........5..8...
12..3..7......5..8............12.4....9......8.......9.6....12....7.......5..8...
12..4.6.......5..8............12.....39......8.......9.6....12.7..........5..8...
12..4..3......5..8............12.4....9......8.......9.6....12.7..........5..8...
12.6...3......5..8............12.4....9......8.......9.6....12.7..........5..8...
12..6..3......5..8............12.....39......8.......9.6....12.7..........5..8...
12..6..3......5..8............12.4....9......8.......9.6....12.7..........5..8...
12..7..3......5..8............12.4....9......8.......9.6....12.7..........5..8...
12...........75..8.......7....12.4...39......8.........6....12............54.8...
12.3...6......5..8............12.4....9......8.......936....12............5..8...
12....6.3.....5..8............12.4...39......8.........6....12............54.8...
12..3.........5..8.......6....12.4...39......8.......9......12....4.......5..8...
12....6.......5..8............12.4..839................6....12....7.......54.8...
12.4...6......5..8....3.......12.4....9......8.......9.6....12............5..8...
12..6.3.......5..8............12.....39......8.......9.6....12.7..........5..8...
12............5..8.......7..7.12.4...3.......8.......9.6....12.....4......5..8...
12.6...4......5..8....3.......12.6....9......8.......9.6....12............5..8...
12.....5......5..8.......6....12.4....3......8.......9.6....12....7.......5..8...
12............57.8............12.4...3.......8.5.....9.6....12...3.........4.8...
12............5..8......7.....12.4...3.......8.5.....9.6....12...3.........4.8...
12..4.........5..8............12.4...3.......8.5.....9.6....12...3.........4.8...
12............5..8....3..6..7.12.4....9......8.......5....7.12............5..8...
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Re: Two equal boxes

Postby m_b_metcalf » Mon Oct 31, 2022 8:44 am

Not sure where this is leading but, for the record:
Code: Select all
 1 2 . 5 . 6 . . .
 3 4 . . 8 . . . .
 . . . . . . . 7 .
 . . . 1 2 . 6 . .
 . . 8 3 4 . . . 2
 . . . . . . 8 . .
 . 9 . . . . 1 2 .
 . . . . . . 3 4 .
 6 . . . . 5 . . .  23 clues, minimal, 3 identical boxes each with four clues.
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Re: Two equal boxes

Postby GouinJP » Sat Nov 05, 2022 7:28 pm

Thank you for all these answers.
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Re: Two equal boxes

Postby JPF » Sat Nov 05, 2022 8:13 pm

Code: Select all
+---+---+---+
|123|...|5.8|
|456|...|.71|
|789|...|63.|
+---+---+---+
|...|123|...|
|...|456|...|
|...|789|...|
+---+---+---+
|5.8|...|123|
|.71|...|456|
|63.|...|789|
+---+---+---+


This puzzle has 2 solutions.
See RSW's post below.


JPF
Last edited by JPF on Sun Nov 06, 2022 10:12 am, edited 1 time in total.
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Re: Two equal boxes

Postby RSW » Sun Nov 06, 2022 12:42 am

JPF wrote:
Code: Select all
+---+---+---+
|123|...|5.8|
|456|...|.71|
|789|...|63.|
+---+---+---+
|...|123|...|
|...|456|...|
|...|789|...|
+---+---+---+
|5.8|...|123|
|.71|...|456|
|63.|...|789|
+---+---+---+

JPF

Has two solutions:
123674598456398271789215634865123947397456812214789365548967123971832456632541789
123967548456832971789541632947123865812456397365789214598674123271398456634215789
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Re: Two equal boxes

Postby JPF » Sun Nov 06, 2022 10:08 am

Hi RSW,

Thanks for pointing out this error.
There are no valid puzzle such that:
  • B1=B5=B9=F (full box)
  • B2,B4,B6,B8 empty
  • B3=B7
There are 7 ed puzzles with 2 solutions:
Code: Select all
123...5..456....18789...6.2...123......456......789...5.....123.18...4566.2...789
123...8.4456...39.789.....5...123......456......789...8.4...12339....456..5...789
123...6.8456....17789...5.....123......456......789...6.8...123.17...4565.....789
123...8.5456....3.789....14...123......456......789...8.5...123.3....456.14...789
123....74456...29.789...3.5...123......456......789....74...12329....4563.5...789
123...96.456....72789...5.1...123......456......789...96....123.72...4565.1...789
123...96.456...8.2789....41...123......456......789...96....1238.2...456.41...789

JPF
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