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
Two equal boxes
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Two equal boxes
by GouinJP » Sat Oct 29, 2022 1:00 pm
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Re: Two equal boxes
by 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
-
m_b_metcalf - 2017 Supporter
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Re: Two equal boxes
by 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 . . .
-
m_b_metcalf - 2017 Supporter
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Re: Two equal boxes
by 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
by 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
-
m_b_metcalf - 2017 Supporter
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Re: Two equal boxes
by dobrichev » Sun Oct 30, 2022 1:38 pm
Likely the empty boxes are considered equal.
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Re: Two equal boxes
by 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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m_b_metcalf - 2017 Supporter
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Re: Two equal boxes
by 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
- coloin
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Re: Two equal boxes
by 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
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Re: Two equal boxes
by 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.
-
m_b_metcalf - 2017 Supporter
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Re: Two equal boxes
by 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
by 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
by JPF » Sun Nov 06, 2022 10:08 am
Hi RSW,
Thanks for pointing out this error.
There are no valid puzzle such that:
JPF
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
- 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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