## Two equal boxes

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

### Two equal boxes

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
GouinJP

Posts: 296
Joined: 06 April 2013
Location: Montreal

### Re: Two equal boxes

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
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Location: Berlin

### Re: Two equal boxes

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
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Location: Berlin

### Re: Two equal boxes

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

Posts: 2336
Joined: 05 May 2005
Location: Devon

### Re: Two equal boxes

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
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Location: Berlin

### Re: Two equal boxes

Likely the empty boxes are considered equal.
dobrichev
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Joined: 24 May 2010

### Re: Two equal boxes

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

m_b_metcalf
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### Re: Two equal boxes

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

Posts: 2336
Joined: 05 May 2005
Location: Devon

### Re: Two equal boxes

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...`
coloin

Posts: 2336
Joined: 05 May 2005
Location: Devon

### Re: Two equal boxes

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
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Joined: 15 May 2006
Location: Berlin

### Re: Two equal boxes

Thank you for all these answers.
GouinJP

Posts: 296
Joined: 06 April 2013
Location: Montreal

### Re: Two equal boxes

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.
JPF
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Posts: 6096
Joined: 06 December 2005
Location: Paris, France

### Re: Two equal boxes

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
RSW

Posts: 581
Joined: 01 December 2018

### Re: Two equal boxes

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...789123...8.4456...39.789.....5...123......456......789...8.4...12339....456..5...789123...6.8456....17789...5.....123......456......789...6.8...123.17...4565.....789123...8.5456....3.789....14...123......456......789...8.5...123.3....456.14...789123....74456...29.789...3.5...123......456......789....74...12329....4563.5...789123...96.456....72789...5.1...123......456......789...96....123.72...4565.1...789123...96.456...8.2789....41...123......456......789...96....1238.2...456.41...789`

JPF
JPF
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Joined: 06 December 2005
Location: Paris, France