Quadriga Sudoku

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

Quadriga Sudoku

Postby m_b_metcalf » Fri Jan 14, 2022 5:19 pm

Elsewhere, JPF wrote:Congratulations to all for having found these sublime Troika so quickly!
May I suggest another challenge : find 4 valid and minimal puzzles forming a grid partition.

This is what my first shot looked like:
Code: Select all
.1......62....9.......4.7.....6...8...5.8.2...6...1.....8.3.....4.7....13......2. 20
5.4.7............8..3....12.2.......1......6.8.....5.37..1.2...6....5.3....8.4... 21
......39.....1.4..9....6...4.....1...3.9.7......42..7.......64...2.......51.6...7 21
...2.8....763...5..8.5.......7.53..9........4..9.......9......5....9.8........9.. 19 9916331

.1......23....8.......5.6.....1...9...5.2.8...9...6.....6.8.....3.2....14......3. 20
..74......5.61......9.....328...5...1..9.3.........12..7......4.......6....5..9.8 21
......5........4.98..7.2.....4...3.6.6......7...84....9..3.1...5.8.9.....2...7... 21
6...39.8...2....7..4.....1.....7...........4.7.3.....5......25......47....1.6.... 19 358381

.1...2..37..4...9...6.......4...5..1.........6..7...8.......4...5...1..29..6...7. 20
....7.6......5...859.1.....3..8.....1....9..6.2...39...6.........7.9.........43.5 21
..49......3...61.......82.7..9.........24.53...5.1....2....7..9.......6..8..2.... 21
8......5...2..........3..4.....6.72..78..............4..358..1.4..3..8....1...... 19 1855212

.1...2..37..5...8...4.......3...1..8.........9..7...5.......2...4...3..15..2...7. 20
.......4..2..3.1...8...7..5..7...4...5...9..7..1.4.3...7...5.39.............1.8.. 21
..5.9.7.......4......16.92.....5....4.8...61..6...8.......8.......97.5....3.....4 21
6..8.......9.....63........2..6...9....32............21.64.....8.2....6..9...6... 19 49572586

.1......62....9.......4.7.....6...8...5.8.2...6...1.....8.3.....4.7....13......2. 20
5.4.7............8..3....12.2.......1......6.8.....5.37..1.2...6....5.3....8.4... 21
...2..39..7..1.....8...6.....7...1.......7..4..94............45..2.9.....51.6...7 21
.....8.....63..45.9..5.....4...53..9.3.9.........2..7..9....6........8........9.. 19 1310972


The large number following the 19 is p4's number of solutions! :cry:

Mike
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Re: Quadriga Sudoku

Postby marek stefanik » Fri Jan 14, 2022 5:54 pm

Well, I don't think there's a way to cheese this one with isomorphism. :)
Good luck, everyone!

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Re: Quadriga Sudoku

Postby Mathimagics » Fri Jan 14, 2022 6:12 pm

The smallest minimal puzzle in a 4-way partition is 19 or less, but we know that most grids have a relatively small supply of 19's.

I would suggest that it might be better to start with grids that have a 17C, this implies 18's and then 19's, which might then be available in sufficient numbers to merit looking at the larger sets in the partition ...
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Re: Quadriga Sudoku

Postby m_b_metcalf » Fri Jan 14, 2022 9:54 pm

Second attempt shows a big improvement:
Code: Select all
....2.6...1..........9.....23...6.......8..9.5......4....4.13....97.....8........ 17
.578....4...6......8...7.....4.9.8.76............72....25.....91......2.....5..6. 21
9......1......597...6.1..32..........7.5.4......3....6....6.........84.5.43..97.. 22
.....3...3.2.4...84.....5.....1...5...1...2.3.98...1..7......8..6..3.......2....1 21   7044

...2...9..1.....3..5...8...2..9........4..5........1..4....6.2.....3.7......1.... 17
..4.53.......7....9.....26..45..1....3.........73.........9...8..6....1..2.7.4.5. 21
76......1.....94.5..3.4...........73....67.8.68...5......5......9.8.2...3.......6 22
......8..8.26........1....7....8.6..1.9.....2....2..49.71...3..5.......4..8...9.. 21   8910

[Edited with better results.]
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Re: Quadriga Sudoku

Postby coloin » Sat Jan 15, 2022 12:56 am

Code: Select all
589732614621854379743916825835129746417568293296347158968471532372695481154283967  solution
....3.........4.........825..5.2.7......68....9....1.8.....1.3..72.......5.2...6.  C20
5.9.........8...79..3..6...........64.7......2...47.5.........2...69...1..4...9..  C20
.....2.1..2..5.....4..1....8..1...........29...63.......8.7.5..3....54..1...8....  C20
.8.7..6.46.1...3..7..9......3...9.4..1.5....3.........96.4............8......3..7  C21  15053 sol
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Re: Quadriga Sudoku

Postby m_b_metcalf » Sat Jan 15, 2022 5:47 am

Code: Select all
....12.5.7.....4......8.......6..3...21.......7..........7....24..3.....3......8. 17
..64......1......9.4.9...1......5.7.6...73.4.5.....2.8.....8.3.....51..6...2..... 22
9..........853....2....76..8...2............5...194....6..4.5........79..57...1.. 21
.3....8.7.....6.2...5.....3.94.....1...8..9....3....6.1.9.......82..........69..4 21   2675 solutions
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Re: Quadriga Sudoku

Postby Mathimagics » Sat Jan 15, 2022 7:36 am

Ok, now you're getting somewhere. Good luck with the hunt! 8-)
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Re: Quadriga Sudoku

Postby m_b_metcalf » Sat Jan 15, 2022 9:29 am

Code: Select all
.46.5.2.....8......5.......7..1.8...8..7...........4...2..4....1......3.........7 17
...3.7....7..9..4.........6....6.95..95.2......2.....8.....381...9......46...1... 21
.......8.2.1......3...1.79.........2......1.3...5.9.7...76......8.2.56.4..3.8.... 22
9.......1.....63.5..84.2....34...........4.6.61..3....5.......9....7.......9..52. 21    (only) 516 solutions


Gasp!!!
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Re: Quadriga Sudoku

Postby Mathimagics » Sat Jan 15, 2022 9:53 am

Good!
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Re: Quadriga Sudoku

Postby m_b_metcalf » Sat Jan 15, 2022 1:55 pm

marek stefanik wrote:Well, I don't think there's a way to cheese this one with isomorphism. :)

Well, I'm tantalisingly close with what Marek describes as 'a cheese' (in which language is that an understood expression?). My trick is to make p1 an x-sudoku:
Code: Select all
.................1..2........3...........4....25...67.81.......4...........5..... 12   <----  p1 is an x-sudoku
5.4........86.5.......39..76....7..2.......39...18.........64....78.....23.....9. 22
.9.71..6...........6.....5.....5.1..78.2.....9.......4...3......5..92.....6...7.8 20
.....82.337..2.94.1..4..8...4.9...8...1.6.5.......3.....9.7..25......316....41... 27   2 solutions


Mike
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Re: Quadriga Sudoku

Postby coloin » Sat Jan 15, 2022 2:31 pm

An improvement for the purists....
Code: Select all
589732614621854379743916825835129746417568293296347158968471532372695481154283967  solution
....3.........4.........825..5.2.7......68....9....1.8.....1.3..72.......5.2...6.  C20
5.9.........8...79..3..6...........64.7......2...47.5.........2...69...1..4...9..  C20
.8.7..6........3..74.91.....3...9.4..1.5...9...6......9..4..........5.8......3...  C20
.....2.14621.5.............8..1...........2.3...3......68.7.5..3.....4..1...8...7  C21 8289 sols


Code: Select all
589732614621854379743916825835129746417568293296347158968471532372695481154283967  solutiom
.......1..2..5.....4.......8..1.9.........2.....3......6..7.5.23.....4..1...8....  C17
.8.7..6.4......3..7..91.....3.....4..1.5...9...6......9..4..........5.8......3...  C19
....3.........4.........825..5.2.7......68....9....1.8.....1.3..72.......5.2...6.  C20
5.9..2...6.18...79..3..6...........64.7.....32...47.5...8.........69...1..4...9.7  C25   2 solutions
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Re: Quadriga Sudoku

Postby Mathimagics » Sat Jan 15, 2022 3:04 pm

coloin: Fantastic effort, well done!! 8-)

The Magic Quadroika can't be far away ...
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Re: Quadriga Sudoku

Postby coloin » Sat Jan 15, 2022 4:19 pm

It has to be there !
advancing on the same grid
Code: Select all
589732614621854379743916825835129746417568293296347158968471532372695481154283967
.8.7..6.4......3..7..91.....3.....4..1.5...9...6......9..4..........5.8......3...  C19
....3.........4.........825..5.2.7......68....9....1.8.....1.3..72.......5.2...6.  C20
5.9.........8...79..3..6...........64.7......2...47.5.........2...69...1..4...9..  C20
.....2.1.621.5.....4.......8..1.9.........2.3...3......68.7.5..3.....4..1...8...7  C22   365 solutions
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Re: Quadriga Sudoku

Postby m_b_metcalf » Sat Jan 15, 2022 4:28 pm

coloin wrote:It has to be there !

I think so too:
Code: Select all
.......1..2..5.....4.......8..1.9.........2.....3......6..7.5.23.....4..1...8....  17
.8.7..6.4......3..7..91.....3.....4..1.5...9...6......9..4..........5.8......3...  19
5.9.3.......8...79..3..6...........64...68...2....715........3...2.9...1...2..9..  22
.....2...6.1..4.........825..5.2.7....7.....3.9..4...8..8..1....7.6......54....67  23, 2 solutions


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Re: Quadriga Sudoku

Postby m_b_metcalf » Sun Jan 16, 2022 10:27 am

Almost there:
Code: Select all
.......1..2..5.....4.......8..1.9.........2.....3......6..7.5.23.....4..1...8.... 17   1.5/1.2/1.2
.8.7..6.4......3..7..91.....3.....4..1.5...9...6......9..4..........5.8......3... 19   2.0/1.2/1.2
..9......6.18.4.........825....2.7.64.7..........47.5...8..1......6......5....9.7 22   7.1/1.2/1.2
5...32..........79..3..6.....5..........68..329....1.8.......3..72.9...1..42...6. 23   1.5/1.2/1.2, 2 clues redundant


Mike

[Edit: for the record, the two redundant clues are r6c7 and r7c8. removing them raises p4's rating to 2.0.]
Last edited by m_b_metcalf on Tue Jan 18, 2022 8:15 am, edited 2 times in total.
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