Quadriga Sudoku

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

Re: Quadriga Sudoku

Postby coloin » Sun Jan 16, 2022 1:50 pm

Really well done...
I don't think there is an absolute requirement to use all the clues,
4 distinct puzzles with disjoint clues in one grid

I tried to find a disjoint 18 to go along with a 17 in this grid ..but proved elusive.
This would have left one more clue to share between puzzle #3 and #4

The grid was chosen because it had a 17 and no U4s [all 2 clue UAs have 18 clues] [ I think it is the only one with this property] [SFB grid]
It also has more puzzles than an average grid...
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Re: Quadriga Sudoku

Postby m_b_metcalf » Sun Jan 16, 2022 2:59 pm

coloin wrote:Really well done...
[snip]
The grid was chosen because it had a 17 and no U4s [all 2 clue UAs have 18 clues] [ I think it is the only one with this property] [SFB grid]

Thanks, but this was joint effort. Without your remembering that nugget of wisdom from the ancient past, I don't think it would have been possible. I tried to find my own 17/19 pairs, but was unsuccessful. I'll now make one last attempt to find a Quadriga on an x--grid, and then stop.

Let's hope jpf is satisfied!

Regards,

Mike
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Re: Quadriga Sudoku

Postby coloin » Sun Jan 16, 2022 3:18 pm

Yes there were 127 of these fully entwined grids found by Red Ed with no U4
I dont think a U4 makes it impossible - but reduces the chances to find disjoint low clue puzzles - and each of the 4 puzzles must have one of the U4 clues !
This grid had the least completions which was coined Russell's Viper !
Code: Select all
123456789456789123789231564234178956695342817817695342368527491572914638941863275 (RV)

I might try that one to find 2 disjoint 18s !!

my last try was in the SF grid with 29 17s
these 17s and 19s from that grid are exclusive ...
Code: Select all
..9.4.7...8........1.....2....8....67........4.....2..3.2.7..................6.18   17   
....4.7.5.8........1.....2....8....67........4.....2..3.2.7..................6.18   17   
....4.7...8...5....1.....2....8....67........4.....2..3.2.7..................6.18   17   
....4.7...8.....9..1.....2....8....67........4.....2..3.2.7..................6.18   17   
....4.7...8........1.9...2....8....67........4.....2..3.2.7..................6.18   17   
....4.7...8........1.....2....8..9.67........4.....2..3.2.7..................6.18   17   
....4.7...8........1.....2....8....679.......4.....2..3.2.7..................6.18   17   
....4.7...8........1.....2....8....67......5.4.....2..3.2.7..................6.18   17   
....4.7...8........1.....2....8....67........45....2..3.2.7..................6.18   17   
....4.7...8........1.....2....8....67........4.....2..3.2.7...9..............6.18   17   
....4.7...8........1.....2....8....67........4.....2..3.2.7.......5..........6.18   17   
....4.7...8........1.....2....8....67........4.....2..3.2.7........9.........6.18   17   
                                                                                         
.3...1.............1...3............79..................................97.......   2 U4s                                                                                           
                                                                                         
...2.1.8...4.6....5.7.......2..5................6.9.3....1.85.........7.9.5...4..   19   
...2.1.8...4.6....5.7.....4.2..5................6.9.3....1.85...........9.5...4..   19   
...2.1.8...4.6....5.7.......2..5..4.............6.9.3....1.85...........9.5...4..   19   
...2.1.8...4.6....5.7.......2..5................6.9.3....1.85..........29.5...4..   19   
...2.1.8...47.....5.7...6...2..5................6.9.3....1.8.6..........9.5...4..   19   
...2.1.8...476....5.7.......2..5................6.9.3....1.8.6..........9.5...4..   19   
...2.1.8...4.6....5.7.....4.2..5................6.9.3....1.8.6..........9.5...4..   19   
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Re: Quadriga Sudoku

Postby Mathimagics » Sun Jan 16, 2022 5:04 pm

Here are all available 18C's for that grid (RV). There are 23 according to blue:

Hidden Text: Show
Code: Select all
.........456.........231....3.............8.7.1...5.........4.1...9...3.9..86....
........9.5.7.....7..2.....23...........4.8...1..9...2.68.............3.......275
.......8...67.......9.....423.....5.....4....8...9...2......491......6.....8.3...
.......89...7..1..7..23........78...6...4............2..8...4....29.......1....7.
.....6...4...8..2......1..........5....3....781..9.....6.5.7..1.....46..9........
....5...94........7....1..............5..28.....6..34.368.....1...9.4.....1......
....5...94.....1...8..........1.8...6..........7...34.3......9......4..8....6..75
....5...94.....1...8..........1.89..6..........7...34.3.............4..8....6..75
...4....9...78......9...56.2..1.........4.8.7.............2..9.57........41......
...45.....5.....23.......6...4...9.6...3.2.1..........3.8...4...............6..75
...45...9....8....7.9....6....1.....6...4.8....7...........7.915.2.......4.......
...45...9....8....7.9....6.2..1.........4.8....7...........7.915.2.......4.......
...45..8...6.8....7.9............9.6...34...7........2.....7.....2....3..4.8.....
...45..8..56........9.......3.....5......2...81.....4....5.......2...6.....8.32..
..3....8....7.9....8.......2.....9.6..534.........5..2..8...4.........3.9...6....
..3...7.......912..8.......2.....9....534.......6..........7..........389.1.6....
..3...7......89.2..8...1...2.....9....534...................4......1..389.1......
.2..........7.9..37.............89..6.5.4.....1...........2...1...9.4.....1....75
.2.....89......1......3.........8.5.6.............5.423.8.........91.6...4..6....
.2...6......7.......9...5.....1.....6.....8.7....9..4.....2..915....4.....1....7.
.2...6......7....3......5........9..6.53............4.....2...15..9.4...9.1....7.
1..........6.8...37.....5.42.....9.....3...1......5.......27......91.....4......5
1.3.......56.....3...2....42......5........1.8.7.9.....6.5.........1...8.....3...
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Re: Quadriga Sudoku

Postby coloin » Sun Jan 16, 2022 5:39 pm

Well that was a good job !!
Code: Select all
.......89...7..1..7..23........78...6...4............2..8...4....29.......1....7.
.....6...4...8..2......1..........5....3....781..9.....6.5.7..1.....46..9........

These ones are exclusive .... there may well be others as I did it by eye !!
unfortunately the converse 45 C has a single mandatory clue
Code: Select all
12345.7...56..9..3.89...5642341..9.6.95..281...76.534.3...2..9.57..1..38.4.8632.5  45
123456789456789123789231564234178956695342817817695342368527491572914638941863275   
                                                                #                   
                                                            mandatory               
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Re: Quadriga Sudoku

Postby Mathimagics » Sun Jan 16, 2022 6:18 pm

Oh, you wanted the disjoint pairs? :roll:

Code: Select all
.......8...67.......9.....423.....5.....4....8...9...2......491......6.....8.3...
....5...94.....1...8..........1.89..6..........7...34.3.............4..8....6..75

.......89...7..1..7..23........78...6...4............2..8...4....29.......1....7.
.....6...4...8..2......1..........5....3....781..9.....6.5.7..1.....46..9........

...45..8..56........9.......3.....5......2...81.....4....5.......2...6.....8.32..
..3...7.......912..8.......2.....9....534.......6..........7..........389.1.6....

...45..8..56........9.......3.....5......2...81.....4....5.......2...6.....8.32..
..3...7......89.2..8...1...2.....9....534...................4......1..389.1......
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Re: Quadriga Sudoku

Postby coloin » Sun Jan 16, 2022 7:07 pm

Excellent this !
Code: Select all
123456789456789123789231564234178956695342817817695342368527491572914638941863275
.......8...67.......9.....423.....5.....4....8...9...2......491......6.....8.3... 18
....5...94.....1...8..........1.89..6..........7...34.3.............4..8....6..75 18
1234.67...5..89.237..23156...4.7...6.953.2817.1.6.5....68527...57291..3.941...2.. 45C 

this is the only 45C [of the 4] pair with all clues indidually removable ..

Can blues program find a 19 or 20 in that 45C before i can ?
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Re: Quadriga Sudoku

Postby Mathimagics » Sun Jan 16, 2022 8:32 pm

coloin wrote:Can blues program find a 19 or 20 in that 45C before i can ?


No. But I have something that might ...

Blue's dll's work with full grids only - eg Find20C, Find19C and Find18C.

These functions return only the first puzzle found. For 18C only he also produced a function to enumerate all available 18C's (which found the 23 puzzles I gave you).

I have a generic program that can look for reductions in a given puzzle by testing all combinations. Its run time depends mainly on how many non-removable clues there are ..

Oh, I see there are 45 !! That's really bad ... it might take some time ....

I will let it run overnight, but there are some early finds reported:
Code: Select all
......7......89...7.....56...4.........3.28...1.........85.7.....2.1..3.94....2.. # 20C
......7......89...7.....56...4.........3.28...1.........8527.....2.1..3.94....... # 20C
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Re: Quadriga Sudoku

Postby coloin » Mon Jan 17, 2022 9:59 am

Well it seems there are at least 129 20C in that 45C from RV
And no 19 found
However I looked at 50 of the reciprocal 25C puzzles and none had 1 solution !
It seems that finding 2 valid disjoint puzzles [eg 22C and 23C] in our 45 sample is quite a big task too !!!!!
Probably expected as a random selection of 25 clues from a grid is unlikely to give a valid puzzle
Well done Mike !
Mathimagics wrote:Here are all available 18C's for that grid (RV). There are 23 according to blue....

This program is amazing, this grid would be one which would take a very long time with checker to find a 17
....so he must employ the band wise analysis [666 and above]

I wonder if this is the most for a grid [without a 17], and the disjoint 18s in a grid are unexpected too !!
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Re: Quadriga Sudoku

Postby coloin » Wed Jan 19, 2022 11:01 pm

m_b_metcalf wrote: for the record.......,

Hi Mike
I have to confess the converse 25C with only 2 solutions was incidental ...
Was it easy or ...... did you generate a lot [ or maybe millions ! ?] of puzzles and then test their converse, unfortunately I could not get gridchecker to invert the puzzle to attempt this !!!
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Re: Quadriga Sudoku

Postby m_b_metcalf » Thu Jan 20, 2022 8:35 am

coloin wrote:I have to confess the converse 25C with only 2 solutions was incidental ...
Was it easy or ...... did you generate a lot [ or maybe millions ! ?] of puzzles and then test their converse, unfortunately I could not get gridchecker to invert the puzzle to attempt this !!!

Well, the method that worked (as opposed to the one that didn't) was to take your 17c+19c puzzles, then to perform a top-down search for a valid, minimal puzzle in the remaining cells, keeping only those p3s with fewer than 23 clues. In a separate program, I simply tested whether the unused cells still remaining formed a valid puzzle with a unique solution and, if so, then checked whether any of its clues were redundant. The number of tries was not in the millions. As always, I use only programs, other that SE, that I have written myself, so it's easy to bend them to my will.

Note that the two redundant clues were found in p4, but they are actually redundant wrt the whole grid. The Quadriga has 79 clues; two remain and can be attached to any or none of the four constituant puzzles.

HTH

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Re: Quadriga Sudoku

Postby coloin » Fri Jan 21, 2022 1:17 am

All very interesting and ultimately successful exercise. Rather than writing programs I am able to manipulate the data and use existing programs - which is looking at from a different angle, but equally rewarding.
I am helped by an old GUI program that Havard developed which I might just share will all now.

I dont think a set of Quadriga puzzles are that rare now ....
I took the C17 from our grid and combined with another C19 to give a C36.
The resultant C45 needed to have every clue removable - otherwise impossible to have 2 disjoint puzzles !
I generated 10000 puzzles from this reduced grid , of which 1450 were C22 or less
I was able to invert [thanks to gridchecker] these puzzles and solve with a mask which ignored the original C36 clues

One C23 puzzle was valid out of these, which uses all the 81C.
Code: Select all
.......1..2..5.....4.......8..1.9.........2.....3......6..7.5.23.....4..1...8....  C17
...7..6........3..7..91.....35....4..1.5...9...6.....89..4..........5.8......3...  C19
.89.....46..8....9..3..68......2.7..4............47.5........3..72.9.......2..96.  C22
5...32.....1..4.7........25........6..7.68..329....1....8..1......6....1.54.....7  C23
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Re: Quadriga Sudoku

Postby JPF » Fri Jan 21, 2022 8:37 am

Congratulations! Well done!

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Re: Quadriga Sudoku

Postby m_b_metcalf » Fri Jan 21, 2022 9:44 am

coloin wrote:One C23 puzzle was valid out of these, which uses all the 81C.

Well, perseverance pays off! Well done. Mike
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Re: Quadriga Sudoku

Postby Mathimagics » Fri Jan 21, 2022 10:04 am

Excellent! Well done coloin! 8-)
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