The New Sudoku Players' Forum

[Hajime]

Joyful Serene Beautiful Nice Cozy Global World Peace = JSB NC GW PAX as a remembrance to the Bed-In for Global Peace by John and Yoko 50 years ago.
Also JSB NC GW PAX is a 9 Sudoku puzzle. The middle boxes of the 8 outer Sudoku variants are the outer boxes of the middle clueless vanilla Sudoku.
The puzzle is "easy" because no additional methods are needed (only singles), but of course it is not that easy. 538 cells to solve.
It is also "minimal" (alternative definition) because if a clue is deleted more methods are needed than "singles only".


Large picture:
https://www.dropbox.com/s/31qoe756cd17m8y/NCGWPAX_large.png?dl=0

Large picture with pencil marks:
https://www.dropbox.com/s/rtyws5wwp5tfyl8/NCGWPAX_pm.png?dl=0

In puzzle code:

Code: Select all

#9//C5,A/O5,W/AA5,G/C29,X/F11,N+3/AA29,NC/C53,P/O53,WA/AA53,JSB
.6....5.......8..9..2..3.....7.....................1...46..1...1.....4...2.....3.
..4............9...6..9..........2..3.2.....88.....5.19...2...6.8..............3.
..48.6.7..9...2.1....5.1..4..1..............6.......3....2.98....2..............9
.9.....5...6.........8.2.36..7....25.........9........5...3...........9..2...4...
.................................................................................
..6.......................96.................8........1..7...6....1.........63...
.5.4..........6..........7...2...9.........67..9....5..46.....8...2...15.....7...
....4..31...16.5............6.....9..........81.......7.........4...5............
........6....6.7......1.5.9...................4......51.9.3.....7....6.......7...
AABBBBBCCDAABBBBCEDAACCCCCEDAFFFCEEEDAAFFFGGEDDDHFFFGEDHHHHHGGEDHIIIIGGEHHIIIIIGG


Enjoy. Please reply if you like this or better: solved it!

Edit: url's and images redirected to dropbox

[tarek]

What is not to like: it is all lovely.

I also like the Implosion concept of the clueless which I did in the past.

Lovely

Tarek

[Mathimagics]

I agree, a very nice puzzle, Hajime, nice job!

No time to P&P solve (no surprise there), and I haven't yet configured my solver for these 9-grid clueless layouts, so I will have to leave the solution verification to tarek, he has time on his hands, I think ...

creint may also be in a position to do this

Regarding the "minimal for singles" property - I think I have discussed, or at least have mentioned, this property before (although I'm not sure exactly where ...). It is certainly a relevant concept, given the size of these puzzles!

How to distinguish this from strongly minimal, which generally means that a puzzle is both minimal and strong (singles only). Perhaps "minimally strong" or "minimally singles-only" might be used for the property in question? Unless someone has a better idea.

Cheers
MM

[tarek]

Because it is an Implosion see:http://forum.enjoysudoku.com/clueless-implosion-t6254.html
You can think of it as a normal clueless where grid 10 = grid 5 you can then paste it (if you have the time) into JSudoku ( you have to do all of the constraints manually though so good luck )

[SudoKai]

At first I thought I made a mistake somewhere when re-creating this Clueless Variant with my software as it was unable to completely solve it, but defining the Hidden Windoku Constraints was all that was needed.

http://www.sudokuwiki.org/Windoku_Strategy
http://sudopedia.enjoysudoku.com/Hypersudoku.html

Are there any other hidden constraints I missed that should be taken into consideration?

[Mathimagics]

Are there any other hidden constraints I missed that should be taken into consideration?

I don't think so - this is an anomaly that only applies to a Windoku puzzle, I would think.

If a software solver has DFS capability (guessing), and it is only configured to use the 4 "normal" Windoku houses, not the full set of 9, this will make no difference, other than needing more iterations to arrive at the solution.

But if your solver is a "no guess" model, ie relies on SST's only, then 4 vs 9 houses can mean the difference between solvability or failure. Especially for this puzzle, with its stated "minimally singles-only" property. Hidden sets (singles, pairs, etc) can't be found for a house that doesn't exist!

And that does raise a little semantic issue (here we go again - so many variants, so many terminologies, so many semantic conundrums!!).

We all have, I think, a common understanding of what "singles only" means for a software solver. But Hajime's example shows that even this apparently simple concept can have nuances.

[EDIT] It should also be possible to create this anomaly with a Jigsaw puzzle - most Jigsaw layouts have "hidden houses", just like Windoku's "hidden windows", so I imagine it would be a fairly simple exercise to find a case where a puzzle can be "singles only" when the software solver is aware of these, but not otherwise ...

[SudoKai]

If a software solver has DFS capability (guessing), and it is only configured to use...

Excluding Brute Force, my solver does not do guess work.

Without the Hidden Windoku Constraints my solver does not completely solve it.

With these constraints defined it does. With all other solving techniques disabled this puzzle can be solved with only singles.

However, it may be considered unfair to use these Hidden Windoku Constraints as not all sudoku players would know about them. On the other hand - they do come in handy for puzzle creators/programmers, but their use (or not used) may alter the difficulty level.

[creint]

Copy paste less than 5 seconds.
Solve within 1 second 119 passes, single solution, with singles and reducers only
Minimal check within 14 seconds: Not minimal, can remove 48 different singles.
Minisat.exe is faster than Minisat.dll

Solution

Hidden Text: Show

Solve order for full 9x9: 9 2 8 5 3 4 7 1 6

Code: Select all

7 6 1 4 9 2 5 8 3       1 9 4 3 5 2 6 8 7       1 5 4 8 9 6 2 7 3
5 3 4 7 1 8 2 6 9       7 2 3 1 8 6 9 5 4       7 9 6 3 4 2 5 1 8
8 9 2 5 6 3 7 1 4       5 6 8 4 9 7 3 1 2       8 2 3 5 7 1 6 9 4
4 1 7 3 2 9 8 5 6       6 5 9 7 1 8 2 4 3       2 3 1 4 6 5 9 8 7
6 5 9 1 8 7 3 4 2       3 1 2 6 4 5 7 9 8       4 7 8 9 2 3 1 5 6
2 8 3 6 4 5 1 9 7       8 4 7 2 3 9 5 6 1       5 6 9 7 1 8 4 3 2
3 4 6 2 5 1 9 7 8       9 3 1 5 2 4 8 7 6       3 4 7 2 5 9 8 6 1
1 7 8 9 3 6 4 2 5       4 8 6 9 7 3 1 2 5       9 1 2 6 8 7 3 4 5
9 2 5 8 7 4 6 3 1       2 7 5 8 6 1 4 3 9       6 8 5 1 3 4 7 2 9
                                                                 
                                                                 
                                                                 
8 9 3 1 6 7 4 5 2                               9 4 6 3 1 8 2 7 5
2 5 6 3 4 9 7 8 1                               5 7 2 9 4 6 8 1 3
7 4 1 8 5 2 9 3 6                               3 1 8 5 7 2 6 4 9
6 1 7 4 9 3 8 2 5             1 6 2             6 3 1 8 5 7 4 9 2
4 3 5 2 7 8 6 1 9             5 9 4             2 9 4 6 3 1 7 5 8
9 8 2 5 1 6 3 4 7             3 8 7             8 5 7 2 9 4 1 3 6
5 7 4 9 3 1 2 6 8                               1 8 5 7 2 9 3 6 4
3 6 8 7 2 5 1 9 4                               4 6 3 1 8 5 9 2 7
1 2 9 6 8 4 5 7 3                               7 2 9 4 6 3 5 8 1
                                                                 
                                                                 
                                                                 
6 5 7 4 8 9 1 2 3       6 7 5 2 4 9 8 3 1       7 9 3 8 2 5 1 4 6
3 2 4 1 7 6 5 8 9       4 8 3 1 6 7 5 2 9       5 1 2 9 6 4 7 8 3
9 1 8 5 2 3 4 7 6       1 2 9 5 3 8 4 6 7       8 6 4 7 1 3 5 2 9
5 7 2 8 6 1 9 3 4       5 6 7 4 2 3 1 9 8       2 3 1 5 7 9 8 6 4
4 3 1 9 5 2 8 6 7       9 3 4 8 7 1 6 5 2       9 8 5 3 4 6 2 7 1
8 6 9 7 3 4 2 5 1       8 1 2 9 5 6 3 7 4       6 4 7 1 8 2 9 3 5
2 4 6 3 1 5 7 9 8       7 5 8 3 9 4 2 1 6       1 2 9 6 3 8 4 5 7
7 9 3 2 4 8 6 1 5       2 4 6 7 1 5 9 8 3       3 7 8 4 5 1 6 9 2
1 8 5 6 9 7 3 4 2       3 9 1 6 8 2 7 4 5       4 5 6 2 9 7 3 1 8


[tarek]

If you recall SudoKai we discovered the extra hidden houses when we were discussing the Sudoku Parquet variant ( I still love it) when we managed to show that it is a sudoku with extra overlapping regions, we discovered these extra regions which can be used to solve without guessing

You will find it very common in most variants

Tarek

[SudoKai]

...the extra hidden houses when we were discussing the Sudoku Parquet variant...

I enjoy Sudoku Parquet myself.

I am just wondering where or how these hidden rules should be defined and used correctly.

Should they be hard coded into the Sudoku software rules or should they rather be used by people solving Sudoku variants/puzzles?

Currently my software considers all Sudoku rules as visible/known to the user. I might have to add the ability to mark Sudoku rules as either visible/known or hidden/concealed.

Either way, this gives me an idea for a side project to go and seek hidden Sudoku constraints.

[Mathimagics]

Hidden houses, whether for Windoku, or for Jigsaws, are really a solving technique/strategy, not a rule.

A "rule" is a constraint specific to a puzzle type, but the existence of "hidden houses" is just a property, a logical consequence of the rules, which may or may not be known to the solver, but is not actually required to solve the puzzle.

The accepted Windoku rule is "place a different digit in every cell of each row, column, Sudoku 3x3 box, and the 4 indicated additional 3x3 boxes".

The 5 "hidden" houses are really a strategy that can be exploited by the solver to find a solution more quickly - for software it just makes sense to define the additional houses, it's more efficient.

For human solvers, it obviously helps, but I don't think it's necessary to mention it when providing a puzzle - you can always inform the would-be solver about this, and perhaps point them to the Windoku Strategy page for information.

To avoid ambiguity, perhaps it's also wise if you only describe a puzzle as "singles only" when it is has this property wrt to the standard puzzle rules. And perhaps we should all adopt this practice.

[tarek]

I agree that with these puzzles only the declared visible houses are mentioned. The hidden houses can be deduced by the solver. With windoku as it is well known and the hidden houses mentioned so many times, the situation can be a bit different where these hidden houses are almost non hidden.

The difficulty and rating for the public has to be based on the declared visible houses unless explicitly mentioned. You can design a puzzle with that in mind that has a difficulty of x using the declared visible houses that can be solved with a difficulty of y when the hidden puzzles are known

[Hajime]

Another JS NC GW PAX, but now inspired by Princess Amy's 12 different Sudoku's around a clueless Flower.

12 center boxes of outer Sudoku's are outer boxes of the clueless flower.

2 puzzles:
- the first is easy (Singles Only) and each Sudoku can be solved independent
- the second is harder, clues from the Flower and more (simple elimination) methods are needed


In puzzle code: The outer Sudoku's are in reading order. The clueless flower at the end:

Code: Select all

#16//k4,JS/t4,W/Ac4,JS/B22,G/AL22,G/B40,X/AL40,X/B58,A/AL58,A/K76,NC/T76,P/AC76,OE/N10,N+2/E28,N+2/w28,N+2/N46,N+2
.7...5........6........2...2.....3.5.1.....79........45..81.......2....6..56...97
CCBBBBBAAECBBBBAADECCCCCAADEEECFFFADEGGFFFAADEGFFFHDDDEGGHHHHHDEGGIIIIHDGGIIIIIHH
15.....2.....3...8.2....59.......8....4......27.......3.5.....9......7......4.1..
....3....73..1...91........3.....6..6.....8..2.4.........8..24.....5...8....9...7
AABBBBBCCDAABBBBCEDAACCCCCEDAFFFCEEEDAAFFFGGEDDDHFFFGEDHHHHHGGEDHIIIIGGEHHIIIIIGG
6...5..3.7.......8......7.6.6.......5.......9..4....5...94.71......9...7..1.32...
...9.42....78..1.3.637......3....9.5.......4...4...7..2.5..8........9..4....675..
...63...88......97.2...4...2.....7....5........3...6.1.............13...6..4..2..
.5....17.213.....5.9......2......86...9.....3........9.....1........92..64...3...
.2....3.9..4.......3..4.8..94.....6...2....1..1.......6...7.......1........6.35.8
..1..8.4......19...6...732..37......5.4...6.36.....28..5.........81.........4....
.6...3....3..............6...1............9.56.8.....3...25.....9.7.............9
.6874.........2.1.1.........2....97.47....2..8.9.......8.1.....5.4.9.............
2.....4.....1..........5.1..8......1..9..............9.73....8....7....4.........
EOEOOEEOOEOOOEEEOOOOEEOOEOEOEEEOOOEOOOOEEOOEEOEEEOOEOOEOOOEEOEOEEOOOEOOEOEOOEOOEE
.................................................................................
.................................................................................
.................................................................................
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The second: the Updown & LeftRight symmetry makes it a bit easier


In puzzle code:

Code: Select all

#16//k4,JS/t4,W/Ac4,JS/B22,G/AL22,G/B40,X/AL40,X/B58,A/AL58,A/K76,NC/T76,P/AC76,OE/N10,N+2/E28,N+2/w28,N+2/N46,N+2
..........12............5..6.......9........88..........6..72.198..2...7...6.....
CCBBBBBAAECBBBBAADECCCCCAADEEECFFFADEGGFFFAADEGFFFHDDDEGGHHHHHDEGGIIIIHDGGIIIIIHH
.36.7.18..........1...8...2..........8.....9...3...2...1..9..5.7..5.8..1.........
...............86...5......9.......82................16.72..4..1...5..86.....4...
AABBBBBCCDAABBBBCEDAACCCCCEDAFFFCEEEDAAFFFGGEDDDHFFFGEDHHHHHGGEDHIIIIGGEHHIIIIIGG
..6.1.2...5..628...9.8............7..........5.......9....98.1...4...........1745
..3.2.8....275..9......3.7..9................3.......2.6.19..........9..9576.....
..6.1.7..97..8...2..3............6..........1......8....2......79..5...8..1.9.3..
..9.8.6..2...1..45......8....1......3..........7............4..8...5..36..3.6.5..
.....1396..9..........36.7.3.......1................2..5.1......7..841....8.6.9..
9543...........5...6.52....8.......7..........1............5.1...318..6...6.3.4..
...7.....75..9...8..6..47.11................76.......4......3...69...............
.........2..9.1..8.3..5..6...1...4...7.....2..........1...2...4..........46.1.79.
.....6...1...2..358.45..6..........26........5.......7..6............45..........
OOEOEEOEOOEOOEEEOOEOEOOOEEOEOOEOOOEEEEOOOOOEEOOEEEEOOOEEEOOOOOEOEOEOOEOEOOOEEEEOO
.................................................................................
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Larger pictures to print (with or without pencil marks) can be found at the SiSeSuSo website:
https://sites.google.com/site/sisesuso/examples/jsbncgwpax-12

Have fun

Edit: url's and images redirected to dropbox