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Sudoku 6D
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=13&t=1468
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Author:  Mathimagics [ Sun Jan 06, 2019 11:15 am ]
Post subject:  Sudoku 6D

Here is a 6-dimensional (and still printer-friendly) Sudoku. Each cell belongs to 6 houses. The dimensions/houses are:

  • rows
  • columns
  • boxes
  • positions in boxes (SudokuP, aka Disjoint Groups (ugh), aka Colour Sudoku)
  • "windows" (Windoku, aka SudokuW)
  • jigsaw regions (SudokuJ)

All should be readily apparent in the grid layout. The 4 standard Windoku boxes are marked with *'s. The SudokuP houses are not marked, but they are intuitively obvious, so should be easy to work with.

This one is singles-only, but should still keep you busy!

Attachment:
Sudoku6D-Sample-001.png
Sudoku6D-Sample-001.png [ 13.35 KiB | Viewed 9150 times ]

Author:  enxio27 [ Sun Jan 06, 2019 7:26 pm ]
Post subject:  Re: Sudoku 6D

Oooh, looks like fun! The "6D" description almost scared me off, but I'm glad I took a closer look!

Author:  Mathimagics [ Mon Jan 07, 2019 10:06 am ]
Post subject:  Re: Sudoku 6D

.
Sorry if I am playing fast and loose with the language somewhat!

By dimension I just mean the number of houses each cell can belong to. So standard Sudoku and standard Jigsaw are 3D, Windoku and SudokuP are 4D, etc.

Incomplete house sets are fractional dimensions (not be confused with fractal dimension). So for X-mode (diagonals), we would add 0.2 (or should that be 0.222222222...?).

I might just do that in the next example, a Sudoku 6.2D, how about that?

I'm hoping you might like to see a harder puzzle at some stage, as we can make these multi-D puzzles quite tough!

Author:  enxio27 [ Mon Jan 07, 2019 4:53 pm ]
Post subject:  Re: Sudoku 6D

Mathimagics wrote:
Sorry if I am playing fast and loose with the language somewhat!


No worries! I figured it out after I looked at it.

Quote:
I might just do that in the next example, a Sudoku 6.2D, how about that?

Sounds interesting!

Quote:
I'm hoping you might like to see a harder puzzle at some stage, as we can make these multi-D puzzles quite tough!

My personal preference is that the more constraints (dimensions) a puzzle has, the less difficult it should be. The additional constraints add enough complexity to make up for a lack of difficulty, IMHO. Others might see it differently, though.

If you can add killers to your generator, you would have the attention of nearly everyone on this forum. ;)

Author:  Mathimagics [ Tue Jan 08, 2019 2:49 am ]
Post subject:  Re: Sudoku 6D

enxio27 wrote:
My personal preference is that the more constraints (dimensions) a puzzle has, the less difficult it should be. The additional constraints add enough complexity to make up for a lack of difficulty, IMHO. Others might see it differently, though.

Good point, and I think that tarek made a similar remark … I may have even made one myself!

enxio27 wrote:
If you can add killers to your generator, you would have the attention of nearly everyone on this forum. ;)

You mean there are more than 3 of us? :shock:

Seriously, though, "Killer 6D" is an excellent idea! 8-)

Hmm... now where did I put that hacksaw?

Author:  Andrew [ Tue Jan 15, 2019 5:59 am ]
Post subject:  Re: Sudoku 6D

Mathimagics wrote:
You mean there are more than 3 of us? :shock:
HATMAN is a fairly regular puzzle poster in this forum. azpaull, wellbeback and I are fairly regular participants. On the Killer Puzzles forum Ed is now the main puzzle poster with wellbeback and I the main posters of walkthroughs.

I'll try your puzzle once I've caught up with Assassins on the Killer Puzzles forum, plus I've still got a couple of HATMAN's puzzles on this forum to catch up with.

Author:  Mathimagics [ Tue Jan 15, 2019 1:49 pm ]
Post subject:  Re: Sudoku 6D

Thanks, Andrew.

Cheers
MM

Author:  Andrew [ Thu Mar 21, 2019 7:59 pm ]
Post subject:  Re: Sudoku 6D

Thanks for the puzzle Mathimagics. As you said it's singles-only; in fact naked singles only.

Straightforward:
I started by eliminating candidates from the rows, columns, box (nonets), jigsaws and standard Windoku windows, for all the given numbers.
Then it was just naked singles, remembering to make the necessary candidate eliminations as described above.
I didn't need to use the SudokuP condition, although that might have made it slightly quicker. I can see from the solution that condition applies.

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

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