4d sudoku - Does it exist?

For fans of Killer Sudoku, Samurai Sudoku and other variants

4d sudoku - Does it exist?

Postby Chris Saint » Mon Jun 23, 2008 9:42 am

Hi everyone,

Firstly I would like to introduce myself I’m Chris for Coventry. I'm massively into my Sudoku. So much in fact I went to Japan on my honeymoon and ended up playing it with some of the best in the world.

Anyway enough about me, I am constantly looking for new ways of playing Sudoku and I have heard from talking to other people from my local Sudoku club that there is a 4d version coming out soon they gave me this url http://www.4dsudoku.net/ .

The question I ask you all. Has anyone heard of it, understand the concept or does anyone have a prototype?
Chris Saint
 
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Postby Glyn » Mon Jun 23, 2008 10:27 am

Hi Chris

At a first glance this seems to be what is more commonly called Disjoint Groups Sudoku (Sudoku-DG). Try googling on that and you find more. The Sudocue and JSudoku programs handle this format and can generate puzzles as well.
Glyn
 
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Postby Chris Saint » Mon Jun 23, 2008 11:18 am

Hi Glyn,

Thanks for your reply I had a look but I couldn’t find a 4d version I’m starting to feel that it's a myth.
The concept sounds amazing though what do you recon.
Chris Saint
 
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Joined: 23 June 2008

Postby Glyn » Mon Jun 23, 2008 4:24 pm

If you have a look at the Wiki page Mathematics of Sudoku you'll pick up various links to material of interest, much of it back at this forum. The stuff relating to the Hypercubes is probably what you are after.
Glyn
 
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4DSudoku.net went Live on Saturday 20th Sept 08

Postby benjsellers » Mon Sep 22, 2008 11:36 am

Dear Chris,

I was pleased to see that you were a keen Sudoku player and I wanted to confirm that we launched both the hand-held physical puzzle and also the online game this weekend - we did an exclusive launch through the Daily Mail.

Please visit; www.4dsudoku.net and give it a go. Currently only four people have succeeded in completing the online version during beta testing and only 3 people have completed the hand-held version - I am pleased to say that I was the first to do both!

I hope you like it

Best regards Ben
benjsellers
 
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Postby Smythe Dakota » Tue Sep 23, 2008 2:44 am

It has been pointed out that vanilla sudoku can be thought of as 6-dimensional, with just 3 values allowed in each dimension.

A completed (or incomplete) sudoku grid can be thought of as a set S of sextuples of the form (a,b,c,d,e,f), where each of the six must have a value of 1, 2, or 3, and which is subject to various constraints.

To translate from vanilla to this picture, any time the digit d (1-9) appears in row r, column c, the following sextuple appears in the set S:

(rH,rL,cH,cL,dH,dL)

where r determines rH and rL as follows:
1 --> 1,1
2 --> 1,2
3 --> 1,3
4 --> 2,1
5 --> 2,2
6 --> 2,3
7 --> 3,1
8 --> 3,2
9 --> 3,3

-- and similarly for columns c and digits d.

Constraints would include:

A. No two elements of the set S may contain the same first four coordinates (i.e. any two elements of S must differ in at least one of the first four coordinates). Translation to vanilla: No cell may contain more than one digit.

B. No two elements of the set S may contain the same 1st, 2nd, 5th, and 6th coordinates. Translation to vanilla: No digit may appear more than once in the same row.

C. No two elements of the set S may contain the same 3rd, 4th, 5th, and 6th coordinates. Translation to vanilla: No digit may appear more than once in the same column.

D. No two elements of the set S may contain the same 1st, 3rd, 5th, and 6th coordinates. Translation to vanilla: No digit may appear more than once in the same box.

A completed grid would correspond to a set S (satisfying the above constraints and) having 81 elements. An incomplete grid would correspond to S having fewer than 81 elements.

Bill Smythe
Smythe Dakota
 
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