Hyperdoku

theonetruepath · Posted: Mon Mar 13, 2006 3:27 am Post subject: Hyperdoku

I suggested this a few months ago in rec.puzzles, and finally someone created an app which implements the idea, although apparently independently:

Modify an ordinary Sudoku by including the extra requirement that the 9 groups defined by 'same co-ordinate within each 3x3' also have the digits 1 to 9.

In other words, the 3x3s are in fact slices of a 3x3x3x3 hyperbox.

Andrew Hood at www.4dsudoku.com has implemented this.

Anyways.... this is probably an easy restriction/feature to add to an existing app, I'm thinking of 'Simple Sudoku' here Angus. Hardly any UI change, just a little check-box: '4D', and another set of groups to add to the logic.

It would be nice also to have a feature to switch rows/columns and boxes/hyperboxes to aid visualisation.
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Patrick Hamlyn posting from Perth, Western Australia
Windsurfing capital of the Southern Hemisphere

Moschopulus · Posted: Tue Mar 14, 2006 12:32 am Post subject:

Also known as sudoku-DG (disjoint groups)

I posted on it here:

http://www.sudoku.com/forums/viewtopic.php?t=3284

there are other links there to where it has been already mentioned.

SudokuPat · Posted: Mon Mar 20, 2006 10:35 pm Post subject:

It's a Java Sudoku ?
it's same of Director sudoku !
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SudokuPat
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pablo · Posted: Wed Mar 22, 2006 10:37 am Post subject: Re: Hyperdoku

[quote] Modify an ordinary Sudoku by including the extra requirement that the 9 groups defined by 'same co-ordinate within each 3x3' also have the digits 1 to 9.

In other words, the 3x3s are in fact slices of a 3x3x3x3 hyperbox.[/quote]
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You might be interested to read my contribution (with a lot of open questions) entitled "back to the roots - stripping the numbers" in the "mathematics of sudoku" discussion group. So some guys already answered one of my questions ...

Actually, what might be interesting to observe, is that you get this "group" (actually, it is a partition) from a "normal" Sudoku by writing out the blocks (the 3x3 boxes) as rows or columns, whatever you prefer, leaving the rest intact. Unfortunately, in a normal Sudoku, what you get isn't a Sudoku anymore, because the new rows and columns don't necessarily have the required property. So with this new kind of hyperdoku you have found a subclass of the "normal" Sudoku which has the added symmetry property: "exchanging rows (or columns) and boxes leads to another Sudoku". Quite interesting!

regards, pablo