OZONE Asylum
Forums
Server-Side Scripting - Oh my!
Creating Sudoku 3x3x3x3
This page's ID:
33324
Search
QuickChanges
Forums
FAQ
Archives
Register
Edit Post
Who can edit a post?
The poster and administrators may edit a post. The poster can only edit it for a short while after the initial post.
Your User Name:
Your Password:
Login Options:
Remember Me On This Computer
Your Text:
Insert Slimies »
Insert UBB Code »
Close
Last Tag
|
All Tags
UBB Help
I have tossed this idea around a bit quite some time ago. Some of the ideas that I have used in similiar work apply very well to this. Instead of thinking of a full sudoku cube, let's take a look at just one of the sub-cubes. You know, one of the 3x3x3 chunks. Any slice in any direction will have exactly 1 of each number. So, let's stack up some X's like so: [code] X.. ... ... ... .X. ... ... ... ..X [/code] If you stack those on top of each other into a cube, you will have one X in each plane in each direction. I think of them as 3d transversals. Know what I mean? Each number has to have that property in each sub-cube. Fit nine of those bad boys into a 3x3x3 space. The only way that I know how to do that is with a latin cube and an orthogonal. [code] cube0: 012 120 201 201 012 120 120 201 012 120 201 012 372 480 561 804 615 723 156 237 048 [/code] Those first 3 squares, when stacked, form a latin cube. Any plane in any direction is a latin square. Next, we have a latin square that is orthogonal to the first three squares. Putting that together, you can create a single sub-cube for a sudoku cube. We now have 0-8 in a cube. Anyway slice you take from that cube in any direction will be 0-8. Now we need two more cubes made almost exactly the same way. The only we are going to change is the orthogonal. Check it: [code] cube1: 012 120 201 201 012 120 120 201 012 201 012 120 615 723 804 237 048 156 480 561 372 cube2: 012 120 201 201 012 120 120 201 012 012 120 201 048 156 237 561 372 480 723 804 615 [/code] We now have 3 sub-cubes that we can assemble into a full-sized sudoku cube. Let's go back to the latin cube: [code] 012 120 201 201 012 120 120 201 012 [/code] So, that exists in 3d space. Where you see a 0, but in cube0. Where you see a 1, put in cube1. Where you see a 2, put in cube2. Tada. Instant sudoku cube. But is it fun or is it boring? Let's take a look at the sudoku at z=0: [code] 372 615 048 804 237 561 156 480 723 615 048 372 237 561 804 480 723 156 048 372 615 561 804 237 723 156 480 [/code] Wait...that's not z=0. That is actually z=3 and it is rotated 90 degrees. Not rotated as a whole, but the sub-cubes in-place. Yes, you can rotate in-place and things will still remain valid. Going to take the top row, just (0,4,8), and rotate them. Watch this: [code] ... ... 048 804 ... ... ... 480 ... 90 clockwise .8. 4.. ..0 .0. 8.. ..4 .4. 0.. ..8 [/code] See? still valid. And holds true for all of the numbers. Pretty cool, but can be annoying. There have been more than a few times when I have accidentally mixed-up an axis here-n-there. But, because remains valid, might not even notice. One day I mixed-up some indexing while playing with orthogonals and it took me over 2 weeks to notice because the validity remained intact. Anyways, back to this: [code] 372 615 048 804 237 561 156 480 723 615 048 372 237 561 804 480 723 156 048 372 615 561 804 237 723 156 480 [/code] Fun or boring? And bear in mind that all of the planes in the cube will look almost exactly like that. At a glance, I would call it boring. But I can see all sorts of patternliciousness in there just waiting to be taken advantage of. And those patterns exist in all 3 dimensions. Can they be manipulated? Can they be broken? So, possible combinations and all that. I have no clue. The tree of possibilities gets too big too quickly for me. I do know that some folks were working on the Min17 problem and completely reduced regular sudoku grids. No clue how they did it. Minimum clues with one solution? I imagine somewhere around 150. But that's a wild guess based on Min17. I might play with a sudoku cube to see if I can break it. You know, just to see if I can make each plane unique. Maybe.
Loading...
Options:
Enable Slimies
Enable Linkwords
« Backwards
—
Onwards »
Maximum Security
OZONE
DHTML/Javascript
Server-Side Scripting - Oh my!
CSS - DOM - XHTML - XML - XSL - XSLT
Stupid Basic HTML
Visual Therapy
Photoshop
Photoshop Pong, Anyone?
***WARNING*** BIG SIG APPROACHING
Photography
3D Modelling & Rendering
Multimedia/Animation
Print Graphics
Holding Pens
Philosophy and other Silliness
Outpatient Counseling
Site reviews!
Mad Scientists' Laboratory
Getting to know the Grail