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 Post subject: 4x4x4 Sudoku Cube using colors instead of numbers
PostPosted: Sat Oct 25, 2008 2:46 pm 
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Joined: Sat Jan 27, 2007 7:43 pm
Location: Shelby Township, MI. USA
I have not been too impressed with the sudoku cubes that are currently on the market. For starters they can’t follow all of the sudoku rules. Sure, each face of the cube contains the numbers 1 through 9 but that’s it, the rules don’t go beyond one face at a time. If you follow a column or row all the way around the puzzle you find that there are 12 places for numbers, so the rules of placing numbers 1 through 9 with no duplicates just can’t be applied to a 3x3x3 cube. Also, I feel that the fact that printed numbers have an orientation to them gives away too much when solving one of these cubes. If you places to pieces next to each other and the printed orientation of the numbers does not match, then you know that these pieces are not positioned correctly.

In order to apply the sudoku rules across all surfaces of the puzzle I used a 4x4x4 cube and 16 numbers instead of 9. This allowed me to have all 16 numbers on each of the 6 faces, without duplicates. Also when you follow any column or row all the way around the puzzle, you will also find all 16 numbers.

The next thing I did was get rid of the numbers. In order to fix the printed number orientation issue I assigned a different color to each number. The16 different colored stickers have no orientation to help you with solving the puzzle.

When working out the pattern I first used numbers as it was much easier to arrange and rearrange them as necessary. I also took care not to have any duplicated edge or corner pieces. I then assigned the following colors to the numbers:

1 purple
2 bright orange
3 aqua
4 green
5 yellow
6 light gray
7 blue
8 light purple
9 bright green
10 red
11 tan
12 gray
13 orange
14 light blue
15 bright yellow
16 white

Any colors could be used so long as you use 16 different ones. I chose the colors above based purely on what I had available.

There may be more than one solution to this cube. I haven’t studied it enough to determine if that is the case or not. Also, I have not scrambled it yet, I’m kind of afraid to :)


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4x4x4 sudoku.jpg
4x4x4 sudoku.jpg [ 41.4 KiB | Viewed 2750 times ]
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4x4x4 sudoku pattern.jpg [ 94.54 KiB | Viewed 2630 times ]
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 Post subject: Re: 4x4x4 Sudoku Cube using colors instead of numbers
PostPosted: Sat Oct 25, 2008 3:36 pm 
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Joined: Mon Sep 29, 2008 9:41 am
Location: Spijkenisse, the Netherlands
Wow, you did that pretty smart. Really cool! Must be a very hard puzzle to solve though! And I agree with you that the 3x3x3 sudocube isn't much of a challenge. This is much sudokuier ( :? )

Sjoerd

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Negyvenháromtrillió-kétszázötvenkétbilliárd-hárombillió-kétszázhetvennégymiliárd-négyszáznyolcvankilencmillió-nyolcszázötvenhatezer :wink: )


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 Post subject: Re: 4x4x4 Sudoku Cube using colors instead of numbers
PostPosted: Sun Oct 26, 2008 2:37 am 
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Joined: Tue Mar 25, 2008 2:51 am
Location: Malibu, California
Nice job! The biggest problem with solving that would probably be that it doesn't even look solved when it is. You'd also probably have to use a LBL-type method (such as this one) just so that you could keep track of things. Or I suppose it's possible to memorize the solution :roll:

In any case, awesome puzzle, much more sudoku-like

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 Post subject: Re: 4x4x4 Sudoku Cube using colors instead of numbers
PostPosted: Sun Oct 26, 2008 11:10 am 
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Joined: Fri Oct 05, 2007 1:45 pm
Finally a true Sudoku Cube. Good work.


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 Post subject: Re: 4x4x4 Sudoku Cube using colors instead of numbers
PostPosted: Mon Oct 27, 2008 4:05 pm 
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Joined: Sat Dec 11, 2004 9:21 am
Location: Montreal, Quebec
last year, I proposed a number variation of this puzzle
solving the orientation problem by using diagonal labels:

viewtopic.php?f=1&t=8365

At some point I got a 4x4x4 Eastsheen and labelled it with off-the-shell
numbers:
Attachment:
MyLevel4D.jpg
MyLevel4D.jpg [ 432.53 KiB | Viewed 2452 times ]


I really like the colour scheme but agree that it is hard to tell which colour
might be missing on a certain face. I think numbers are easier to work with...

Since then, I have hired a summer student who worked on generating
such puzzles at random. You may want to check his web page:

http://www.cs.mcgill.ca/~tgeogh/cubegen.html

The issue with this puzzle is that either you know the solved state (and then
solving it is the same as any 4x4x4) or you don't (in which case finding the
solved state seems close to a nightmare!!!).

We are working on a computer program to solve a random (solvable) puzzle.
But are not there yet... Even, generating random solvable puzzle is a non-trivial
question !

This puzzle is a lot of fun !!!


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