## Sudoku Revenge Cube

Everything about Sudoku that doesn't fit in one of the other sections

### Sudoku Revenge Cube

Anybody has heard of the term "Rubik's Revenge"? Basically it's a 4x4x4 cube that works on the same priniciple as the normal 3x3x3 Rubik's Cube, only 10 times harder. There was also a 5x5x5 "Professor's Cube" offered in the market but apparently it was too difficult and was reserved only for professors with at least a Fields Medal nomination or 50+ world recognized publications in the fields of Mathematics or Computer Science...

I just want to see, is it possible to construct a "sudoku" puzzle on such a cube, such that all 6 4x4 faces and all 12 lines running around groups of 4 faces contain the cells 1 to 16? In other words:

Code: Select all
`                a01 a02 a03 a04                a05 a06 a07 a08                a09 a10 a11 a12                a13 a14 a15 a16b01 b02 b03 b04 c01 c02 c03 c04 d01 d02 d03 d04 e01 e02 e03 e04 b05 b06 b07 b08 c05 c06 c07 c08 d05 d06 d07 d08 e05 e06 e07 e08 b09 b10 b11 b12 c09 c10 c11 c12 d09 d10 d11 d12 e09 e10 e11 e12 b13 b14 b15 b16 c13 c14 c15 c16 d13 d14 d15 d16 e13 e14 e15 e16                 f01 f02 f03 f04                f05 f06 f07 f08                f09 f10 f11 f12                f13 f14 f15 f16`

The follow lines all contain the numbers 1 to 16:
b[01..04]+c[01..04]+d[01..04]+e[01..04]
a[01,05,09,13]+c[01,05,09,13]+f[01,05,09,13]+e[16,12,08,04]
a[13..16]+d[01,05,09,13]+f[04..01]+b[16,12,08,04]

It'd be great fun to make such a Rubik's Revenge cube with a full sudoku grid replacing the coloured squares!

PS: To impose greater restrictions, perhaps we could force each of the 6 face squares to be 4x4 magic squares!
udosuk

Posts: 2698
Joined: 17 July 2005

Synchronicity...

I was lying awake thinking about exactly the same "Sudoku-cube" at almost exactly the same time that you posted your message..

I haven't programmed it up yet but it should be easy to check if it is possible and if so to make up some puzzles along those lines...

How to play it though? Would need to sell some little paper cubes for people to write on!

Cheers

Gordon
gfroyle

Posts: 214
Joined: 21 June 2005

The short answer is yes. I have seen a computer program that generates puzzles like this. But as it's over a month since I last visited these forums, the link has just faded into memory...

And as for your magic square suggestion, I don't think it's possible to do that, becase iirc there's only 9 different arrangements for 4x4 magic squares...
Lardarse

Posts: 106
Joined: 01 July 2005

Lardarse wrote:And as for your magic square suggestion, I don't think it's possible to do that, becase iirc there's only 9 different arrangements for 4x4 magic squares...

No you're thinking 3x3 magic squares. There's only 1 which means 8 if you count reflections and rotations. There are 880 4x4 magic squares.
ab

Posts: 451
Joined: 06 September 2005

Guys, thanks so much for all your response, and nice to know I'm having similar thoughts with a guru like Gordon.

It's true there are 880 different 4x4 magic squares (reflections & rotations discarded). However, if you only want pan-magic (diabolic) ones and consider row/column exchanges, there are only 3 essentially different models. Could Lardarse be thinking along that line when he claimed there are "only 9 arrangements"? Of course, on the cube there need not be only essentially different pan-magic squares...

As for the commercial point of view, I think it's reasonable to sell those sudoku puzzles cubes as foldable cardboards, unless you want people to play them as Rubik's Revenge Cubes too!
udosuk

Posts: 2698
Joined: 17 July 2005