## Soduko Cubes: For Sub-humans and Programmers

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### Soduko Cubes: For Sub-humans and Programmers

Soduko Cubes: For Sub-humans and Programmers

My long-time duplicate bridge partner frequently solves Soduko puzzles that are
published in the Washington Post. I mentioned that I had constructed a "Soduko
cube" and proceeded to describe the particulars. When finished with the explanation,
he said he would "rather have a root canal with power tools" than solve such a
puzzle. I went on to say that it wasn't really meant for humans, just sub-humans
and programmers.

Let me describe the particulars. The standard Soduko square is a 9x9 arrangement
of cells. The related Soduko cube is a 9x9x9 arrangement of 729 cells in three
dimensions.

The cube may be "sliced" in 27 ways:
1) Nine slices correspond to the front/back view.
2) Nine slices correspond to the left/right side view.
3) Nine slices correspond to the top/bottom view.

The 27 squares below are different slices of the first ever (to my knowledge)
Soduko cube. The digits in each square adhere to the usual row, column,
and 3x3 box permutation constraints.

Notice:
1) The top row of square (AY) is the same as the bottom row of (AZ).
2) The left column of (AY) is the same as the right column of (AX).
Same cells -- different views.

I did not know, but only suspected, that such a cube could be constructed,
and was quite pleased when the first solution appeared. Here it is:

Soduko Cube #1:

Code: Select all
`     Left Side Views        Front Views           Top Views           (X)                  (Y)                  (Z)    9 6 5 8 7 1 4 3 2    2 9 6 8 7 3 5 1 4    9 4 1 2 8 6 3 5 7    3 8 4 2 6 5 7 9 1    1 8 4 2 6 5 3 7 9    6 3 7 5 1 4 9 8 2    2 1 7 4 3 9 6 8 5    5 3 7 4 9 1 2 8 6    5 8 2 3 9 7 4 6 1    4 2 6 3 8 7 1 5 9    9 6 3 7 5 2 8 4 1    8 6 9 7 3 1 2 4 5(A) 8 9 1 6 5 2 3 7 4    4 5 2 6 1 8 9 3 7    7 5 4 9 2 8 1 3 6    7 5 3 1 9 4 2 6 8    8 7 1 3 4 9 6 5 2    1 2 3 4 6 5 8 7 9    5 4 9 7 1 3 8 2 6    6 1 5 9 3 7 4 2 8    4 1 8 6 5 2 7 9 3    6 7 2 5 4 8 9 1 3    3 4 8 1 2 6 7 9 5    3 7 5 1 4 9 6 2 8    1 3 8 9 2 6 5 4 7    7 2 9 5 8 4 1 6 3    2 9 6 8 7 3 5 1 4    4 3 8 6 5 2 1 7 9    3 7 5 1 4 9 6 2 8    3 7 6 4 5 1 2 9 8    7 2 1 3 9 4 5 6 8    9 6 2 3 8 7 4 5 1    8 2 5 7 3 9 1 4 6    5 9 6 7 1 8 2 4 3    8 4 1 5 2 6 9 3 7    4 1 9 6 2 8 7 3 5    3 7 5 9 4 1 8 2 6    5 2 4 8 6 1 7 9 3    2 3 1 5 4 6 9 8 7(B) 6 4 2 8 7 3 9 1 5    7 1 8 9 3 4 2 6 5    6 9 8 1 7 3 5 2 4    1 8 9 5 2 6 4 3 7    6 3 9 2 7 5 1 8 4    5 4 7 8 9 2 6 1 3    2 6 7 4 8 5 3 9 1    2 9 7 4 5 8 3 1 6    7 5 3 9 1 4 8 6 2    8 1 3 2 6 9 7 5 4    1 5 6 7 9 3 8 4 2    9 6 2 3 8 7 4 5 1    9 5 4 1 3 7 6 8 2    4 8 3 6 1 2 5 7 9    1 8 4 2 6 5 3 7 9    1 7 2 9 4 3 8 5 6    4 1 8 6 5 2 7 9 3    2 5 8 9 7 3 6 1 4    6 5 9 1 8 7 3 2 4    7 5 3 9 1 4 8 6 2    1 9 4 8 6 2 5 7 3    8 4 3 5 2 6 9 1 7    6 2 9 7 3 8 1 4 5    7 6 3 1 4 5 8 2 9    9 1 8 2 6 5 7 4 3    1 8 7 4 9 3 5 2 6    4 7 5 2 8 9 3 6 1(C) 5 3 7 4 1 9 6 8 2    3 9 6 5 2 7 4 1 8    3 1 2 6 5 4 7 9 8    2 6 4 7 3 8 5 9 1    2 4 5 1 8 6 3 7 9    9 8 6 3 1 7 4 5 2    3 8 1 6 9 2 4 7 5    8 3 4 2 6 1 9 5 7    6 2 9 7 3 8 1 4 5    4 9 5 3 7 1 2 6 8    9 7 2 8 4 5 6 3 1    8 4 1 5 2 6 9 3 7    7 2 6 8 5 4 1 3 9    5 6 1 3 7 9 2 8 4    5 3 7 4 9 1 2 8 6    2 5 3 7 9 4 6 1 8    1 2 3 4 6 5 8 7 9    4 3 9 6 2 7 1 8 5    4 7 6 5 1 8 9 3 2    5 4 7 8 9 2 6 1 3    2 7 1 3 8 5 4 6 9    9 8 1 2 6 3 7 5 4    9 8 6 3 1 7 4 5 2    6 5 8 9 1 4 3 7 2    6 3 9 1 5 2 4 8 7    7 1 5 2 4 6 9 3 8    3 9 2 1 7 8 6 5 4(D) 1 2 8 3 4 7 5 9 6    2 3 9 7 8 1 5 4 6    8 4 6 5 3 9 2 1 7    5 4 7 6 8 9 1 2 3    4 6 8 9 5 3 7 2 1    7 1 5 2 4 6 9 3 8    7 1 5 8 3 6 2 4 9    3 5 2 6 7 9 1 8 4    1 8 7 4 9 3 5 2 6    3 6 4 9 2 5 8 7 1    8 9 1 5 3 4 2 6 7    5 2 4 8 6 1 7 9 3    8 9 2 4 7 1 3 6 5    6 7 4 1 2 8 3 9 5    9 6 3 7 5 2 8 4 1    8 1 9 3 2 6 5 4 7    7 5 4 9 2 8 1 3 6    8 6 5 1 4 9 7 2 3    5 3 2 4 7 9 1 8 6    6 9 8 1 7 3 5 2 4    9 4 3 2 7 6 8 5 1    7 6 4 8 5 1 3 2 9    3 1 2 6 5 4 7 9 8    1 2 7 8 5 3 6 9 4    2 8 1 7 3 4 9 6 5    8 4 6 5 3 9 2 1 7    6 8 4 3 9 5 1 7 2(E) 4 7 5 9 6 8 2 3 1    5 7 1 4 6 2 3 8 9    5 7 1 4 6 2 3 8 9    3 9 6 2 1 5 8 7 4    9 2 3 8 1 7 4 6 5    2 3 9 7 8 1 5 4 6    9 2 8 1 4 7 6 5 3    1 8 9 3 4 5 6 7 2    3 9 6 5 2 7 4 1 8    1 5 7 6 8 3 4 9 2    4 6 7 2 8 1 9 5 3    7 1 8 9 3 4 2 6 5    6 4 3 5 9 2 7 1 8    2 3 5 7 9 6 8 4 1    4 5 2 6 1 8 9 3 7    6 4 7 1 8 5 2 9 3    8 6 9 7 3 1 2 4 5    7 1 2 5 3 8 9 4 6    1 9 8 6 3 2 4 7 5    2 3 1 5 4 6 9 8 7    5 8 6 4 9 1 2 3 7    3 2 5 9 4 7 8 6 1    4 7 5 2 8 9 3 6 1    3 9 4 7 6 2 5 1 8    7 5 4 8 9 6 3 1 2    3 9 2 1 7 8 6 5 4    1 5 7 6 2 4 8 9 3(F) 9 6 3 5 2 1 7 4 8    6 8 4 3 9 5 1 7 2    9 2 3 8 1 7 4 6 5    8 1 2 4 7 3 6 5 9    1 5 7 6 2 4 8 9 3    4 6 8 9 5 3 7 2 1    4 3 6 2 5 9 1 8 7    7 4 6 8 1 2 5 3 9    2 4 5 1 8 6 3 7 9    2 8 9 7 1 4 5 3 6    5 2 3 9 6 7 4 1 8    6 3 9 2 7 5 1 8 4    5 7 1 3 6 8 9 2 4    9 1 8 4 5 3 7 2 6    8 7 1 3 4 9 6 5 2    3 9 4 2 1 8 7 6 5    5 8 2 3 9 7 4 6 1    5 2 3 7 9 4 8 6 1    2 1 7 9 5 6 8 4 3    4 1 9 6 2 8 7 3 5    4 6 8 1 2 3 7 9 5    6 5 8 3 7 4 1 9 2    7 6 3 1 4 5 8 2 9    9 7 1 5 8 6 2 4 3    1 4 3 6 2 9 5 7 8    6 5 8 9 1 4 3 7 2    7 4 6 8 1 2 5 3 9(G) 7 8 6 1 3 5 4 2 9    1 2 7 8 5 3 6 9 4    1 8 9 3 4 5 6 7 2    9 2 5 8 4 7 3 1 6    3 9 4 7 6 2 5 1 8    3 5 2 6 7 9 1 8 4    8 7 2 5 6 1 9 3 4    9 7 1 5 8 6 2 4 3    8 3 4 2 6 1 9 5 7    5 3 1 4 9 2 6 8 7    2 3 5 4 7 9 1 8 6    2 9 7 4 5 8 3 1 6    4 6 9 7 8 3 2 5 1    8 4 6 2 3 1 9 5 7    6 1 5 9 3 7 4 2 8    5 8 6 4 3 7 9 2 1    6 3 7 5 1 4 9 8 2    6 8 4 3 1 2 5 7 9    9 4 3 8 2 1 6 5 7    8 2 5 7 3 9 1 4 6    7 1 9 6 5 8 3 2 4    1 7 2 6 9 5 4 3 8    1 9 4 8 6 2 5 7 3    2 3 5 4 7 9 1 8 6    8 6 7 5 1 3 2 9 4    2 7 1 3 8 5 4 6 9    5 2 3 9 6 7 4 1 8(H) 2 5 9 7 8 4 1 6 3    9 4 3 2 7 6 8 5 1    4 6 7 2 8 1 9 5 3    4 3 1 9 6 2 7 8 5    5 8 6 4 9 1 2 3 7    8 9 1 5 3 4 2 6 7    6 9 4 3 7 8 5 1 2    4 6 8 1 2 3 7 9 5    9 7 2 8 4 5 6 3 1    7 2 8 1 5 6 3 4 9    7 1 9 6 5 8 3 2 4    1 5 6 7 9 3 8 4 2    3 1 5 2 4 9 8 7 6    3 5 2 9 4 7 6 1 8    3 4 8 1 2 6 7 9 5    7 2 1 5 6 9 3 8 4    9 4 1 2 8 6 3 5 7    1 9 7 8 6 5 4 3 2    8 6 5 7 4 3 2 1 9    3 7 6 4 5 1 2 9 8    3 5 2 9 4 7 6 1 8    4 3 9 1 8 2 5 7 6    2 5 8 9 7 3 6 1 4    8 4 6 2 3 1 9 5 7    5 9 2 4 7 8 6 3 1    4 3 9 6 2 7 1 8 5    9 1 8 4 5 3 7 2 6(I) 3 1 4 2 9 6 8 5 7    8 6 5 1 4 9 7 2 3    2 3 5 7 9 6 8 4 1    6 7 8 3 5 1 9 4 2    7 1 2 5 3 8 9 4 6    6 7 4 1 2 8 3 9 5    1 5 3 9 2 4 7 6 8    5 2 3 7 9 4 8 6 1    5 6 1 3 7 9 2 8 4    9 4 6 8 3 7 1 2 5    6 8 4 3 1 2 5 7 9    4 8 3 6 1 2 5 7 9    2 8 7 6 1 5 4 9 3    1 9 7 8 6 5 4 3 2    7 2 9 5 8 4 1 6 3`

1) Square (AY) is the solution to the puzzle originally published in
the Washington Post on August 21, 2005.

2) The standard Soduko square has 27 permutation constraints.
The Soduko cube has 486 permutation constraints, some of which
apply to multiple slices.

3) My next project, to please myself and for the amusement of the
Soduko community is to make a puzzle with a Soduko cube as the answer.
Are there any sub-humans or programmers up to the challenge?

holdout

Posts: 35
Joined: 30 August 2005
Location: Bowie, Maryland USA

### Re: Soduko Cubes: For Sub-humans and Programmers

holdout wrote:My next project, to please myself and for the amusement of the Soduko community is to make a puzzle with a Soduko cube as the answer.

One simple but-not-too-interesting unique-solution "sudoku cube" puzzle would consist of the solution cube with all six face-layers removed (i.e. the 7x7x7 "core" of the above cube). It could probably be carved up quite a bit more, I guess.
r.e.s.

Posts: 337
Joined: 31 August 2005

Sorry if I've misunderstud this, but as far as I can tell, it's the same idea as the "Dion Cube" that The Telegraph did maybe six months ago. There ought to be some information on it at www.sudoku.org.uk, so maybe you could check and tell me if I've misunderstood your idea.
PaulIQ164

Posts: 533
Joined: 16 July 2005

To PaulIQ164:

I did a Google search on "Dion Cube" and found your reference.
Yes, it appears that I have re-discovered the same thing.
Thank you.
holdout

Posts: 35
Joined: 30 August 2005
Location: Bowie, Maryland USA

Still impressive ... and nicely presented as well.
Nick67

Posts: 113
Joined: 24 August 2007