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        riddles >> general problem-solving / chatting / whatever >> Rubik's Cube as a 2D puzzle (is this new?)
        
(Message started by: amichail on Feb 3^rd, 2009, 12:56pm)

Title: Rubik's Cube as a 2D puzzle (is this new?)
Post by amichail on Feb 3^rd, 2009, 12:56pm

It seems similar to a Rubik's Cube, but doesn't require 3D thinking (and so might be more suitable for a 2d computer display):

1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3

4 4 4 5 5 5 6 6 6
4 4 4 5 5 5 6 6 6
4 4 4 5 5 5 6 6 6

7 7 7 8 8 8 9 9 9
7 7 7 8 8 8 9 9 9
7 7 7 8 8 8 9 9 9

You can rotate an entire row or column of 9 numbers, but rotations must be done 3 steps at a time.

For example, rotating the second row to the right yields:

1 1 1 2 2 2 3 3 3
3 3 3 1 1 1 2 2 2
1 1 1 2 2 2 3 3 3

4 4 4 5 5 5 6 6 6
4 4 4 5 5 5 6 6 6
4 4 4 5 5 5 6 6 6

7 7 7 8 8 8 9 9 9
7 7 7 8 8 8 9 9 9
7 7 7 8 8 8 9 9 9

Is this an original puzzle? If not, where I can find info on it?

Title: Re: Rubik's Cube as a 2D puzzle (is this new?)
Post by ThudanBlunder on Feb 3^rd, 2009, 1:13pm

on 02/03/09 at 12:56:33, amichail wrote:

Is this an original puzzle? If not, where I can find info on it?

No, it's called Sudoku. :P

Title: Re: Rubik's Cube as a 2D puzzle (is this new?)
Post by amichail on Feb 3^rd, 2009, 1:15pm

on 02/03/09 at 13:13:19, ThudanBlunder wrote:

No, it's called Sudoku. :P

While it has nothing to do with Sudoku, I can see that the layout could give people that impression.

Title: Re: Rubik's Cube as a 2D puzzle (is this new?)
Post by ThudanBlunder on Feb 3^rd, 2009, 1:16pm

on 02/03/09 at 13:15:06, amichail wrote:

While it has nothing to do with Sudoku, I can see that the layout could give people that impression.

As you haven't stated the objective, Sudoku is as good a name as any.

Title: Re: Rubik's Cube as a 2D puzzle (is this new?)
Post by amichail on Feb 3^rd, 2009, 1:18pm

on 02/03/09 at 13:16:12, ThudanBlunder wrote:

As you haven't stated the objective, Sudoku is as good a name as any.

The objective is the same as Rubik's cube: each grid must have only one number/color.

Title: Re: Rubik's Cube as a 2D puzzle (is this new?)
Post by Grimbal on Feb 4^th, 2009, 2:43am

It is like a Rubik's Doughnut.

Well, the numbrosia game has some similarity. Rotations are not limited to 3, you can add or remove values to a row or column and the goal is to minimize the number of moves.

But I just realized that cells are restrained to 9 position. In the following picture you can see that letters don't mix. A's remain A's, B remains B's, etc. Each letter is called an orbit.

That means that the solution is unique (each orbit has only one of each digit. And with a little care, you can solve each orbit individually.


a b c   a b c   a b c
d e f   d e f   d e f
g h i   g h i   g h i

a b c   a b c   a b c
d e f   d e f   d e f
g h i   g h i   g h i

a b c   a b c   a b c
d e f   d e f   d e f
g h i   g h i   g h i

Title: Re: Rubik's Cube as a 2D puzzle (is this new?)
Post by amichail on Feb 4^th, 2009, 12:01pm

on 02/04/09 at 02:43:13, Grimbal wrote:

Well, the numbrosia game has some similarity. Rotations are not limited to 3, you can add or remove values to a row or column and the goal is to minimize the number of moves.

I'm the one who created Numbrosia, but it has a problem: it's too easy to solve if you don't care about the number of moves.

It seems that people generally just want a hard puzzle to solve, so I want to come up with something difficult.

Title: Re: Rubik's Cube as a 2D puzzle (is this new?)
Post by Grimbal on Feb 4^th, 2009, 3:04pm

Uh, yes, I realized afterward that it was you. No wonder it looks familiar.

As for the difficulty, I'd rate this one as easy.

Title: Re: Rubik's Cube as a 2D puzzle (is this new?)
Post by Hippo on Apr 5^th, 2009, 8:42am

on 02/04/09 at 15:04:39, Grimbal wrote:

Uh, yes, I realized afterward that it was you. No wonder it looks familiar.

As for the difficulty, I'd rate this one as easy.

Yes, it's easy ... if the permutation on each orbit is even, you can easily move numbers in given orbit to their positions in 1,2,3,4,5,7,6 order each in at most 4 moves (rotation involving only 3 pieces). This gives 4*7*9 moves upper bound for entire puzzle. It can be made faster by not doing orbits independently ...