cubical question

[muktakul_25]

27 cubes with 9 different colors of 3 cube group with same color. The objective is to assemble the smaller cubes into a one big cube with all nine colors displayed on all the six faces of the resultant cube.

[geo0939]

Rubic cube?

[crofter]

No - this is not the Rubik's cube, but very similar!

I reckon that this is impossible!

Each cube will need to go in ONE corner position, ONE edge position and ONE centre position to cover all six faces without duplication of colours. Since there are only six faces, there are only six centre positions. These can be filled with any SIX of the colours, but not all NINE.

Hence the conditions are impossible to satisfy! QED

[juliefer]

I think it can be done, crofter.

One colour is used for two of the corner cubes (diametrically opposite each other) with the third cube of this colour put in the middle of the larger cube, where it will not be seen - hence the colour shows once on each external face of the larger cube.

Six of the other colours are each used for one of the corners, for the centre position in one face and for one of the edge positions.

The last two colours are each put in three edge positions.

muktakul, it's easiest to start with the two diametrically opposite cubes, then put the other corner cubes into position, then the edge cubes and finish with the centre cubes. You may have to rearrange the edge and centre ones a few times but, as long as you arrange the two colours that are only used for edge cubes carefully, it should not take long.

I tried several times to post this answer yesterday evening but the system kept coming up �page not found� when I pressed the Submit button - still, better late than never!

[crofter]

Thanks for that julifer and apologies muktakul. I thought that the solution had to be more symmetrical than it was - if that makes sense!

[crofter]

muktakul - Following the words of juliefer, the nine colours can be labellled 1 through 9. The bottom layer is then:

7 8 9
4 5 6
1 2 3

The middle layer is:

5 6 4
3 1 2
8 9 7

And the top layer:

2 3 1
9 7 8
6 4 5

There are some neat cyclic patterns in the solution. It's like a 3D sudoku!

[juliefer]

Crofter, that was good of you to take the trouble to work out the complete answer.

Don't you think so, muktakul?

[crofter]

juliefer I thought that was the least I could do after giving such misinformation earlier!