16 Dec 2009 18:05

## Help requested: Rubik's-Cube type problem related to an art project I'm doing

If you could answer this question for me, I would be greatly appreciative. It is related to an art project that I'm doing.  I can't answer it.

Let's say you have a hat containing 9 marbles of different shades of gray, with the shades numbered 1 through 9. Using these 9 marbles, one can obtain 84 unique combinations of three marbles per combination.

Question: Is there a way of listing these 84 combinations (of three marbles per combination) so that BOTH of the following criteria are met:
1. On the list, each combination has two of the same marbles as the one below it.
Example:
combination 1: 1, 2, 3
combination 2: 1, 2, 4
combination 3: 1, 3, 4
combination 4: 2, 3, 4
combination 5: 2, 3, 5

2. Like in the example above, as you move from one combination to the next on the list, the one marble that is different will have changed by only one integer.

Thank you very much for your assistance.

Sincerely,
Hal

__._,_.___