Two standard dice are renumbered so that each die is different, but together the pair still gives the same probabilities for rolling sums of 2 to 12 as a standard pair.

If each die is numbered with integers all greater than 0, then what are the numbers on the renumbered dice?

One possibility:

1 2 2 3 3 4
1 3 4 5 6 8

    1   3   4   5   6   8
  |
1 | 2   4   5   6   7   9
  |
2 | 3   5   6   7   8  10
  |
2 | 3   5   6   7   8  10
  |
3 | 4   6   7   8   9  11
  |
3 | 4   6   7   8   9  11
  |
4 | 5   7   8   9  10  12

Posted by Thalamus on 2004-07-20 12:06:25