Two six sided dice are marked with 12 different integers, so that any number from 1 to 36 can be derived when both dice are thrown and the showing face-up values are added.
What is the lowest possible value of the highest number on one of the dice faces?

(In reply to Possible solution by broll)

broll's solution (1,3,5,7,9,11)(0,1,12,13,24,25) fails in that there are only 11 different integers [1 being duplicated]. By subtracting the value N from each face on the "higher" die and adding the value N to each face of the other, one can get a solution where there are 12 different integers.

The lowest non-duplicate pair that could sum to 36 would be 19 and 17. An offset of +6 and -6 OR +8 and -8 respectively to broll's offered solution will provide these values, yet will, again, yield only 11 different integers [with 7 or 17 being duplicated depending on the offset].

The solution may then be where broll's offered solution is offset by +5 and -5 respectively, giving a solution of (6,9,10,12,14,16)(-5,-4,7,8,19,20), with 20 being the lowest possible of the highest value.

Edited on October 30, 2011, 12:55 pm

Posted by Dej Mar on 2011-10-30 12:47:33