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 solution by Charlie)

The basic solution provided fails in the same manner as did broll's post...there are only 11 different integers, with 1 being duplicated. The problem states that the two six sided dice are marked with 12 different integers, thus a hypothetical best solution would have the highest values on one die being 17 and 19 on the other.  My attempts at finding such has failed, thus I adopted broll's base solution with offset to provide a possible 16-20 solution.

Edited on October 31, 2011, 3:27 am

Posted by Dej Mar on 2011-10-31 03:08:23