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 Solving the wrong problem by Steve Herman)

Your idea that 6 would be the answer if the dice faces were (1,2,3,4,5,6) and (0,6,12,18,24,30), I believe, is "off".

As negative values are permitted (in the phrasing of the problem), one could have the first die offset by a huge negative value and the other an equal positive value and still provide the same sums of 1 to 36. Thus there would be no definitive lowest value of the highest value on one of the die faces. I rather interpreted that the value sought is the number of the highest value of one of both dice, and of this value, the lowest possible.  In your example (if duplicates were permitted), the value would be 30.

Edited on October 31, 2011, 3:44 am

Posted by Dej Mar on 2011-10-31 03:40:10