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 re(3): Possible solution CONCERNS EVERYBODY by broll)

Thanks for including me in the committee, broll. (Sorry for my mistake, I must have had an error in the spreadsheet.)

Given Charlie's numbers and offsetting them to get 12 distinct values with the lowest possible highest value, the numbers on  the faces of each die are found as:
(-15, -9, -3, 3, 9, 15) and (16, 17, 18, 19, 20, 21).

I, too, am interested in the proof that 21 is the the lowest possible highest value. I am also curious as to what other variations to the special dice there may be with this sought value.

Posted by Dej Mar on 2011-10-31 13:23:53