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?

The basic solution, without optimization would be the base-6:

0,1,2,3,4,5
1,7,13,19,25,31

or the same with 1 added to each face of the top die while 1 is subtracted from the bottom.

But of course any number could be added to one side and subtracted from the other, so why not make the highest on each die 18?

13,14,15,16,17,18
-12,-6,0,6,12,18

Posted by Charlie on 2011-10-30 14:31:06