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 Special dice (Posted on 2011-10-30)
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?

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 re: Possible solution | Comment 3 of 18 |
(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

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