A magician told his friend(X) that he will do a magic trick and gave X 3 cards with 5 distinct non-negative integers written on each card. X was asked to choose a number from each card and tell the sum of the 3 chosen numbers to him. For every possible sum X told him, he answered all the 3 chosen numbers correctly. If you sum all these possible sums, what is the minimum value it can take?

Note: The integers on a card are distinct but integers on two different cards may not be distinct.

(In reply to my minimumm- spoiler by Ady TZIDON)

unfortunately your solution fails because among several other numbers the sum 3 can be achieved by choosing either A:3 B:0 C:0 or A:1 B:2 C:0 and thus if the magician is given a sum of 3 he can not determine the 3 numbers given.

Posted by Daniel on 2009-05-11 15:16:31