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 189 can be the answer by Ritesh)

The possible totals for the three numbers chosen from the set are:

 3 , 4 , 7 , 16 , 43 , 5 , 8 , 17 , 44 , 11 , 20 , 47 , 29 , 56 , 83 , 6 , 9 , 18 , 45 , 12 , 21 , 48 , 30 , 57 , 84 , 15 , 24 , 51 , 33 , 60 , 87 , 42 , 69 , 96 and 123.

These add up to 1323, rather than the 189 you mention.

 

Posted by Charlie on 2011-04-28 23:27:57