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.

This has a hint of a card trick where the top left corner bears a decimal number but is also a power of 2 (32, 16, 8, 4, 2, 1).  Each card has on it all and only those numbers which can be formed from that corner number and any other card(s) whose left 'pip(s)' may make that number.

Eg: 12 can only be on the cards with 'pips' 8 and 4.

I think this is where Charlie's lie in his comment.   Unsure if this line of inquiry actually brings up the 5 numbers per card, certainly allows overlap, but what about that minimum value? 

Posted by brianjn on 2009-05-11 10:08:20