Machine and Cards
Source: Iran pre-preparation course examination 2011- P1
February 25, 2011
combinatorics proposedcombinatorics
Problem Statement
We have some cards that have the same look, but at the back of some of them is written and for the others .(We can't see the back of a card so we can't know what's the number on it's back). we have a machine. we give it two cards and it gives us the product of the numbers on the back of the cards. if we have cards with on their back and cards with on their back, at least how many times we must use the machine to be sure that we get the number ? (15 points)