MathDB
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 00 and for the others 11.(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 mm cards with 00 on their back and nn cards with 11 on their back, at least how many times we must use the machine to be sure that we get the number 11? (15 points)