The NFoH
Source: Iranian National Olympiad (3rd Round) 2006
September 11, 2006
floor functionvectorcombinatorics proposedcombinatorics
Problem Statement
The National Foundation of Happiness (NFoH) wants to estimate the happiness of people of country. NFoH selected random persons, and on every morning asked from each of them whether she is happy or not. On any two distinct days, exactly half of the persons gave the same answer. Show that after days, there were at most persons whose “yes” answers equals their “no” answers.