In a tennis tournament there are 111 entrants. It is a singles knockout tournament and you as secretary have to arrange the matches. What is the minimum number of matches that would have to be arranged with this number of entrants?
When faced with this problem most people draw little diagrams showing the actual pairings in each match and the number of byes. Others try and work it out in reference to 2^n (i.e. 4, 8, 16). In fact the answer is 110 matches and one can work this out at once without any complicated math. To work it out one must shift attention from the winners of each match to the losers (in whom no one is usually very interested). Since there can only be one winner there must be 110 losers. Each loser can only lose once so there must be 110 matches.
DAMN. MIND. BLOWN.
From Lateral Thinking.