For those that are good with numbers I am sure you will not have any problems with this one either. In a singles tennis tournament, 111 players participated. They used a new ball for each match. When a player lost one match, he was eliminated from the tournament. How many balls did they need?
Uh, I'll venture a guess. 55 matches would eliminate 55, leaving 56 players. Another round of 28 matches would leave 28 players. Another round of 14 matches leaves 14. The next round of 7 matches leaves 7 players. Three more matches leave 4, then 2 matches leave 2, and 1 more leaves 1 winner. So 55 + 28 + 14 + 7 + 3 + 2 +1 matches are needed. 110 balls. Okay, how wrong am I?
You'd require an unlimited number of tennis balls. As you put it, when a player loses a match, "he" is eliminated. There's no indication that women players are eliminated. On the assumption they don't get fed up with playing tennis every day, they'll still be on the court playing. Assuming that women are eliminated too, there is a simpler solution. Since there are 111 players, then 110 of them must lose a game for there to be a single winner. Therefore, they must play 110 games and use 110 balls. So, if there were 1,865,465,102 players in the tournament, how many balls would be needed?
You know, when I started out trying to figure out the first problem, I took out a pen and paper and started writing. I figured out quickly that it wasn't necessary and saw the obvious.
Ok, I like that and I don't like it because it doesn't make any sense to me. I just can't see how it is possible.
