Answer to Riddle #83: Knockout Competion with 15 players.
83. John runs a tennis club. He's to organise a knockout tournament. He puts out the sign up sheet and after a week he has 15 sign-ups. John is confused, he can't work out how to organise a knock out tournament with 15 players, and doesn't know how many courts to book.
He asks Arabella, the professor. She knows instantly, without giving it a second's thought...
How does Arabella do this? She doesn't have time to plan the whole tournament.
I've been racking my brain to come up with puzzles, and I remembered this one:
Before reading the answer can I interest you in a clue?
So there are 14 games.
Professor Arabella realises that since it's a knockout tournament there will be someone eliminated in every game. And a winner. In a knockout competition there will always one less game than there are players.
It's probably worth mentioning that (in theory at least,) whilst a knockout competition will always produce the best competitor as the winner of the final, but that is all it will do. You can not assume that the losing finalist will be the 2nd best. Or that the semi-finalists are the 3rd and 4th placed. After all the two best teams/players could meet in the first round.
Google aced this one, ChatGPT not so much.
If you're curious what Bard made of this puzzle...
Arabella knows how to organize a knockout tournament with 15 players because she knows that there will be one less match than there are players. This is because in a knockout tournament, each match eliminates one player, and we want to end up with a single winning player at the end. Therefore, to eliminate 14 players in the first round, we need 7 matches, and then one player gets a bye to the next round. So the total number of matches in the first round is 7 + 1 = 8.
In the second round, there will be 4 matches, and in the third round there will be 2 matches. In the final round, there will be 1 match. So the total number of matches in the tournament is 8 + 4 + 2 + 1 = 15.
Arabella does not need to plan the whole tournament in order to know how many courts to book. She only needs to know the number of matches that will be played in each round. In this case, there will be 8 matches in the first round, 4 matches in the second round, 2 matches in the third round, and 1 match in the final round. So Arabella needs to book at least 15 courts to accommodate all the matches of the tournament.
If you're curious what ChatGPT made of this puzzle...
The below answer IS WRONG
Arabella likely knows that a knockout tournament with 15 players would require four rounds to determine the winner. She also knows that each round would require half the number of players from the previous round to be eliminated.
Using this information, Arabella can quickly determine that in the first round, 8 players would compete, with 7 players receiving a bye. In the second round, 4 players would compete, with 4 players receiving a bye. In the third round, 2 players would compete, with 2 players receiving a bye. And finally, in the fourth and final round, the remaining 2 players would compete for the championship.
Regarding the number of courts to book, Arabella would know that during each round, half the players would be eliminated and thus, the number of matches would halve. Therefore, during the first round, there would be 8 matches, requiring at least 8 courts. During the second round, there would be 4 matches, requiring at least 4 courts. During the third round, there would be 2 matches, requiring at least 2 courts. And during the final round, there would be 1 match, requiring at least 1 court.
So in total, John would need to book at least 8+4+2+1 = 15 courts to accommodate all the matches of the tournament.
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