FILE No.94Unsolved
The town chess club held a 64-player knockout tournament. Lose once and you are out. There are no draws. Matches continue until a champion is decided.
The organizer asked the scorekeeper how many matches there would be. The scorekeeper began adding: "Round 1 is 32 matches, round 2 is 16 ...".
How many matches are played in total until the champion is decided?
If you get stuck, open the hints one at a time, in order.
How many players does one match eliminate?
How many players are left at the end?
How are matches related to eliminated players?
How many matches are played in total until the champion is decided?
Choose the answer closest to the truth.
63
The answer is: 63.
Every match eliminates exactly one player. Everyone except the champion (63 players) must lose exactly once, so there are 63 matches.
Adding up the rounds, 32 + 16 + 8 + 4 + 2 + 1 = 63, gives the same result.
Adding round by round hides the much simpler way of looking at it.
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