Track / Stage 4 / 100 of 340 #360 of 2000

Problem 360

AMC 12 late, AIME early

Combinatorics Difficulty 4.8 Find the answer

$6 \cdot 9$ Suppose there are $n$ teams participating in a volleyball tournament, and the tournament is conducted in a knockout (elimination) format. In the tournament, every two teams that meet play one match, and each match must have a winner and a loser, with the losing team being eliminated from the tournament. How many matches will be played in total by the time the champion is determined?

Your answer

Official solution

[Solution] In each match, exactly 1 team exits the competition. By the time the champion team is determined, a total of $n-1$ teams have exited the competition, which of course means that a total of $n-1$ matches have been played.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.