This article is from the Puzzles FAQ, by Chris Cole email@example.com and Matthew Daly firstname.lastname@example.org with numerous contributions by others.
97 baseball teams participate in an annual state tournament.
The way the champion is chosen for this tournament is by the same old
elimination schedule. That is, the 97 teams are to be divided into
pairs, and the two teams of each pair play against each other.
After a team is eliminated from each pair, the winners would
be again divided into pairs, etc. How many games must be played
to determine a champion?
In order to determine a winner all but one team must lose.
Therefore there must be at least 96 games.