MathDB
Singles Tennis

Source:

January 9, 2009

Problem Statement

There are 100 100 players in a singles tennis tournament. The tournament is single elimination, meaning that a player who loses a match is eliminated. In the first round, the strongest 28 28 players are given a bye, and the remaining 72 72 players are paired off to play. After each round, the remaining players play in the next round. The match continues until only one player remains unbeaten. The total number of matches played is <spanclass=latexbold>(A)</span> a prime number<spanclass=latexbold>(B)</span> divisible by 2<spanclass=latexbold>(C)</span> divisible by 5 <span class='latex-bold'>(A)</span>\ \text{a prime number} \qquad <span class='latex-bold'>(B)</span>\ \text{divisible by 2} \qquad <span class='latex-bold'>(C)</span>\ \text{divisible by 5} <spanclass=latexbold>(D)</span> divisible by 7<spanclass=latexbold>(E)</span> divisible by 11 <span class='latex-bold'>(D)</span>\ \text{divisible by 7} \qquad <span class='latex-bold'>(E)</span>\ \text{divisible by 11}