Difference between revisions of "2003 AMC 10B Problems/Problem 15"
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Revision as of 18:04, 12 June 2011
Problem
There are players in a single tennis tournament. The tournament is single elimination, meaning that a player who loses a match is eliminated. In the first round, the strongest
players are given a bye, and the remaining
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
$\textbf{(A) } \text{a prime number}
\qquad\textbf{(B) } \text{divisible by 2}
\qquad\textbf{(C) } \text{divisible by 5}
\qquad\textbf{(D) } \text{divisible by 7}
\qquad\textbf{(E) } \text{divisible by 11}$ (Error compiling LaTeX. Unknown error_msg)
Solution
Notice that players need to be eliminated for there to be declared a winner. Notice also that every match eliminates exactly one person. Therefore,
matches are needed to eliminate
people and therefore declare a winner. The rest of the information is irrelevant. Therefore, the total number of matches is
.
See Also
2003 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |