2016 AMC 8 Problems/Problem 18
Contents
Problem
In an All-Area track meet, sprinters enter a
meter dash competition. The track has
lanes, so only
sprinters can compete at a time. At the end of each race, the five non-winners are eliminated, and the winner will compete again in a later race. How many races are needed to determine the champion sprinter?
Solution
Solution 1
From any th race, only
will continue on. Since we wish to find the total number of races, a column representing the races over time is ideal.
Starting with the first race:
Adding all of the numbers in the second column yields
Solution 2
Every race eliminates players. The winner is decided when there is only
runner left. Thus,
players have to be eliminated. Therefore, we need
games to decide the winner, or
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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All AJHSME/AMC 8 Problems and Solutions |
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