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. You can construct the equation:
-
=
. Thus,
players have to be eliminated. Therefore, we need
games to decide the winner, or
Solution 3 (Cheap Solution using Answer Choices)
Since is a power of
the answer will be in the form of
We can see that this is odd and the only option is
Video Solution
~savannahsolver
See Also
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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