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?
Answer Choices:
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E.
Solution:
Divide the sprinters into groups of . Run races to eliminate sprinters, leaving winners. Divide the winners into groups of , run races to eliminate sprinters, leaving winners. Finally run the last race to determine the champion. The number of races run is .
When all the races have been run, sprinters will have been eliminated. Since sprinters are eliminated in each race, there are races needed to determine the champion.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions