2015 AMC 8 Problems/Problem 24
Contents
[hide]Problem
A baseball league consists of two four-team divisions. Each team plays every other team in its division games. Each team plays every team in the other division games with and . Each team plays a game schedule. How many games does a team play within its own division?
Solution 1
On one team they play games in their division and games in the other. This gives .
Since we start by trying M=5. This doesn't work because is not divisible by .
Next, does not work because is not divisible by .
We try does work by giving , and thus games in their division.
seems to work, until we realize this gives , but so this will not work.
Solution 2
, giving . Since , we have . Testing all of the cases we get tha .
This gives , as desired. The answer is .
See Also
2015 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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