2012 AMC 8 Problems/Problem 14
Contents
[hide]Problem
In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of 21 conference games were played during the 2012 season, how many teams were members of the BIG N conference?
Solution 1
This problem is very similar to a handshake problem. We use the formula to usually find the number of games played (or handshakes). Now we have to use the formula in reverse.
So we have the equation . Solving, we find that the number of teams in the BIG N conference is .
Solution 2
(If someone understands what I'm trying to do here and can explain it better, please edit it)We know that every team has to play a game with every other team, so we just need to find out how many consecutive numbers, to , can fit into 21. We know that , and since this doesn't count to team that shook hands with the other , we know that there are teams in the BIG N conference.
Video Solution
https://youtu.be/zzU98Bk1TrE ~savannahsolver
See Also
2012 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AJHSME/AMC 8 Problems and Solutions |
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