# What is the least amount of people that can be in the auditorium?

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There is a special auditorium that holds 100 people. It is not full. Each person claps seven times after a performance. Every time ten claps are heard, the man in the front twitches. Every third twitch, one of the actors hops. Every two hops, a person in the crowd cheers. Every four cheers, the actors bow. If they only bowed once, what is the least amount of people that can be in the auditorium?

BONUS! How many bows will the actors do if the auditorium is full?

posted Jul 15, 2015

+1 vote

One bow = 4 cheers.
4 cheers = 8 hops.
8 hops = 24 twitches.
24 twitches = 240 claps.
240/7 = 34.28

Since you can't have a fraction of a person, there must have been at least 35 people.

BONUS!

100 people = 700 claps.
700 claps = 70 twitches.
70 twitches = 23 hops. (You can't have .3 of a hop)
23 hops = 11 cheers. (You can't have half of a cheer)
11 cheers = 2 bows. (You can't have three-quarters of a bow)

At most, they will bow twice.

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