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How many people are there if everyone shakes hands and there are 66 handshakes?
Wiki User
∙ 11y ago
Assuming that each person shakes hands with every other person, there are 12 people.
Let n be the number of people.
Then each person shakes hands with (n-1) people and if you ask every person how many hand shakes they made and total them you will get a total of n(n-1) handshakes.
However, each handshake involves two people and has been counted twice - once by each person that shook hands - thus number of hand shakes is half of this, giving:
n(n-1)/2 = 66
⇒ n(n-1) = 132
⇒ n2 - n - 132 = 0
⇒ (n - 12)(n + 11) = 0
⇒ n = 12 or -11
You can't have -11 people, therefore there are 12 people.
Wiki User
∙ 11y ago
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10
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Type your answer here... 6
How many handshakes can occur between 5 people if everyone shakes hands?
10
Examples of hard riddles or quizzes?
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In a room there are N number of people if everyone shakes hands how many handshakes are made?
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If at a party there are a total of 741 handshakes and each person shakes hands with everyone else at the party exactly once how many people are at the party?
38
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If each of seven persons in a group shakes hands with each of the other six persons then a total of forty-two handshakes occurs?
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How many handshakes if 4 people shakes hands with every other person in the room?
Type your answer here... 6
If there are 8 people at a party and every person shakes hands with everyone else at the party how many handshakes will there be?
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