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Aiden received 16 cards at a party Each person exchanged exactly 1 card with each of the other people How many people were present at the party?
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∙ 13y ago
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∙ 13y ago
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At a party 28 handshakes were exchanged How many people were present at the party?
The underlying assumption is that each person shakes the hand of each other person. If there are "n" people, each will shake the hands of "n-1" other people. To avoid counting double, the result has to be divided by 2. Therefor, the number of handshakes is equal to n(n-1)/2. Trying this out for several values of "n" should be faster than using the quadratic formula. (If you use the quadratic formula, you will probably get a positive and a negative solution - you can discard the negative solution.)
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Each handshake involves two people. If everyone shook only once then there were 36 x 2 ie 72 guests.
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21 people shake hands with each other How many hand shakes are exchanged?
210
