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22 people attend a party. Each person shakes hands with at most 20 other people. What is the maximum possible number of handshakes, assuming that any two people can shake hands at most once?

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 May 22, 2020
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22 persons shaking hands with 20 persons (each) result in 22 x 20  =  440 handshakes.

However, this is double the actual amount since, when person A is shakomg hands with

person B, B is then (also) shaking hands with person A.

So, we need to divide the answer that we got by 2:  440 / 2  =  220 handshakes.

 
 May 22, 2020

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