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

tertre  Feb 18, 2018
 #1
avatar+88898 
+2

 

Notice that  the 23rd person can shake hands with 22 other people

And the 22nd person can shake hande with 21 people [ this person has already shaken hands with the 23rd person]

And the 21st person can shake hands with 20 people[ this person has already shaken hands with the first two ]

 

So....the total possible handshakes are

 

22  +  21  + 20  + ......+  1  =

 

 1 + 2 + 3 +  ......+ 20 + 21 + 22

 

Which is just the sum of the first 22 positive integers and is given by :

 

(22)(23) / 2   =   11 * 23  =  253 handshakes

 

 

cool cool cool

CPhill  Feb 18, 2018
 #2
avatar+3039 
+1

Thank you, CPhill! Amazing!

tertre  Feb 18, 2018
 #3
avatar+604 
+1

ab=ba, so 23*22/2=253 handshakes

mathtoo  Feb 18, 2018

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