+4609 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?
+128407
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
