19 people (a1, a2, ….. , a19) are invited to a party. The host and the hostess shake hands with each invitee and also with each other. The invitees shake hands in a circular fashion, i.e. the pairs (a1, a2), (a2, a3), ……..,(a18, a19), (a19, a1) shake hands. So, in all there are 58 handshakes. Let S be a set of people such that every pair in S shake hands. The size of S is at most
Any pair of 2 persons, host, hostess
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