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Select the correct answer21 people meet and shake hands. The maximum number of handshakes possible if there is to be no ‘cycle’ of handshakes is? (A cycle of handshakes is a sequence of people a1, a2, … , aK such that the pairs (a1, a2), (a2, a3),… , (a (k-1), ak), (ak, a1) shake hands)radio_button_unchecked17radio_button_unchecked18radio_button_unchecked19radio_button_unchecked20

Question

Select the correct answer21 people meet and shake hands. The maximum number of handshakes possible if there is to be no ‘cycle’ of handshakes is? (A cycle of handshakes is a sequence of people a1, a2, … , aK such that the pairs (a1, a2), (a2, a3),… , (a (k-1), ak), (ak, a1) shake hands)radio_button_unchecked17radio_button_unchecked18radio_button_unchecked19radio_button_unchecked20

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Solution

The maximum number of handshakes possible without a cycle is when each person shakes hands with only one other person. This forms a linear sequence of handshakes. In this case, the number of handshakes is one less than the total number of people. So, for 21 people, the maximum number of handshakes without a cycle is 21 - 1 = 20. Therefore, the correct answer is 20.

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