Question

A group of 4 children is playing in the park. Before leaving, each of them shakes hands once with every other group member. How many handshakes are done altogether?

Answer 1

One person can shake hands with 14 others at max.

Then second person is left with 13 more to go.

Proceeding this way last person will not need any handshake to be done explicitly.

So 14 rounds with number of shakes ranging from 14 (first round) to 1 (last round).

If we combine first and last round, then there are 15 shakes.

Then we combine second(13) and second last(2) round, again 15 shakes.

For 14 rounds, 7 such pairs of 15 shakes are possible.

Hence answer to the problem is 7 * 15 = 105 hand shakes.

Thank you

PS: This method can be scaled to any level.