Suppose there are five people, the first one wants to shake hands with the other four people, and the second one has already shaken hands with the first one. Then shake hands with the other three people and so on ***4+3+2+ 1 time = 10/time.

Arithmetic progression with a tolerance of 1.

We set the maximum term as x, that is, the number of times the first person shakes hands with others is x.

According to arithmetic progression's summation formula

(x+ 1)*x/2=2 1

The solution is x=6.

So there are 6+ 1=7 people.

That is 6+5+4+3+2+ 1=2 1 handshake.