11.
Every handshake takes 2. If no one shakes hands twice with another, there are 10+1 total people shaking hands (11).
Name them 1 thru 11. Make a line and 11 goes down the line and shakes 10 hands and then leaves. 10 then shakes 9 hands and leaves. 8 then shakes 7 hands and leaves. Etc. 2 shakes hands with 1 and leaves. 1 just leaves.
11— 10 hs
10— 9 hs
9— 8 hs
8— 7 hs
7— 6 hs
6— 5 hs
5— 4 hs
4— 3 hs
3— 2 hs
2— 1 hs
1— leaves
Total handshakes 55, total people 11.
