A1. At the reception with the mayor, 7 awardees were invited. The mayor shook hands with each of them, and all the awardees also shook hands with each other. How many handshakes were there in total?
(A) 21
(B) 28
(C) 36
(D) 42
(E) 56
A1. The mayor shook hands with seven people, as did each of the awardees. We must also consider the same handshakes: mayor - 1st awardee = 1st awardee - mayor, 1st awardee - 2nd awardee = 2nd awardee - 1st awardee, etc. The number of handshakes, taking this into account, can be calculated as: $7 \cdot 7-(1+2+3+4+5+6)=28$. 

The number of handshakes can also be calculated as: $\frac{8 \cdot 7}{2}=28$.