Q. It was Maria's first day at school. The teacher suggested that it would be a good idea for each child to meet every other child in the class. The teacher said, "When you meet, please shake hands and introduce yourself by name."
If there were 11 children in the class, how many total handshakes were there?
 


Answer
55
Solution:
The class has 11 children. The first child shakes hands with the other 10 children. The second child has already shaken hands with the first child, and so has to shake hands with only the other 9 children. In this manner, the second-last child has to shake hands with only one child, and the last child has already met all the children. Thus, the number of handshakes is
10 + 9 + ........ + 2 + 1 = 55.
If there were 11 children in the class, then there were 55 total handshakes.