Suppose you are organizing a business meeting and are in cha

Suppose you are organizing a business meeting and are in charge of facilitating the introductions. How would you arrange a group of n people so each person can shake hands with every other person? How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd?

Solution

1 shakes with alt the other n -1 people
2 shakes with all the other n - 2 people and so on

Total shakes = n-1+ n-2 + n -3 and so on

The last active person will either shake with someone else (be the shaker)
or have his/her hand shaken (be the shakee), depending on whether n is odd or even