Each person shakes hand with other.
So 1 person will shake hand with 22 other people.
There are total 23 people, so total number = 23*22
but,if A shakes B, or B shakes A, its the same thing so divide that by 2 to get 23*22/2 = 253
This is the maximum handshakes possible!
Now, suppose there are 3 people : a, b and c
So, cyclic handshakes(when they are seated in a circle) would be ab, bc and ac -> Thus only 3 hand shakes
So, for 23 people, there would be 23 handshakes...