I am trying to figure out why this is possible or not?
In a group of 47 people, can each person shake hands with exactly 9 other people?
Let's count the total number of handshakes.
If each of the 47 people shake hands with exactly 9 other people.
. . There will be: . handshakes.
But "X shakes hands with Y" and "Y shakes hands with X" is the same handshake.
. . Hence, our number is twice as large as it should be.
. . And, obviously, 423 is not divisible by 2.
Therefore, it is not possible.