# Math Help - Help

1. ## Help

I am trouble trying to figure out why this is possible or not? In a group of 47 people can each person shake hands with exactly nine other people?

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: . $47 \times 9 \:=\:423$ 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.

3. It is really very easy.
In any graph there must be an even number of odd vertices.
Try to draw a graph in which an edge is determined by a handshake.