Hello, chadlyter!

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 istwice as largeas it should be.

. . And, obviously, 423 is not divisible by 2.

Therefore, it is not possible.