VN-TST 2009 Problem 6

There are $6n + 4$ mathematicians participating in a conference which includes $2n + 1$ meetings. Each meeting has one round table that suits for $4$ people and $n$ round tables that each table suits for $6$ people. We have known that two arbitrary people sit next to or have opposite places doesn't exceed one time.

1. Determine whether or not there is the case $n = 1$ .
2. Determine whether or not there is the case $n > 1$ .