There are 6n \plus{} 4 mathematicians participating in a conference which includes 2n \plus{} 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 \equal{} 1.
2. Determine whether or not there is the case n>1. combinatorics unsolvedcombinatorics