6n + 4 mathematicans take part in a conference
Source: Vietnam TST 2009, Problem 6
May 1, 2009
combinatorics unsolvedcombinatorics
Problem Statement
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 people and round tables that each table suits for 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 .