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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 4 4 people and n n round tables that each table suits for 6 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 n > 1.