Combinatorics · Counting · Perfect matching · Distributions
Problem 3, 2018
A mathematical commission has \(2n\) members, where \(n \geqslant 3\). Every member of the commission is in a quarrel with exactly one other member (the relation is symmetric). In how many ways can the commission be divided into three committees - one for setting the problems, one for grading them, and one for organising the competition - so that each committee has at least two members, and no two members who are in a quarrel end up on the same committee?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Municipal Competition 2018, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source