MathDB
combinatorics

Source:

February 20, 2016
combinatorics

Problem Statement

kk is a positive integer. AA company has a special method to sell clocks. Every customer can reason with two customers after he has bought a clock himself ;; it's not allowed to reason with an agreed person. These new customers can reason with other two persons and it goes like this.. If both of the customers agreed by a person could play a role (it can be directly or not) in buying clocks by at least kk customers, this person gets a present. Prove that, if nn persons have bought clocks, then at most nk+2\frac{n}{k+2} presents have been accepted.