MathDB
Combi I

Source: Soulami, "Les olympiades de mathématiques"

May 9, 2004
functioncombinatorics proposedcombinatorics

Problem Statement

I'll post some nice combinatorics problems here, taken from the wonderful training book "Les olympiades de mathmatiques" (in French) written by Tarik Belhaj Soulami. Here goes the first one: Let I\mathbb{I} be a non-empty subset of Z\mathbb{Z} and let ff and gg be two functions defined on I\mathbb{I}. Let mm be the number of pairs (x,  y)(x,\;y) for which f(x)=g(y)f(x) = g(y), let nn be the number of pairs (x,  y)(x,\;y) for which f(x)=f(y)f(x) = f(y) and let kk be the number of pairs (x,  y)(x,\;y) for which g(x)=g(y)g(x) = g(y). Show that 2m≤n+k.2m \leq n + k.
Back to ProblemsView on AoPS