MathDB
Symmetry?

Source: 2006 Swedish Mathematical Competition #5

January 5, 2018
combinatoricssymmetrySweden

Problem Statement

In each square of an m×nm \times n rectangular board there is a nought or a cross. Let f(m,n)f(m,n) be the number of such arrangements that contain a row or a column consisting of noughts only. Let g(m,n)g(m,n) be the number of arrangements that contain a row consisting of noughts only, or a column consisting of crosses only. Which of the numbers f(m,n)f(m,n) and g(m,n)g(m,n) is larger?
Back to ProblemsView on AoPS