MathDB

Indian Team Selection Test 2010 ST3 P3

Source:

May 22, 2010

geometryrectangleinequalitiesalgebra unsolvedalgebra

Problem Statement

Let

A=(a_{jk})

be a

10\times 10

array of positive real numbers such that the sum of numbers in row as well as in each column is

1

. Show that there exists

j<k

and

l<m

such that

a_{jl}a_{km}+a_{jm}a_{kl}\ge \frac{1}{50}