MathDB

There are some checkers in

n\cdot n

size chess board.Known that for all numbers

1\le i,j\le n

if checkwork in the intersection of

i

th row and

j

th column is empty,so the number of checkers that are in this row and column is at least

n

.Prove that there are at least

\frac{n^2}{2}

checkers in chess board.

Problem Statement