MathDB

integers 1 to n^2 in a nxn , yellow / blue the largest in each row / column

Source: Ukraine TST 2009 p11

May 4, 2020

combinatoricsColoringminmax

Problem Statement

Suppose that integers are given

m <n

. Consider a spreadsheet of size

n \times n

, whose cells arbitrarily record all integers from

1

{{n} ^ {2}}

. Each row of the table is colored in yellow

m

the largest elements. Similarly, the blue colors the

m

of the largest elements in each column. Find the smallest number of cells that are colored yellow and blue at a time