MathDB

One side of a square sheet of paper is colored red, the other - in blue. On both sides, the sheet is divided into

n^2

identical square cells. In each of these

2n^2

cells is written a number from

1

k

. Find the smallest

k

,for which the following properties hold simultaneously: (i) on the red side, any two numbers in different rows are distinct; (ii) on the blue side, any two numbers in different columns are different; (iii) for each of the

n^2

squares of the partition, the number on the blue side is not equal to the number on the red side.

Problem Statement