MathDB

There is a

2n\times 2n

rectangular grid and a chair in each cell of the grid. Now, there are

2n^2

pairs of couple are going to take seats. Define the distance of a pair of couple to be the sum of column difference and row difference between them. For example, if a pair of couple seating at

(3,3)

and

(2,5)

respectively, then the distance between them is

|3-2|+|3-5|=3

. Moreover, define the total distance to be the sum of the distance in each pair. Find the maximal total distance among all possibilities.

Problem Statement