MathDB

Let

n

be a positive integer. An

n\times n

board consisting of

n^2

cells, each being a unit square colored either black or white, is called convex if for every black colored cell, both the cell directly to the left of it and the cell directly above it are also colored black. We define the beauty of a board as the number of pairs of its cells

(u,v)

such that

u

is black,

v

is white, and

u

and

v

are in the same row or column. Determine the maximum possible beauty of a convex

n\times n

board.
Proposed by Ivan Novak

Problem Statement