MathDB

Marc has an

n\times n

board, where

n\ge 3

is an integer, and an unlimited supply of green and red apples. Marc wants to place some apples on the board, so that the following conditions hold.
[*] Every cell of the board has exactly one apple, be it red or green. [*] All rows and columns of the board have at least one red apple. [*] No two rows or columns have the same apple color sequence. Note that rows are read from left to right, and columns are read from top to bottom. Also note that we do not allow a row and a column to have the same color sequence.
Find, in terms of

n

, the minimal number of red apples that Marc needs in order to fill the board in this way.

Problem Statement