MathDB

Cookies should be placed on a

7 \times 7

chess board, so that never four cookies can form a rectangle whose sides are parallel to those of the chessboard. Find the maximum number of biscuits that can be positioned in this way.
Note: If you do the same job for a

13 \times 13

chessboard, you get a biscuit. If you solve it for an infinite number of squares of chessboards, you get two biscuits. If you solve them for all sidelengths, , you even get two three biscuits (We cannot distribute more cookies, otherwise we run the risk of them to form a rectangle).

Problem Statement