MathDB

The Proenc has a new

8\times 8

chess board and requires composing it into rectangles that do not overlap, so that: (i) each rectangle has as many white squares as black ones; (ii) there are no two rectangles with the same number of squares. Determines the maximum value of

n

for which such a decomposition is possible. For this value of

n

, determine all possible sets

{A_1,... ,A_n}

, where

A_i

is the number of rectangle

i

in squares, for which a decomposition of the board under the conditions intended actions is possible.

Problem Statement