The Proenc has a new 8×8 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 A1,...,An, where Ai is the number of rectangle i in squares, for which a decomposition of the board under the conditions intended actions is possible. geometryrectanglecombinatoricscombinatorial geometry