1.1. [3] On a chessboard, white and black pieces are placed. In each row (column), the white pieces are twice as many as the black pieces in that row (column). What is the maximum number of pieces that can be placed on the board?

Answer. 48 pieces.
Solution. The number of figures in each column is a multiple of 3, so it is at most 6. Then the number of figures on the board is at most $8 \cdot 6 = 48$. For example, we place 32 white figures on the white squares, and 16 black figures on the main "black" diagonal and the two parallel "black" diagonals with "length" 4.