4. The board for playing "Battleship" is $10 \times 10$. What is the maximum number of ships of size $1 \times 4$ that can be placed on it?
Answer: 24.

Solution: It is easy to show by trial that 24 ships can be placed. Let's color the board in 4 colors as shown in the figure. Note that each ship of size $1 \times 4$ contains one cell of each color, and there will be 24 yellow cells.

![](https://cdn.mathpix.com/cropped/2024_05_06_fd03a0ae01aeee9276eag-3.jpg?height=450&width=477&top_left_y=1201&top_left_x=824)