[ Chessboards and chess pieces ]  [Examples and counterexamples. Constructions]

For the game "Battleship" on an $8 \times 8$ grid, 12 "two-deck" ships were placed. Is it necessarily possible to place a "three-deck" ship? (A "two-deck" ship is a rectangle $1 \times 2$, and a "three-deck" ship is $1 \times 3$. Ships can touch each other, but they must not overlap.)
Example of placing "two-deck" ships, in which there is no room left for a "three-deck" ship, see the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_fe32e688207a541a0cbdg-11.jpg?height=457&width=460&top_left_y=0&top_left_x=799)

## Answer

Not necessarily.