2. Arrange the smallest square area using square tiles of sizes $1 \times 1$, $2 \times 2$, and $3 \times 3$, such that the number of tiles of each size is the same.
Answer:

![](https://cdn.mathpix.com/cropped/2024_05_06_35052e7d512455511f98g-03.jpg?height=808&width=805&top_left_y=670&top_left_x=523)

Solution. Let $n$ be the number of squares of each type. Then $n + 4n + 9n = 14n$ must be a perfect square. The smallest $n$ for which this is possible is 14. The figure shows an example of how to construct a 14x14 square (other arrangements are possible, as long as there are 14 squares of each type).