Problem 4. From four matchsticks, a small square can be made, as shown in the drawing. From 12 matchsticks, a larger square $2 \times 2$ can be made, composed of 4 small squares, as shown in the $\qquad$ figure. How many matchsticks are needed to make a square $10 \times 10$, composed of 100 small squares?
Solution. The outer boundary of the square will consist of $4 \cdot 10=40$ tiles. For each of the internal dividing lines, 10 tiles are needed. The number of dividing lines is $2 \cdot 9=18$ (9 horizontal and 9 vertical). Therefore, $40+18 \cdot 10=220$ tiles are required.

![](https://cdn.mathpix.com/cropped/2024_06_05_a1dcf8241dfa57377282g-01.jpg?height=257&width=254&top_left_y=1876&top_left_x=1226)