Problem 4. A square area was paved with square tiles (all tiles are the same). A total of 20 tiles adjoin the four sides of the area. How many tiles were used in total?

![](https://cdn.mathpix.com/cropped/2024_05_06_03b105aa15b6031ee02fg-1.jpg?height=314&width=325&top_left_y=1945&top_left_x=1548)
Answer: 36 tiles.

Solution. Let's call the tiles adjacent to the top side of the platform "top tiles". Similarly, we define "right", "left", and "bottom" tiles. Notice that if we add the number of top tiles, the number of bottom tiles, the number of right tiles, and the number of left tiles, we will count the corner tiles twice, so the result will be 4 more than the total number of boundary tiles, i.e., we will get $20+4=24$. Then the number of tiles adjacent to one side of the square is $24: 4=6$. Therefore, the total number of tiles is $6 \cdot 6=36$.