# 4. Variant 1.

A square piece of paper is folded as follows: the four corners are folded to the center so that they meet at one point (see figure),

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-04.jpg?height=393&width=396&top_left_y=2189&top_left_x=862)
resulting in a square again. After performing this operation several times, a square with a side length of 3 cm and a thickness of 16 sheets of paper is obtained. Find the side length of the original square in centimeters.
Answer: 12.

Solution: After each operation, the thickness of the square doubles, and the area is halved. Since the thickness has become 16 sheets, the operation was applied 4 times. In this process, the area decreased by a factor of 16 and became equal to 9 square centimeters. Therefore, the area of the original square was $16 \times 9 = 12 \times 12 = 144$ square centimeters. Thus, the side length of the original square is 12 cm.