## [Dissections into Parts with Special Properties]

 Divisibility of Numbers. General PropertiesAuthors: $\underline{\text { Akopyan E., Martynova N. }}$

How many equal octagons can a square of size $8 \times 8$ be divided into? (All cuts must follow the grid lines.)

#
Clearly, the number of cells in one polygon is a divisor of the number 64. One and two cells cannot form an octagon, so the possible options are: $4, 8, 16$ or 32 cells. Corresponding examples are shown in the figure.
![](https://cdn.mathpix.com/cropped/2024_05_06_5e05e09159d75892ee01g-17.jpg?height=440&width=2058&top_left_y=1482&top_left_x=0)

## Answer

2, 4, 8 or 16.