8. Clone 1

Which of the four figures shown can be cut along the grid lines into two parts that can be used to form a $5 \times 5$ square? The figures can be rotated and flipped.

![](https://cdn.mathpix.com/cropped/2024_05_06_d0dc74dfba1714359e24g-10.jpg?height=300&width=394&top_left_y=498&top_left_x=340)

A

![](https://cdn.mathpix.com/cropped/2024_05_06_d0dc74dfba1714359e24g-10.jpg?height=297&width=228&top_left_y=500&top_left_x=711)

B

![](https://cdn.mathpix.com/cropped/2024_05_06_d0dc74dfba1714359e24g-10.jpg?height=294&width=417&top_left_y=498&top_left_x=1045)

C

![](https://cdn.mathpix.com/cropped/2024_05_06_d0dc74dfba1714359e24g-10.jpg?height=300&width=368&top_left_y=495&top_left_x=1461)

D
Answer: A, B, G

## Solution

We will show how to cut figures A, B, and G.
![](https://cdn.mathpix.com/cropped/2024_05_06_d0dc74dfba1714359e24g-10.jpg?height=1130&width=808&top_left_y=1218&top_left_x=675)

Now, we will prove that figure V cannot be cut. Highlight three squares in it and note that no two of them can remain in the same part, as the side length of the resulting figure would exceed 5 cells. On the other hand, since we are cutting the figure into two parts, there will be a part that contains at least two of the highlighted squares. This leads to a contradiction.

![](https://cdn.mathpix.com/cropped/2024_05_06_d0dc74dfba1714359e24g-11.jpg?height=517&width=605&top_left_y=278&top_left_x=788)

## Clone 2

Which of the four figures can be cut along the grid lines into two parts that can be used to form a $5 \times 5$ square? The figures can be rotated and flipped.

![](https://cdn.mathpix.com/cropped/2024_05_06_d0dc74dfba1714359e24g-11.jpg?height=405&width=1476&top_left_y=1071&top_left_x=353)

Answer: B, V, G

## Clone 3

Which of the four figures can be cut along the grid lines into two parts that can be used to form a $5 \times 5$ square? The figures can be rotated and flipped.

![](https://cdn.mathpix.com/cropped/2024_05_06_d0dc74dfba1714359e24g-11.jpg?height=389&width=1488&top_left_y=1853&top_left_x=338)

Answer: A, V, $\Gamma$

## Clone 4

Which of the four figures can be cut along the grid lines into two parts that can be used to form a $5 \times 5$ square? The figures can be rotated and flipped.

![](https://cdn.mathpix.com/cropped/2024_05_06_d0dc74dfba1714359e24g-12.jpg?height=339&width=1488&top_left_y=493&top_left_x=318)

Answer: B, $\Gamma$