## Task 2 - 240612

Michael draws five different pictures: Picture a) to e). He claims that they are nets of cubes.
a)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0245.jpg?height=280&width=131&top_left_y=1599&top_left_x=560)
b)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0245.jpg?height=226&width=122&top_left_y=1646&top_left_x=750)
c)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0245.jpg?height=222&width=186&top_left_y=1648&top_left_x=935)
d)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0245.jpg?height=220&width=122&top_left_y=1649&top_left_x=1184)
e)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0245.jpg?height=214&width=165&top_left_y=1652&top_left_x=1371)

(1) Identify all the pictures from a) to e) for which Michael's claim is true! (No justification is required.)

(2) Show that it is possible to cut out nine cube nets of the type found in (1) from a square grid net with a side length of $8 \mathrm{~cm}$, as shown in picture f).

It is allowed to obtain the cube nets unchanged or flipped (mirrored). Each cube net found in (1) should appear at least once. The side length of the individual squares in (1) should be the same as in (2), i.e., $1 \mathrm{~cm}$.

Draw such nine cube nets in a grid net! How many fields of the grid net will not be used?

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0245.jpg?height=462&width=463&top_left_y=2005&top_left_x=1276)
(1) Exactly the images a), c), and e) are cube nets.

(2) A possible arrangement of nine cube nets of the required type is shown in the figure. Ten cells of the grid are not needed.

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0246.jpg?height=459&width=466&top_left_y=233&top_left_x=795)