The figure on the side shows the painted surface of a rhombus-shaped tile. Of the five patterns below, only one cannot be assembled with copies of this tile. Which is that pattern?

![](https://cdn.mathpix.com/cropped/2024_05_01_1c2853cb1112cfb2ee2dg-10.jpg?height=206&width=237&top_left_y=1719&top_left_x=156)
A)

![](https://cdn.mathpix.com/cropped/2024_05_01_1c2853cb1112cfb2ee2dg-10.jpg?height=137&width=229&top_left_y=1782&top_left_x=411)
B)

![](https://cdn.mathpix.com/cropped/2024_05_01_1c2853cb1112cfb2ee2dg-10.jpg?height=137&width=163&top_left_y=1782&top_left_x=655)
C)

![](https://cdn.mathpix.com/cropped/2024_05_01_1c2853cb1112cfb2ee2dg-10.jpg?height=137&width=234&top_left_y=1785&top_left_x=840)
D)

![](https://cdn.mathpix.com/cropped/2024_05_01_1c2853cb1112cfb2ee2dg-10.jpg?height=140&width=192&top_left_y=1780&top_left_x=1092)
E)
Solution

## ALTERNATIVE E

We show on the side two tiles. Tile 1 is the tile from the statement, with which the figures in alternatives $A$), $B$), C) and $D$) were formed. The figure in alternative $E$) was made with two copies of tile 1 and two copies of tile 2. Since it is not possible to obtain tile 2 by translation or rotation of tile 1, it follows that we cannot build the figure in alternative $E$) with copies of tile 1.

![](https://cdn.mathpix.com/cropped/2024_05_01_1c2853cb1112cfb2ee2dg-32.jpg?height=131&width=294&top_left_y=851&top_left_x=984)