The family entrusted the selection of the tiles for the kitchen renovation to their two children. One of them prefers the coloration visible on the front cover, while the other prefers the one on the back cover. In the end, they decide to choose the one with more brown color. Which one did they choose?
We can see two types of tile patterns in Figure 1 and Figure 2, respectively.

In Figure 3, the area of the gray part is 16 times the shaded area in the tiling pattern shown in Figure 2. The combined area of the bold-drawn one-sixth circular sector and the hatched circular segment, when multiplied by 16, gives the shaded pattern in Figure 1. This latter area is clearly larger (by the area of the hatched circular segment) than one-sixth of the circle's area, while the gray area is smaller (by the area of the two hatched circular segments).

Therefore, the children chose the pattern corresponding to Figure 1.

Based on the work of Gábor Sámuel (Budapest, Berzsenyi D. Gymnasium, 9th grade)

Note. The originally brown, now shaded areas were calculated by most: the area in Figure 1 is $\frac{\pi}{3}-\frac{\sqrt{3}}{4} \approx 0.6142$, and in Figure 2 it is $\frac{\sqrt{3}}{2}-\frac{\pi}{6} \approx 0.342416$ times the area.
![](https://cdn.mathpix.com/cropped/2024_05_02_560a3232e2bdc4d1d1feg-1.jpg?height=1486&width=568&top_left_y=604&top_left_x=778)