4. An eight is a figure consisting of two equal circles that are drawn against each other, like $8, \infty$ or 8. In the figure, you see 66 circles stacked in the shape of a triangle.

How many eights can you find in this stack?
A) 99
B) 108
C) 120
D) 135
E) 165

![](https://cdn.mathpix.com/cropped/2024_04_17_227837a5972cf599de5fg-1.jpg?height=254&width=300&top_left_y=2072&top_left_x=1529)
A4. E) 165 First, we count the horizontal eights ( $\infty$ ). The left circle of such an eight must lie in one of the gray circles, see the figure. Conversely, we can create a horizontal eight by choosing a gray circle and then taking it together with its right neighbor. The number of horizontal eights is therefore equal to the number of gray circles, which is $66-11=55$. Due to symmetry, there are also exactly 55 of each of the two types of diagonal eights ( 8 and 8 ). In total, there are thus $3 \cdot 55=165$ eights.

![](https://cdn.mathpix.com/cropped/2024_04_17_87bdce5b1b523bcd9951g-1.jpg?height=254&width=280&top_left_y=2043&top_left_x=1522)