Problem 8.1. The cells of the pyramid are filled according to the following rule: above every two adjacent numbers, their arithmetic mean is written. Some numbers were erased, and the structure shown in the figure was obtained. What number was in the bottom right cell? (The arithmetic mean of two numbers is their sum divided by 2.)

![](https://cdn.mathpix.com/cropped/2024_05_06_b135fe79f2e6ed0cbffag-1.jpg?height=395&width=519&top_left_y=382&top_left_x=483)
Answer: 6.

Solution. Let's restore the numbers in the table by going through it from top to bottom. For example, if the numbers 21 and $x$ are in the second row, then from $18=\frac{1}{2}(21+x)$ we get $x=15$. Similarly, in the third row, we get that next to the number 14 is 16, and next to it is -26; in the last row, the numbers are $42,10,22$ and 6.