11.1. In each cell of a $6 \times 6$ table, numbers are written. All the numbers in the top row and all the numbers in the left column are the same. Each of the other numbers in the table is equal to the sum of the numbers written in the two adjacent cells - the cell to the left and the cell above. What number can be written in the top-left corner cell if the number in the bottom-right corner cell is 2016?
Answer: 8. Let $a$ be the number written in the corner cell at the top left. Then the table is filled in sequentially. For the bottom right corner, we get the relation $252 a = 2016$, from which it follows that $a = 8$.

Comment. An answer with a chain of calculations - 7 points. An answer obtained using combinatorial considerations - Pascal's triangle - 7 points.

![](https://cdn.mathpix.com/cropped/2024_05_06_7350f50326e4669d07cfg-3.jpg?height=426&width=431&top_left_y=621&top_left_x=1441)