## 12. Glorious Great-grandfather

“I am 91 years old, I have four children, eleven grandchildren, and many great-grandchildren. If you ask me how many exactly, I will only answer you that the product of their number multiplied by[^13]

66
the number of my grandchildren and by my age equals a number that is written as follows: first comes the number of great-grandchildren, then a zero, and then the number of great-grandchildren again.”

What can you say about this?
12. Let $n$ be the number of great-grandchildren we are looking for. Based on the words of the great-grandfather, we can write

$$
11 \cdot n \cdot 91 = 1001 n = \ll n 0 n \gg.
$$

From this, it follows that $n$ is a two-digit number, i.e., it is between 10 and 99. The information provided by the great-grandfather, to put it mildly, is not very complete.