Rubanov I.S.

The number 1 is written on the board. If the number $a$ is written on the board, it can be replaced by any number of the form $a+d$, where $d$ is coprime with $a$ and $10 \leq d \leq 20$.

Is it possible to obtain the number $18!$ on the board after several such operations?
Note that the number $18!-19$ ends with 1. We will add 10 to the number on the board. Each time, we will get a number ending in 1, and thus coprime with the number 10, so the operation is possible. Eventually, the number $18!-19$ will appear on the board. We will add 19 to it and get $18!$.