Question 74
The positive integers $a_0, a_1, \dots, a_9$ and $b_1, b_2, \dots, b_9$ are such that $a_9 \lt b_9$, $a_k \neq b_k$ and $1 \le k \le 8$. A cash machine is loaded with $n \ge a_9$ leva. For any $1 \le i \le 9$ it is allowed to withdraw $a_i$ leva (if the machine has at least $a_i$ leva), and after that the bank puts in the machine $b_i$ leva. It is also allowed to withdraw $a_0$ without any action from the bank. Find all positive integers $n$ for which the cash machine can be emptied by the above described operations.