13.206. A three-digit number ends with the digit 2. If it is moved to the beginning of the number, the resulting number will be 18 more than the original. Find this number.
## Solution.

Let the desired three-digit number be of the form $100x + 10y + 2$; then after moving the digit 2, it will take the form $200 + 10x + y$ (1). According to the problem, $200 + 10x + y - (100x + 10y + 2) = 18$, from which we get $10x + y = 20$. Substituting this expression into (1), we get $200 + 20 = 220$. Therefore, the original three-digit number is 202.

Answer: 202.