8.3. To the number 2014, a digit was added on the left and on the right. The six-digit number thus obtained became divisible by 36. Find all such six-digit numbers.
Answer: 220140, 720144, 320148.

A number is divisible by 36 if and only if it is divisible by 4 and by 9. According to the divisibility rule for 4, the digit $a$ must be appended to the right so that the two-digit number $4a$ is divisible by 4. There are three possible options: 0, 4, and 8. According to the divisibility rule for 9, the digit $b$ must be appended to the left so that the sum of the digits of the number $b2014a$ is divisible by 9. The options $a=0, 4$, and 8 uniquely lead to $b=2, 7$, and 3.

Remark. Only an answer with verification but without an explanation of the absence of other numbers is worth up to 2 points.