9-3. Arina wrote down all the numbers from 71 to 81 in a row without spaces, forming a large number 717273...81. Sofia started appending the next numbers to it (i.e., she first appended 82, then 83, ...). She stopped when the large number became divisible by 12. The last number she appended was $N$. What is $N$?
Answer: 88.

Solution. A number is divisible by 12 if and only if it is divisible by 3 and by 4. For a number to be divisible by 4, the number formed by its last two digits must also be divisible by 4. Therefore, the last number that Sofia writes must be divisible by 4.

The nearest number that is divisible by 4 is 84, but the number 71727374...84 has a sum of digits equal to 158, which means it is not divisible by 3. The next number that is divisible by 4 is 88. The sum of the digits of the number 71727374...88 is 216, which means the entire number is divisible by 3.