Problem 2. The number 27 is written on the board. Every minute, the number is erased from the board and replaced with the product of its digits, increased by 12. For example, after one minute, the number on the board will be $2 \cdot 7+12=26$. What will be on the board after an hour?
# Answer: 14

Solution. Let's find the next few numbers that will appear on the board. After 26, it will be 24, then $20, 12, 14, 16, 18$ and again 20. Notice that the sequence has looped and each subsequent number will coincide with the one that is 5 positions earlier. Therefore, after an hour, that is, 60 minutes, the number written will be the same as the one written 55 minutes earlier, which in turn coincides with the one written 50 minutes earlier, and so on, down to the one written 5 minutes earlier, which is the number 14.