5.4. The number 61 is written on the board. Every minute, the number is erased from the board and replaced with the product of its digits, increased by 13. That is, after one minute, the number on the board will be $19 (6 \cdot 1 + 13 = 19)$. What number will be on the board after an hour?
Answer: 16.

Let's consider the numbers that will be written on the board over the first few minutes:

| After one minute | $6 \cdot 1+13=\mathbf{1 9}$ |
| :---: | :---: |
| After two minutes | $1 \cdot 9+13=\mathbf{2 2}$ |
| After three minutes | $2 \cdot 2+13=\mathbf{1 7}$ |
| After four minutes | $1 \cdot 7+13=\mathbf{2 0}$ |
| After five minutes | $2 \cdot \mathbf{1}+13=\mathbf{1 3}$ |
| After six minutes | $1 \cdot 3+13=\mathbf{1 6}$ |
| After seven minutes | $1 \cdot 6+13=\mathbf{1 9}$ |

Notice that after the sixth minute, the numbers start to repeat. In one hour (60 minutes), exactly 10 cycles of six minutes will pass. Therefore, after one hour, the number that can be read on the board will be 16.

+ complete justified solution

$\pm$ the pattern is correctly identified and the correct answer is given, but the justification is not complete

dry the pattern is correctly identified, but the correct answer is not obtained