The number 61 is written on the board. Every minute, the number is erased from the board and the product of its digits, increased by 13, is written in its place. After the first minute, the number 19 is written on the board ( $6 \cdot 1+13=19$). What number will be on the board after an hour?
Let's consider the numbers that will be written on the board over the first few minutes:

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

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 on the board will be 16.

## Answer

16.