4.1. On a grid sheet, a $1 \times 5$ rectangle was painted. Each minute, all those uncolored cells that have at least one side-adjacent cell already colored are colored. For example, after one minute, 17 cells will be colored. How many cells will be colored after 5 minutes?
Answer: 105

Solution 1. Note that after 5 minutes, we will get a stepped figure, in which the rows will have $5,7,9,11,13,15,13,11,9,7$ and 5 cells. In total, this is 105.

Solution 2. Note that if we shorten the strip to $1 \times 1$, 44 cells will disappear, which is $4 \cdot 11=44$. If there is only one cell at the beginning, then in the first move, 4 cells will appear, in the second 8, then $12,16,20$. Adding them up, we get $44+4+8+12+16+20=104$, and one more initial cell.