7.2 Out of 24 matches, a figure in the form of a $3 \times 3$ square is laid out (see figure), the side length of each small square is equal to the length of a match. What is the smallest number of matches that can be removed so that there are no whole $1 \times 1$ squares left, formed from matches.

![](https://cdn.mathpix.com/cropped/2024_05_06_5a22ed0820d13cab1688g-1.jpg?height=257&width=254&top_left_y=1502&top_left_x=1552)
Answer: 5 matches.

Solution: Estimation: It is impossible to manage with four matches, as by removing a match, we "ruin" no more than two squares (each match is a side of one or two adjacent squares), but initially, we have 9 small squares. Example for 5 matches:

![](https://cdn.mathpix.com/cropped/2024_05_06_5a22ed0820d13cab1688g-1.jpg?height=252&width=255&top_left_y=2187&top_left_x=772)