4. A rectangle $11 \times 12$ is cut into several strips $1 \times 6$ and $1 \times 7$. What is the minimum total number of strips?
Solution. Answer: 20. The example is shown in the figure.

Evaluation: we will paint every seventh diagonal so that 20 cells are shaded (see figure). Each strip contains no more than one cell, so there are no fewer than 20 strips.
![](https://cdn.mathpix.com/cropped/2024_05_06_8917cb8e47235e5c3454g-1.jpg?height=368&width=698&top_left_y=2147&top_left_x=736)