7.1. What is the maximum number of L-shaped pieces

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consisting of three $1 x 1$ squares, that can be placed in a 5x7 rectangle? (The L-shaped pieces can be rotated and flipped, but they cannot overlap).
Solution: The area of the corner is 3, and the area of the rectangle is 35, so 12 corners cannot fit into the rectangle. The image below shows one way to place 11 corners in the rectangle.

![](https://cdn.mathpix.com/cropped/2024_05_06_16f9c3863cc94eacc671g-1.jpg?height=317&width=397&top_left_y=1863&top_left_x=310)

Answer: 11