In the image, there is a game board and a path that Jindra intended to follow from the bottom right corner to the top left. He then realized that his map was incorrectly rotated, meaning he would not start in the bottom right corner. The shape of the intended path could not be changed, and he had to follow it with the map correctly oriented.

For each of the three possible rotations, redraw the given path and determine how many gray squares this path crosses.

(E. Semerádová)

![](https://cdn.mathpix.com/cropped/2024_04_17_c38afaf85505d4b5c3c0g-4.jpg?height=491&width=500&top_left_y=1939&top_left_x=778)
When gradually turning the knob, we get:
![](https://cdn.mathpix.com/cropped/2024_04_17_c38afaf85505d4b5c3c0g-5.jpg?height=492&width=1556&top_left_y=293&top_left_x=252)

In each case, the path passes through seven, eight, and four gray squares, respectively.