25. A scout is in a house with four windows arranged in a rectangular shape. He needs to signal to the sea at night by lighting a window or several windows. How many different signals can he send?
25. Let's schematically represent the windows and measure them:

![](https://cdn.mathpix.com/cropped/2024_05_21_00604dc020e3721fc1f4g-181.jpg?height=260&width=257&top_left_y=635&top_left_x=914)

a) Lighting all four windows gives one signal;

b) Lighting one of the windows is perceived as one signal, as in the dark, the position of the windows relative to the house cannot be distinguished;

c) Lighting two windows can give 4 different signals: one signal by lighting windows 1,4 or 2,3; one signal by lighting windows 1,2 or 4,3; two signals by lighting windows 1,3 and 2,4, i.e., we have the following configurations:

1) 
2) $\bullet \cdot 3)$

- 4) 

d) Lighting three windows can give four signals: $1,2,3$; $2,3,4$; $3,4,1$ and $4,1,2$, i.e., we have the following configurations:
1)
2)
3)
4)

In total, we have different signals: $1+1+4+4=10$.