A house catches fire. A firefighter remains on the middle step of a ladder, spraying water on the fire. The flames subside and he climbs up five steps. The wind blows and the firefighter descends seven steps. A little later, he climbs up eight steps and stays there until the fire is out. Then, he climbs the last seven steps and enters the house. How many steps does the firefighter's ladder have?
(a) 25
(b) 26
(c) 27
(d) 28
(e) 29
The correct option is (c).

The up-and-down movement of the firefighter from the middle step until reaching the last step is given by

$$
\overbrace{+5}^{\text {up }} \underbrace{-7}_{\text {down }} \overbrace{+8}^{\text {up }} \overbrace{+7}^{\text {up }}
$$

such that the firefighter climbs $8+5=13$ steps above the middle step, reaching the last step of the ladder. Therefore, the ladder has 13 steps above the middle step, and equally 13 steps below the middle step. Therefore, the ladder has $13+1+13=27$ steps. See a diagram of the firefighter's movement.

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-054.jpg?height=442&width=923&top_left_y=1338&top_left_x=652)