5.1. (13 points) On the picture, the entrance and exit of the maze are marked with arrows. You can move through it such that on this picture you can only move right, down, or up (you cannot turn around). How many different ways are there to navigate this maze?

---

The translation maintains the original text's formatting and structure.
Answer: 16.

Solution. Let's call a place in the maze a fork if from it you can move in two possible directions.

![](https://cdn.mathpix.com/cropped/2024_05_06_e9ab2720010b11e95d06g-2.jpg?height=337&width=360&top_left_y=668&top_left_x=1565)
Moving up or to the right after entering, we arrive at one of the forks marked on the diagram with the symbol $\times$. From each of them to the exit from the maze, we will encounter three forks marked on the diagram with the symbol $\bullet$, so the total number of paths is $2 \cdot 2 \cdot 2 + 2 \cdot 2 \cdot 2 = 16$.

![](https://cdn.mathpix.com/cropped/2024_05_06_e9ab2720010b11e95d06g-2.jpg?height=332&width=368&top_left_y=1236&top_left_x=844)