Task 1. In the fields of the given tape, fill in the blanks with natural numbers so that the product of any three consecutive numbers is equal to 30. How many solutions does the problem have?

![](https://cdn.mathpix.com/cropped/2024_06_05_dc4d34c0a9dd2a3ba572g-01.jpg?height=113&width=807&top_left_y=655&top_left_x=517)
Solution. There are two ways to represent the number 30 as a product of three natural numbers: $30=1 \cdot 5 \cdot 6$ or $30=2 \cdot 3 \cdot 5$. In the case $30=1 \cdot 5 \cdot 6$ we have two possibilities:

| 5 | 6 | 1 | 5 | 6 | 1 | 5 | 6 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| 5 | 1 | 6 | 5 | 1 | 6 | 5 | 1 |

In the case $30=2 \cdot 3 \cdot 5$ we have the following two additional possibilities:

| 5 | 3 | 2 | 5 | 3 | 2 | 5 | 3 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| 5 | 2 | 3 | 5 | 2 | 3 | 5 | 2 |

Thus, the problem has four solutions.