Find all triples of natural numbers $a, b, c$ such that $a<b<c$ and the value of the fraction $\frac{1}{7}(44-a b c)$ is a natural number.

(Bird's)
Let's denote the numerator of the fraction, i.e., the expression $44 - a b c$ as $p$. For the given fraction to be a natural number, $p$ must be a natural number divisible by seven and less than 44. Therefore, the possible values for $p$ are $42, 35, 28, 21, 14, 7$. These values correspond to the following values of the product $a b c$: 2, 9, 16, 23, 30, 37. We will write these numbers as the product of three distinct natural numbers: 2 ... not possible, 9 ... not possible, $16 = 1 \cdot 2 \cdot 8$, 23 ... not possible, $30 = 1 \cdot 2 \cdot 15 = 1 \cdot 3 \cdot 10 = 1 \cdot 5 \cdot 6 = 2 \cdot 3 \cdot 5$, 37 ... not possible. The solutions are thus the following ordered triples of numbers $a, b, c$:

$$
[1,2,8],[1,2,15],[1,2,13],[1,5,6],[2,3,5]
$$