15. From the book by A. Conan Doyle (English writer) "The Adventures of Sherlock Holmes".

The doctor and his guest Sherlock Holmes were sitting by the open window. Laughter and cheerful voices of a large group of children could be heard from the garden.

Guest. Tell me, please, how many children do you have?

Host. These are not only mine, but children from four families. My team is the largest, my brother's is smaller, my sister's is even smaller, and my uncle's is the smallest group. They are making such a chaotic noise because there are not enough of them to form two teams of 9 people each. An interesting coincidence: if you multiply the four numbers representing the number of children in our families, you get the number of our house, which you know.

Guest. I studied mathematics in school. I will try to calculate the number of children in each of your families.

After some calculations, the guest said, "There is not enough data to solve the problem. Can you tell me if your uncle had one child or more?" The host gave the required answer, the content of which we do not know.

Guest. Now I can give an exact answer about the number of children.

Question. What was the house number and how many children were there in each of the four families?
15. The guest knew that all children were under 18, and he knew the house number $(N)$. Let the number of children in each family be $a, b, c, d$ respectively. Then

$$
a+b+c+db>c>d .
$$

The uncle should not have three children. Suppose $d=3$, then $c \geqslant 4, b \geqslant 5, a \geqslant 6$, so $a+b+c+d=6+5+4+3=18$. But this contradicts the condition. Therefore, the uncle has 2 or 1 child.

Let's construct a table of all cases.

The product must be the same for both $d=1$ and $d=2$. The smallest product that appears in both cases is 120. Therefore, $N=120$.

If the uncle has two children, then $a=5, b=4, c=3, d=2$.

76

If the uncle has one child, there are two possible cases:

$a=8, b=5, c=3, d=1$ or $a=6, b=5, c=4, d=1$.

But the guest gave a definite answer, so $d=2, \quad a=5$, $b=4, c=3$.