Problem 7.1. Denis thought of four different natural numbers. He claims that

- the product of the smallest and the largest numbers is 32;
- the product of the two remaining numbers is 14.

What is the sum of all four numbers?
Answer: 42.

Solution. There are two ways to represent the number 14 as the product of two numbers: $1 \cdot 14$ and $2 \cdot 7$; therefore, the second and third largest numbers are 1 and 14 or 2 and 7. The first case does not work for us, as 1 cannot be the second largest number. So, the second largest number is 2, and the third largest is 7.

Since our four numbers are distinct, the smallest (first by size) number is 1. Then the largest number is 32. From this, it is not difficult to find the sum of all the numbers.