Problem 1. On the board are written three positive integers $x, y$ and $z$. Maria writes down in her notebook the product of some two of these numbers and decreases the third number on the board by 1. With the new three numbers, she performs the same operation and so on, until one of the numbers on the board becomes 0. What will be the sum of the numbers in Maria's notebook?
Solution: The product of the numbers on the board decreases by the number written in the notebook with each move. When one of the numbers becomes equal to 0, the product of the numbers on the board also becomes 0. Therefore, the sum of the numbers in the notebook is $x y z$.