5. (3 points) Anya, Vanya, Danya, Manya, Sanya, and Tanya were collecting apples. It turned out that each of them collected a whole percentage of the total number of apples collected, and all these numbers are different and greater than zero. What is the minimum number of apples that could have been collected?

Answer: 25
Solution:

Example: there are many different examples, for instance $1+2+3+4+5+10$.

Evaluation (proof that there are no fewer than 25 apples):

Let Anya have collected the fewest apples, and this number is at least 2. Then we get that the total collected is no less than $2+3+4+5+6+7=27$ apples.

If Anya has 1 apple and there are a total of $n$ apples, then $\frac{1}{n}$ is an integer percentage, i.e., $n$ is a divisor of 100, and at least $1+2+3+4+5+6=21$. The smallest suitable number is 25.