This is a nice problem that formed part of my University's math workshops for highschool students:
How many numbers of 7 or less digits whose last 3 (digits) are 388 are multiples of 388?
It is indeed a really nice mathematical problem.
- A pdf file with a quick and (more or less) formal solution that doesn't involve much theory. Check it
- The latex file of the pdf document.
- A python file with the code to check the solution.