# Counting Up = Counting Down

Hansel has to count upwards from 1, increasing the value by $$n$$ each second.
Gretel has to count downwards from 1000, decreasing the value by $$m$$ each second.

If $$m$$ and $$n$$ are both positive integers, at how many (distinct) seconds can they possibly say the same number at the same time?

×