# How to come up the number of nodes on a given level in heaps?

CLRS asked it's readers to prove that there are at most $\lceil n/2^{h+1} \rceil$ nodes of height $h$ in any n-element heap as an exercise.
The principle of Mathematical Induction can be used to prove this as explained here.

My question is how one can come up with this formula at first place. Are there any key observations that lead us to this expression initially. And then proof by induction that this will hold true for all positive integer.