How many energy eigenstates can "fit" inside a one-dimension box of length L?
All of them.
It's not clear what you mean by "fit", but there are an infinite number of energy eigenstates available and any superposition of any number of these is possible. Google for "infinite square well eigenfunction" for more information.
Thank you! That is what I thought but wasn't sure if the "fit" was a trick statement.
Separate names with a comma.