I was struggling with this but this comment chain has clarified it - you can re-use an egg if it doesn't break. So for example if n = 2 and m = 14, if on your first two tries your eggs break then you don't get any more tries.

Ran into the same problem as Blind4Basics, but this comment thread gave me enough of a hint to research how to solve it. Learnt something new, thanks :)

Tough kata for me, now to study the best solutions.