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Tried to run it with n=50000, and it didn't time out.
len(candidates) = 3395 (increases with O(log(n))
hamm = 2379126835648701693226200858624
Yes, this implies that we know the height of the big building, in which the child is playing on the nth floor. Why not say the roof?
It could say "A child plays with a ball on the nth floor of a big building at a height h which is known", but I don't see the point of having a parameter n when it isn't used anywhere.
Isn't the question formulated wrongly. Shouldn't the boy be playing on the roof of the building, and not on the nth floor? We only know the height of the building, and not which floor n he is on (or how high a floor is).