However, he is not very clever.
From my experience in the real world, I know that an unprotected egg will smash when dropped from one story, guaranteed. No need to go up 14 or 27 or even two stories.
(I also know that it is possible to devise protective enclosures to keep an egg from breaking when dropped from 6 stories. The Society of Women Engineers often sponsors competitions. Been there, got the T-shirt.)
"This is a math puzzle plain and simple."
You're being asked to accept that it's possible for an egg, or some other fragile object like, say, a baby, to survive a drop from the first or any other floor, and proceed to solve the math problem.
However, I think it would be a valuable exercise to try and make a more formal statement of the situation so that the parts of the problem that don't line up squarely with the premise (i.e. eggs often crack when dropped from ~4ft high) were more explicit.
That way, the problem could be introduced both ways at the outset, so that you have the motivating image along with the actual constraints of the problem.
I've heard this problem specified as involving fossilized dinosaur eggs in order to get around this problem.
Except of course, the article doesn't mention what the landing surface is, or whether it is what we think of as an egg, or some hypothetical super-egg. This would seem to be discounted by the "There are no tricks, gotchas or other devious ruses" clause, however. If the point of the article is to make it purely a mathematical problem, then pretty much anything except an egg would work, like "A strong box".
Otherwise, it's pretty much a "work out this problem but automatically disregard anything that I don't think should be part of the solution" interview question, that whilst I have no doubt are asked by many middle manager interviewers, would imagine is a little below microsoft or google.
Poor specifications lie at the root of many a programming problem.
The real thing I'm wondering is why are you making a big deal about this? You obviously have the mental capacity to come up with the concept that it's a special material, why can't you just pretend that's what it is and not make a big pedantic joke about it? What is added to this discussion by pointing out something we all know - that eggs break when you drop them from shoulder height.
The alternative is to specify the problem in purely dense mathematical terms. However, I think this way is much better because to understand what the question is really asking without getting into this "eggs break easily" stuff is actually common sense. If someone can't use common sense to figure out what the question is asking without coming up with second grade smart aleck reasons why the problem doesn't work then I think the interviewer would have the answer they would looking for out of the exercise anyway. :)
An interview isn't a written exam. You don't lose points for bringing up real-world considerations - quite the contrary! But the interviewer might ask you to solve the math problem anyway (perhaps by modifying the question a bit, on the fly).
Assume two sets of integers (1..n) and (n+1..100), where 1 <= n <= 100. Your goal is to discover the value of n by asking whether a given number falls within set 1 or set 2. If you propose more than one number that belongs to set 2, you can propose no further numbers. What is the maximum number of proposals necessary to determine n?
If it helps, you can analogize this problem to dropping two fragile objects out of a 100-story building or something. Just don't forget the failure mode of "clever".
An object that survies from being dropped from height x may not survive being dropped a second time from height x.