This puzzle is extremely popular with math teachers. Indeed, it appears on a number of very popular lists!
Suppose that we wish to know which windows in a 36-story building are safe to drop eggs from, and which will cause the eggs to break on landing. We make a few assumptions:
An egg that survives a fall can be used again.
A broken egg must be discarded.
The effect of a fall is the same for all eggs.
If an egg breaks when dropped, then it would break if dropped from a higher window.
If an egg survives a fall then it would survive a shorter fall.
It is not ruled out that the first-floor windows break eggs, nor is it ruled out that the 36th-floor windows do not cause an egg to break.
If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way. Drop the egg from the first-floor window; if it survives, drop it from the second floor window. Continue upward until it breaks. In the worst case, this method may require 36 droppings. Suppose 2 eggs are available. What is the least number of egg-droppings that is guaranteed to work in all cases?
Which Way Did the Bicycle Go? (page 53)
Konhauser J.D.E., D. Velleman, and S. Wagon (1996)
Dolciani Mathematical Expositions - No. 18
The Mathematical Association of America.
I decided to take a formal look at it whereupon it became amply clear that the treatment of this puzzle in the official literature only scratches the surface. This puzzle is a real treasure trove!
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