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Egg-Dropping Problem

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This page is under construction.

For the time being ....

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:

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!

So .... during my 2002 sabbatical I decided to investigate this gem more thoroughly. I published the results in an electronic paper entitled "The Joy of Egg-Dropping in Braunschweig and Hong Kong". This paper contains a number of on-line computational modules.

I strongly recommend this paper to lecturers who teach subjects that are related to robust decision-making under severe uncertainty.

This puzzle is interesting because it has a solution that is optimal with respect to both Laplace's Principle of Insufficient Reason and Wald's Minimax paradigm.

Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of the organizations he is associated/affiliated with.

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