Dropping eggs

[I think I’ve heard some version of this problem before, but heard this one from Sophia Drossopoulou and Alex Summers.]

There’s a certain kind of egg about which you wonder: What is the highest floor of a 36-story building from which you can drop an egg without it breaking? All eggs of this kind are identical, so you can conduct experiments. Unfortunately, you only have 2 eggs. Fortunately, if an egg survives a drop without breaking, it is as good as new–that is, you can then conduct another dropping experiment with it. What is the smallest number of drops that is sure to determine the answer to your wonderings?

January 2009

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