313.Two Eggs, One Hundred Floors
★★★puzzlesTower Research Capital
You have two identical eggs and a 100-storey building. There is a critical floor such that an egg dropped from it or any higher floor breaks, while a drop from any lower floor leaves the egg intact. A broken egg cannot be reused. Playing optimally against the worst case, what is the smallest number of drops that always suffices to identify the critical floor?
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Once the first egg breaks you must climb one floor at a time with the second. So each successive first-egg drop should cover a shorter stretch, exactly offsetting the drop you have already spent.
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