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Two eggs and thirty-six floors

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A building has 36 floors. Eggs break when dropped from a certain floor or above, and survive (undamaged, reusable) from below it. You have two eggs.

What is the smallest number of drops that always suffices to find the critical floor, and from which floors should you drop? Then explain why the answer for 100 floors is 14.

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Once the first egg breaks, the second must be dropped floor by floor from just above the last surviving floor. So each successive gap between first-egg drops should shrink by one, to keep the worst case constant.

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Balance-Scale Weighing ProblemsThe Egg Drop With k Eggs and n FloorsMastermind: Deduction From FeedbackSearching a Unimodal FunctionAdaptive Versus Pre-Committed Weighing Strategies

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