How can you drop two eggs the fewest amount of times, without them breaking?
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Drop the egg from half way up the building. This divides the search space in half. If it breaks, start on the bottom floor and work your way up. If it doesn't, start on the next floor up and continue up.
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Don't know if this is meant to be a trick or joke question - but if you hardboil eggs and drop them from a very tiny height without added impact other than gravity - you could theoretically drop them several times without their breaking. No idea why anyone would want to do that though.
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