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Two-Egg 100-Story Drop

HardStrategy00:00
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Your question is Two-Egg 100-Story Drop. Take a moment with it on the right.

Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).

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Problem

You have 2 eggs and access to a 100-storey building. Eggs can be very hard or very fragile. You need the highest floor an egg can be dropped without breaking, and you are allowed to break 2 eggs. How many drops do you need to make?