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Lift vs Stairs Optimization

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Your question is Lift vs Stairs Optimization. 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

Tell me how you would compute the minimum possible difference between time taken when traveling by lift versus climbing by stairs, given energy changes per lift floor and per-stairs time depending on current energy.