Why the first lift is usually going the wrong way

Question

You work on the second-from-top floor of a tall building with a single lift that travels continuously up and down, stopping at every floor. Whenever you want to go down to lunch, you press the button, and the first lift to arrive is almost always going up. Your colleague on the second floor complains of the opposite: her first lift is almost always going down. Explain. Is the lift conspiring against you? What happens with several lifts?

Accepted Answer

No conspiracy. At a random moment the lift is far more likely to be below your high floor than above it, and a lift below you arrives going up. One lift. Picture the lift bouncing between the ground floor and the top floor at constant speed. At a random instant its position is uniformly distributed over the building's height. If you are on the second-from-top floor of a 20-storey building, about 18/19 of the building is below you, so the lift is below you about 95 per cent of the time. A lift below you, moving continuously, reaches your floor while travelling up. Only in the rare case that it…

Why the first lift is usually going the wrong way

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