Curious Escalator Math

Sep 20, 2004

This puzzler came from Irving Biggio. Here it is:

He writes, "Unlike many of your puzzlers, this one is actually about transportation. In our fair city of London, England-- not far from the real Cambridge—many of the Underground, or subway, stations have three escalators.

It's always the case that two of them are up escalators, and one is a down escalator. It doesn't matter which way the rush hour crowds are moving, or if more people are arriving or leaving, or the time of day: There are always two that go up, and one that goes down. The same is true for underground stations out in the suburbs."

Why is this?

Now, Irving's been kind enough to provide some wrong answers to explain this phenomenon.

For example, it's easier to go down than to go up. Or, people going down can also take the stairs. But, he adds parenthetically, most of the Underground stations don't have stairs.

He also provides a hint: When the station with the escalators is elevated above ground, the opposite situation holds. That is, there are two escalators going down, and one going up.

Think you know why the Brits have designed their subway this way?
RAY: The train riders are always trickling in, and one escalator is sufficient to handle the people who are trickling in. But when the train arrives, it's got a thousand people on it and they're all leaving, you need the two escalators going in the same direction to accommodate them. Otherwise people have to spend the night in the subway station.

Tell us who the winner is.

TOM: All right. The winner to this puzzler is Richard Waite from Seattle, Washington. And for having his answer selected at random from among all of the correct answers that we got (two), Richard will get a $26 gift certificate to the Shameless Commerce Division at, where he can get, among other things, a distressed Car Talk T-shirt. Distressed.

RAY: Well, wouldn't you be distressed if someone painted Car Talk on you?

TOM: Yeah, well, I guess this style of shirt is also known as "pigment dyed." It has that worn out look. I mean we were kids when our mother would throw out a shirt that looked like this. But now you pay extra for it.

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