How many families own pianos? Say one out of three. Then there are about 250,000 pianos in Chicago. How often would each be tuned? Maybe once every five years. That makes 50,000 tunings a year. How many pianos can one tuner tune in a day? Four? And how many in a year? Assuming 250 working days, one tuner can handle 1,000 pianos a year. So there's work for approximately 50 piano tuners in Chicago -- which, as it turns out, is reasonably close to the actual number in the Yellow Pages. Why was guesswork so accurate? The law of averages is partly responsible. At any point, your assumptions may be too high or too low. But because of the law of averages, your mistakes will frequently balance out. By the way, the Mariana Trench is about six nautical miles deep, and a cannonball drops at a rate of ten feet per second. So it took the cannonball about an hour to reach the bottom.

Could this be guess? If you know Earth's highest point Mount Everest, is 29,000 feet, you might reasonably conclude that its lowest point would be close to the same distance. Then you might imagine that a heavy object would take one second to fall through the water of a 10-foot-deep swimming pool. These estimates would bring you close enough to the correct answer.

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