Cover by Philipp K. Janert

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Chapter 7. Guesstimation and the Back of the Envelope

LOOK AROUND THE ROOM YOU ARE SITTING IN AS YOU READ THIS. NOW ANSWER THE FOLLOWING QUESTION: how many Ping-Pong balls would it take to fill this room?

Yes, I know it’s lame to make the reader do jot’em-dot’em exercises, and the question is old anyway, but please make the effort to come up with a number. I am trying to make a point here.

Done? Good—then, tell me, what is the margin of error in your result? How many balls, plus or minus, do you think the room might accommodate as well? Again, numbers, please! Look at the margin of error: can you justify it, or did you just pull some numbers out of thin air to get me off your back? And if you found an argument to base your estimate on: does the result seem right to you? Too large, too small?

Finally, can you state the assumptions you made when answering the first two questions? What did or did you not take into account? Did you take the furniture out or not? Did you look up the size of a Ping-Pong ball, or did you guess it? Did you take into account different ways to pack spheres? Which of these assumptions has the largest effect on the result? Continue on a second sheet of paper if you need more space for your answer.

The game we just played is sometimes called guesstimation and is a close relative to the back-of-the-envelope calculation. The difference is minor: the way I see it, in guesstimation we worry primarily about finding suitable input values, whereas in a typical back-of-the-envelope ...

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