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How Many Jelly Beans?

Reader B.G. (Bellingham) sent an interesting item from the March issue of National Geographic (2009). The context was a one-page article on estimation, accompanied by this photo of Jelly Beans in a jar. The challenge given was to estimate the number of beans in the jar. He guessed 3600. What is your guess?

On a related National Geographic blog, the idea of Fermi estimation is suggested, which involves breaking questions into pieces and then generating rough approximations.

For example, in the case of the jelly beans, the suggested process is this sequence of steps:

  1. Count the jarís radius (r) in beans
  2. Estimate its height (h) in beans
  3. Use these numbers to calculate the jarís occupied volume V = 3r2h, where π has been rounded off to three
Try it using both the bean's width and length...do you get the same estimate?

If you feel the need to know the exact number of jelly beans, go to the National Geographic blog, locate your mouse on the jar photo, and magically the exact answer will appear.

[Note: Just in case this link dies in the future, you could also calculate 2tan(1.570348499)-.002086 in radian mode.]