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Nice writeup!

That said, I got ~500 gumballs in the machine ((container diameter / gumball diameter)^3 * .64) so both guesses of 100 and 1000 should be within an order of magnitude. ;)




Aside: If an order of magnitude is a factor of 10^1, half an order of magnitude is actually 10^0.5 ~= 0.3.

So rounding 500 to the nearest order of magnitude gives 1000. 310 is the mid point.




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