ANSWERS: 3
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You count them. The proof will be the counting itself. You could try to pick the average area occupied by a bean, and the area of the jar, and then do a simple calculus*. But still, you would need to test it in order to prove it, and the only way to test it is to count it. * If all you need is an average, you would pick the average area occupied by an average bean, take the area of the jar (area of the base * height), and divide the jar area by the avg. bean area.
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Several possible ways of doing it approximately - by weight, by volume, maybe even by magneto resonance. but unless you know all the beans are exactly the same, you can't be sure.
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EITHER WEIGHT OR A COUNT.
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