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I'm trying to solve a brainteaser:

A 2D circle (cake) is cut randomly with straight lines n-times. What's the expected number of pieces?

Could you give me a hint on how to approach this? Is it possible to solve it analytically or by simulation?

Thanks!

Filip
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    As a start, find the probability that two lines cross – Empy2 Mar 14 '24 at 23:06
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    What is the probability distribution on the lines, i.e. how are the lines chosen? – Travis Willse Mar 14 '24 at 23:51
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    While not the same problem, https://en.wikipedia.org/wiki/Bertrand_paradox_(probability) illustrates how important it is to specify how the lines are chosen. There are several different "uniform" distributions to choose from, and they presumably all yield different results. – Arthur Mar 14 '24 at 23:52

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