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Suppose there are N types of surprise mystery toys uniformly distributed in cereal boxes. How many boxes would a kid have to buy to collect them all on average? Now suppose there are M kids efficiently trading. How many boxes sold before all kids have all toys?
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Ah so “efficiently trading” is just collecting M copies of each? My hunch is MN + logN in that case but will have to think more. Intuitively when you still need to collect many copies of each toy each new purchase is useful. Things are harder when M is small
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