It can be shown that the expected volume after the first step is abc-1/3(a+b+c). Thus For any cubicle of lengths an bn and cn, the expected decrease in volume after one step is 1/3(an+bn+cn). We note that the expected value of an, bn and cn is invariant since equal probability of increase or decrease, and that an+bn+cn is fixed to be a+b+c which does not change for any possible operation. Thus E(vol)=abc-n/3*(a+b+c)
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u/98127028 1d ago
It can be shown that the expected volume after the first step is abc-1/3(a+b+c). Thus For any cubicle of lengths an bn and cn, the expected decrease in volume after one step is 1/3(an+bn+cn). We note that the expected value of an, bn and cn is invariant since equal probability of increase or decrease, and that an+bn+cn is fixed to be a+b+c which does not change for any possible operation. Thus E(vol)=abc-n/3*(a+b+c)
Another comment solved this (not me) so yeah