I am working on a set of problems with historic context, and I do not seem to be able to retrack, why I consider this problem historic:
Three dice are thrown each round. The question is, how often does one have to throw the three dice until each of the dice has shown six at least once.
I do know the answer to the problem and how it is derived, but I do not find any references to it. I read the 1708 book by Bernoulli today, and he is commenting on several problems by Huygens that are similar. For some reason I believe the problem above was by Moivre, but I can not find any references. I do know, that Moivre knew about the inclusion-exclusion formula which is used here.
Maybe someone has heard of this type of problem? Some people have pointed out similarities to the coupon collector, but i would like to trace back this specific problem.
EDIT: The expected time until each die has shown a six at least once is given by the following formula. Let $W_i\sim Geo(p)$ with $p=1/6$ and $i=1,...n$. Let $T_n$ be the time until all dice have shown a six at least once, then $$\mathbb E(T_n)=\mathbb E(\max_{i}W_i)=\sum_{k=1}^n\binom nk\frac{(-1)^{k+1}}{1-(1-p)^k}\sim -\frac{\ln(n+1)+\gamma_E}{\ln(1-p)}$$
