olymmath

HMMT November 2009 T11

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In general, if there are dd doors in every room (but still only 1 correct door) and rr rooms, the last of which leads into Bowser's level, what is the expected number of doors through which Mario will pass before he reaches Bowser's level?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{d\left(d^{r}-1\right)}{d-1}

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