How many packs to complete the sticker album?
Asked at Jane Street, DE Shaw
A promotion hides one of N equally likely distinct stickers in every pack. You keep buying packs until you own all N.
Estimate the expected number of packs by Monte Carlo, then compare against the exact answer.
N = 6 -> ~14.7 packs
Show a hint
Break the collection into stages: how many packs, on average, to go from j distinct stickers to j + 1? Each stage is a simple geometric wait.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.