Last year the inhabitants of Elfland (which are -of course- Elfs) had a referendum and decided to stop using barter and to adopt their own currency (the Elfcoin).
On January 1st, 2020 the central bank of Elfland released $100$ banknotes worth $1$ Elfcoin each so that the elfs can use them as currency in the next years. The bank is obviously worried about the wearing out of the banknotes, so they decided to recall $10$ banknotes every year and to replace them with $10$ new banknotes. The operation of recalling old banknotes and replacing them with new banknotes is done "atomically" on January the 1st of every year after 2020. The $10$ banknotes to recall are chosen at random among all the banknotes in Elfland every year, thus it could be the case (for example) that one or more banknotes released in 2021 are recalled in 2022.
Since no other country uses Elfcoin, the banknotes never exit Elfland. Moreover, the elfs never destroy or hide banknotes.
- After how many years you would expect that all the $100$ original banknotes will be recalled?
- What if the bank recalls $10$ random banknotes replacing them with $15$ new banknotes? (or with any other number greater than $10$ of banknotes)?