You got 16 types of coins to collect, and you can only buy a box which contains 1 of them with probability evenly distributed.
For every 4 duplicate coins you collect, you can redeem 4 duplicate coins for 1 of those which you don't have. (You save your chance and use it in the end to avoid buying coins which you have redeemed.)
Suppose you already have $x$ types of coins and $y$ duplicate coins, how many boxes will you need to buy in order to collect all of the coins?