A trading card series has 200 different cards in it, which are sold in 5-card packages.
Each package has a random sampling of the cards (assume that any card of the 200 has an equal chance of being in a package).
On the average, how many packages will need to be bought to collect the complete series if...
A: all the cards in a package will always be different
B: a package can have repeats
(a) When all the cards in the package are different then the required number of packages on the average is approximately 233.16, which becomes 233 when rounded up to the nearest integer.
(b) When it's possible for a given card to have repeats, the required average number of packages is approximately 235.52, which becomes 236 when rounded up to the nearest integer.
*** Challenging but interesting! Will try to posit an analytical solution when feasible!
Edited on September 19, 2022, 6:29 am
Puzzle Answer
