The audience chooses 5 arbitrary cards from a regular 52-card deck, and hands those 5 cards to a magician.
The magician chooses 4 cards, then reveals those 4 cards one at a time to his assistant.
The assistant promptly tells the magician what the 5th card is.
QUESTION 1: Figure out how to do this. That is, figure out how to choose, for any size-5 subset of cards, an ordering of 4 of those cards so that the assistant can tell just from the 4 cards and the ordering of those 4 cards what the 5th is.
QUESTION 2: What's the largest deck (more than 52 cards) that this trick can be done with, assuming that the magician will be given 5 cards and he must choose 4 to reveal?