Pat the Mathemamagician Part 2 Sal the Magician asks you to pick any five cards from a standard deck. You do so, and then hand them to Sal’s assistant Pat. Then you pick one of the five cards, and Pat puts it back into the deck, and takes the remaining 4 cards, arranges them in some way. Sal is blindfolded, and does not witness any of this. Then Sal takes off the blindfold, takes the pile of 4 cards, reads the four cards that Pat has arranged, and is able to find the fifth card in the deck (even if you shuffle the deck after the assistant puts the card in the deck!). Assume that neither Sal nor Pat have supernatural powers, and that the deck of cards is not marked, and that the pile of 4 cards that Pat arranges does not have any funny folding, or weird angles, etc. How does Sal do this one? This one really has me stumped, maybe I am missing something...

One needs to cheat a bit. There are $48$ missing cards, which can be thought of as $1$ to $48$. (The **meaning** of these numbers depends on the $4$ remaining cards, but Sal knows these.)

Pat and Sal have to encode every integer from $1$ to $48$, using the $4$ cards. There are $24$ permutations of the $4$ cards, not enough. But if Pat is allowed to present the $4$ cards to the magician all faces up or all faces down, there is enough information.