A king has a daughter and wants to choose the man she will marry.  There are three suitors from whom to choose, a Knight, a Knave, and a Commoner.  The king wants to avoid choosing the Commoner as the bridegroom, but he does not know which man is which.  All the king knows is that the Knight always speaks the truth, the Knave always lies, and the Commoner can do either.  The king will ask each man one yes/no question, and will then choose who gets to marry the princess.  What question should the king ask and how should he choose the bridegroom?

A followup question:

Suppose the three suitors know each other (an assumption that’s not needed in the original problem).  Then find a new strategy for the king where the king only needs to ask a question of any two of the three suitors in order to pick the bridegroom.

In this problem, you and a partner are to come up with a scheme for communicating the value of a hidden card.  The game is played as follows:

• Your partner is sent out of the room.
• A dealer hands you 5 cards from a standard 52 card deck.
• You look at the cards, and hand them back to the dealer, one by one, in whatever order you choose.
• The dealer takes the first card that you hand her and places it, face up, in a spot labeled “0”‘.  The next three cards that you hand her, she places, similarly, in spots labeled “1”, “2”, and “3”.  The last card that you hand her goes, face down, in a spot labeled “hidden”.  (While you control the order of the cards, you have no control over their orientations, sitting in their spots; so you can’t use orientation to transmit information to your partner.)
• Your partner enters the room, looks at the four face-up cards and the spots in which they lie and, from that information (and your previously-agreed-upon game plan), determines the suit and value of the hidden card.

Question: What is the foolproof scheme that you and your partner settled on ahead of time?

As a follow-up question, consider the same problem but with a 124-card deck.