epgy:ai13:day_9

# Day 9

Question of the Day: Two information theoreticians, Alice and Bob, perform a trick with a shuffled deck of cards, jokers removed. Alice asks a member of the audience to select five cards at random from the deck. The audience member passes the five cards to Alice, who examines them, and hands one back. Alice then arranges the remaining four cards in some way and places them face down, in a neat pile.

Bob, who has not witnessed these proceedings, then enters the room, looks only at the four cards, and correctly determines the missing fifth card, held by the audience member. How is this trick done? Try to come up with the simplest solution possible.

Note: The only communication between Alice and Bob is through the arrangement of the four cards. There is no encoded speech or hand signals or ESP, no bent or marked cards, no clue in the orientation of the pile of four cards (i.e. it would suffice for Bob to be read the list of the four cards in order.)

# Morning

• 9:00 - Dr. Mirjam Eladhari, mirjam_e, mirjame@gmail.com, University of Malta
• 9:30 - Dr. Tracy Holsclaw, iam.random, iamrandom@iamrandom.com, UC Irvine
• 10:45 - Brandon Tearse, [hangout], tearseb@gmail.com, Google

Logic - Prolog

```factorial(0,1).

factorial(N,F) :-
N>0,
N1 is N-1,
factorial(N1,F1),
F is N * F1.```

Logic

• Logic is the science of the correctness or incorrectness of reasoning.
• Or, more to the point, Logic is the study of the evaluation of arguments.
• A statement is a declarative sentence, or part of a sentence, that can be either true or false.
A deductive argument is one in which the author intends the evidence to be so strong that it is impossible for the premises to be true and the conclusion false, or the conclusion follows necessarily from the premises.
An inductive argument is one in which the author intends the evidence only to be so strong that it is improbable that the premises could be true and the conclusion false, or the conclusion is likely true if the premises are true.

Most common example

• All men are mortal
• Socrates was a man
• Socrates was mortal

Truth Tables

• and
• or
• implication
• not

Satisfiability - Conjunctive Normal Form

Deduction:

• A → B and A, so B

Induction:

• A and B, so maybe A → B

Abduction:

• A → B and B, so maybe A