# Preview of the Session of September 28, 2013

1. Math warm up. We will begin this session as every other one with some simple questions, so as to get us all in the mood to tackle harder problems.
2. # Knights and knaves, and the occasional normal

 Aristotle says: I invented logic

Knights and Knaves is a logic game, or series of puzzles going apparently quite far back. Raymond Smullyan, who not only is a mathematician, but also a professional magician and professional concert pianist, developed their stories in a series of books. In the island of knights and knaves there live two types of people, the straight as an arrow knights who can never lie even if their life depended on it, and the insidious knaves, who never, never tell the truth. There is really no way to tell which is which from their appearance. You, on meeting a group of islanders, have to tell who are knights and who are knaves from their answers to some questions, or other statements they make. To make matters more complicated, recently some normals have settled on the island; they look just like the knights and knaves, but they sometimes answer truthfully, other times lie. Being able to reason logically is very important in mathematics and the point of the game we will be playing is to learn some logic, and make us aware of some logical pitfalls.

Aristotle probably did not invent logic, but he wrote the first comprehensive treatise on logic, a treatise that remained the final word on the subject for over 2000 years.
3. # Problems

The heart of the session. This time we will work on, discuss and enjoy some interesting problems from the Moscow Math Circle book.