Welcome to Week 4 of the Wednesday Morning Math Challenge. You can find solutions to the Week 3 puzzles here, along with — more importantly — discussions of some ways to approach them. Remember that the real goal here is to think creatively.

Here are three new problems.

**1.** An island is inhabited only by knights and knaves. Knights always tell the truth; knaves always lie. You meet two inhabitants, Bob and Simon. Simon says, “One of us is a knight.” Bob says, “Simon is a knave.” Can you determine who is a knight and who is a knave?

**2.** In a small town, there is a single male barber. The barber shaves all the men who do not shave themselves, and no one else. Does the barber shave himself?

**3.** What is the smallest positive integer not definable in fewer than twelve words? (No hyphens!)