The Wednesday Morning Math Challenge: Week 4

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!)