A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet two inhabitants: Zoey and Mel. Zoey tells you that Mel is a knave. Mel says, “Neither Zoey nor I are knaves. Can you determine who is a knight and who is a knave?
This is a typical puzzle of the sort that was popularized by Raymond Smullyan in his many logic books. You can find dozens of variations all over the Internet, but this site from the University of Hong Kong is particularly useful for finding easy ones that grow “progressively more difficult.”
Although Smullyan definitely gets the credit for making these puzzles widely known, they actually go back earlier than his first book, which was aptly and recursively named What is the Name of This Book? In fact, I first came across them pre-Smullyan when I was a kid in the mid ’50s, particularly in Maurice Kraitchik’s Mathematical Recreations, a book that I still have. And going back before I was born there was a variation published by the famous philosopher Nelson Goodman, where the two groups of people are called nobles and hunters rather than knights and knaves:
Three inhabitants A, B, C meet some day, and A says either “I am a noble” or “I am a hunter”, we don’t yet know which. Then B, in reply to a query, says “A said, ‘I am a hunter'”. After that, B says “C is a hunter”. Then, C says “A is noble”. Now the problem is, which is each, and why?
These puzzles can be used in many different math classes, since they don’t exactly match any particular math curriculum but they clearly provide practice in logic, which is the foundation of mathematics. (I know, some people think numbers are the foundation of math, but actually logic is.)
Smullyan came to my attention in 1978 with the book referred to above. I was teaching at Lincoln-Sudbury at the time, in the flexible era of the ’70s which conservatives disparaged but which let me modify existing curricula and design entirely new courses. One such course — Codes, Logic, and Semantics — was the perfect vehicle for exploring Smullyan’s work. He continued to inspire me in the following decades, when I read eight more of his books (a small fraction of his entire oeuvre):
- The Chess Mysteries of Sherlock Holmes
- This Books Needs No TItle
- The Lady or the Tiger?
- Alice in Puzzle-Land
- 5000 B.C. and Other Philosophical Fantasies
- To Mock a Mockingbird
- Forever Undecided
- The Godelian Puzzle Book: Puzzles, Paradoxes and Proofs
Like many mathematicians, Smullyan was also a magician, a musician, and a philosopher. He was born in 1919 and died in 2017, truly at a ripe old age.