Have you ever arrived at the wrong solution to a problem, but been so confident in your answer that it took you forever to see the error of your ways? This week, we’re featuring three straightforward puzzles that commonly elicit not just incorrect answers, but unwavering confidence from those who supply them.

This week’s puzzles all hail from What is the Name of This Book?, an outstanding collection of math, logic, and paradoxical puzzles by Raymond M. Smullyan. One of them is a classic. The other two are of Smullyan’s creation. All three will challenge you to scrutinize your reasoning.

### Sunday Puzzles #37, #38, and #39: Avoiding Being Wrong

Puzzle #37: A Puzzling Proverb

An old proverb says: “A watched pot never boils.” Anyone who’s bothered to test this proverb themselves knows the statement to be false; a pot placed on a hot stove will eventually boil, whether it’s watched or not.

But what if we modify the proverb? What if, instead, it says: “A watched pot never boils unless you watch it.” Stated more precisely, “A watched pot never boils unless it is watched.” Is this statement true or false?

Puzzle #38: A Puzzling Picture (Part I)

A man was looking at a portrait when a passerby asked him, “Whose picture are you looking at?” The man replied: “Brothers and sisters have I none, but this man’s father is my father’s son.”

Whose picture was the man looking at?

Puzzle #39: A Puzzling Picture (Part II)

Suppose, in the above situation, the man had instead answered: “Brothers and sisters have I none, but this man’s son is my father’s son.” Now whose picture is the man looking at?

We’ll be back next week with the solutions—and a new puzzle! Got a great brainteaser, original or otherwise, that you’d like to see featured? E-mail me with your recommendations. (Be sure to include “Sunday Puzzle” in the subject line.)

### SOLUTION To Sunday Puzzle #36: Surveying The Mad King’s Kingdom

Last week, I challenged you to deduce how you and a fellow inmate won your freedom on your fifth day of imprisonment by a mad king. The key to solving the puzzle, I hinted in the title of the post, was to think like two people: yourself, and your fellow prisoner.

Several of you arrived at the correct conclusion, but commenter trimeta provided the most thorough rundown of both prisoners’ logic, and why the captives won their freedom on their fifth day of imprisonment, and no sooner:

Day 1: if one prisoner sees 11, 12, or 13 villages, then they can be certain there are 13 villages, and will say so at 5 PM on this day.

Day 2: if one prisoner sees 0, 1, or 2 villages, they can be certain that *if* there were 13 villages, then the other prisoner would have seen 11, 12, or 13 villages, and would have called out the answer on Day 1. Since they didn’t, they can be certain there are 10 villages, and will say so at 5 PM on this day.

Day 3: if one prisoner sees 8, 9, or 10 villages, they can be certain that *if* there were 10 villages, the other prisoner would have seen 0, 1, or 2 villages, and would have called out the answer on Day 2. Since they didn’t, they can be certain there are 13 villages, and will say so at 5 PM on this day.

Day 4: if one prisoner sees 3, 4, or 5 villages, they can be certain that *if* there were 13 villages, the other prisoner would have seen 8, 9, or 10 villages, and would have called out the answer on Day 3. Since they didn’t, they can be certain there are 10 villages, and will say so at 5 PM on this day.

Day 5: if one prisoner sees 6 or 7 villages, they can be certain that *if* there were 10 villages, the other prisoner would have seen 3 or 4 villages, and would have called out the answer on Day 4. Since they didn’t, the other prisoner must also be seeing 6 or 7 villages, and both prisoners are certain there are 13 villages and will say so at 5 PM on this day.