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, weâre featuring three straightforward puzzles that commonly elicit not just incorrect answers, but unwavering confidence from those who supply them.

This weekâ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 Smullyanâ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: âA watched pot never boils.â Anyone whoâs bothered to test this proverb themselves knows the statement to be false; a pot placed on a hot stove will eventually boil, whether itâs watched or not.

But what if we modify the proverb? What if, instead, it says: âA watched pot never boils unless you watch it.â Stated more precisely, âA watched pot never boils unless it is watched.â 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, âWhose picture are you looking at?â The man replied: âBrothers and sisters have I none, but this manâs father is my fatherâs son.â

Whose picture was the man looking at?

Puzzle #39: A Puzzling Picture (Part II)

Suppose, in the above situation, the man had instead answered: âBrothers and sisters have I none, but this manâs son is my fatherâs son.â Now whose picture is the man looking at?

Weâll be back next week with the solutionsâand a new puzzle! Got a great brainteaser, original or otherwise, that youâd like to see featured? E-mail me with your recommendations. (Be sure to include âSunday Puzzleâ in the subject line.)

### SOLUTION To Sunday Puzzle #36: Surveying The Mad Kingâ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 prisonersâ 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 didnâ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 didnâ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 didnâ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 didnâ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.