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

This weekâs 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 Smullyanâs 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: âA watched pot never boils.â Anyone whoâs bothered to test this proverb themselves knows the statement to be false; a pot placed on a hot stove will eventually boil, whether itâs watched or not.*

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*But what if we modify the proverb? What if, instead, it says: âA watched pot never boils unless you watch it.â Stated more precisely, âA 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, âWhose picture are you looking at?â The man replied: âBrothers and sisters have I none, but this manâs father is my fatherâs son.â*

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*Whose picture was the man looking at?*

**Puzzle #39: A Puzzling Picture (Part II)**

*Suppose, in the above situation, the man had instead answered: âBrothers and sisters have I none, but this manâs son is my fatherâs son.â Now whose picture is the man looking at?*

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Weâll be back next week with the solutionsâand a new puzzle! Got a great brainteaser, original or otherwise, that youâd like to see featured? E-mail me with your recommendations. (Be sure to include âSunday Puzzleâ in the subject line.)

### SOLUTION To Sunday Puzzle #36: Surveying The Mad Kingâs 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.

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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 didnât, 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 didnât, 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 didnât, 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 didnât, 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.

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*Contact the author at rtgonzalez@io9.com and @rtg0nzalez. Art by Sam Woolley.*

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