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€śA watched pot never boils.â€ť 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.*

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*But what if we modify the proverb? What if, instead, it says: â€śA watched pot never boils unless you watch it.â€ť Stated more precisely, â€śA watched pot never boils unless it is watched.â€ť 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€śWhose picture are you looking at?â€ť The man replied: â€śBrothers and sisters have I none, but this manâ€™s father is my fatherâ€™s son.â€ť*

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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: â€śBrothers and sisters have I none, but this manâ€™s son is my fatherâ€™s son.â€ť Now whose picture is the man looking at?*

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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€śSunday Puzzleâ€ť 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.

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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 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.

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

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