# Tagged Questions

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### Blue Eyes: A Logic Puzzle, has a puzzling solution (a.k.a. What does common knowledge have to do with it?)

In Blue eyes: a logic puzzle (specifically, the follow up questions), the most common answer is that it needs to be common knowledge that someone has blue eyes for all the blue-eyed people to leave. ...
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### Two doors, 2 guards logic problem (“is XOR a hypothetical statement?”)

You're trapped in a room with 2 doors, one on your left and one on your right. One door leads to heaven, one door leads to hell. There are two birds in the room. One is a bad bird, which always ...
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### Math brain buster [closed]

Amon, Beta, and Cora each have 2 occupations from the following list: dentist, engineer, teacher, painter, writer, lawyer. No two have the same occupation. a. The dentist had lunch with the ...
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### The famous Portia's casket problem

Gold casket: the portrait isn't in the silver casket. Silver: the portrait isn't in this casket. Lead: the portrait is in this casket. At least one of the statements was true and at least one of them ...
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### Island of knights and knaves

This question is about an island of knights and knaves, where knights always speak the truth and knaves always lie. You encounter two people A and B. Determine, if possible, what each of them are if ...
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### knight and knave problem

For this question, suppose you are on the island of knights and knaves. Remember that knights always speak truth while knaves always tell a lie. (a) Suppose you come across two of the natives. You ask ...
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### Is there no solution to the blue-eyed islander puzzle?

Text below copied from here The Blue-Eyed Islander problem is one of my favorites. You can read about it here on Terry Tao's website, along with some discussion. I'll copy the problem here as ...
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### Four men seated in a boat puzzle

I am looking for an elegant way to solve this rather simple logic puzzle using mathematical logic (statements, conjunctions, disjunctions, implications, tautologies, predicate logic and so on). I am ...
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### Solve this logical puzzle only using logical equivalencies. Is there a shorter way to do it?

Here's a puzzle: Four friends have been identified as suspects for an authorized access into a computer system. They have made statements to the investigating authorities. Alice said "Carlos ...
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### To Mock A Mockingbird: Two barbers (logic puzzle)

I suspect an error in the solution given to a logic problem in the book To Mock a Mockingbird (Chapter 3 Problem 2). Problem Suppose I told you that the town contains two barbers, Arturo and ...
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### Express logic puzzles with proposition calculus notation

I’m trying to solve a logic puzzle that goes like this: The police have three suspects for the murder of Mr. Cooper: Mr. Smith, Mr. Jones, and Mr. Williams. Smith, Jones, and Williams each declare ...
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### What is the name of the logical puzzle, where one always lies and another always tells the truth?

So i was solving exercises in propositional logic lately and stumbled upon a puzzle, that goes like this: Each inhabitant of a remote village always tells the truth or always lies. A villager will ...
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### Which sentence among the three sentences is the lie?

The second statement is the lie or the third statement is the lie. This statement is a truth, or the last statement and the second statement cannot both be truths. The first statement is the lie and ...
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### How to solve this type of Puzzles (Syllogism)?

I have seen lot of questions of below type predictions. I can't figure out the answer. Is there any common method to solve this ? Please consider the following example ...
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### Irreversible chess [closed]

Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...
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### Puzzle: Can arithmetic be axiomatized with a single two-term relation?

Following my question about defining multiplication in terms of divisibility, can all of arithmetic be axiomatized with a single two-term relation? Asaf Karagila comments on my question that the ...
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### Logic Puzzle of the age of three sons

There is a puzzle, it goes something like this: Someone talks to a guy, and asks, Give me the age of my three sons, The other guy asks for some clues: The product of the age of the three sons (of ...
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### Knights & Knaves Logic Problem Help

Can anyone please help me with this knights & knaves logic problem? It is from Raymond Smullyan's Forever Undecided. P= Proposition, and Q = Different Proposition. Properties: 1) R(P) -> B(P) ...
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### Knights and knaves: Who are B and C? (task 26 from “What Is the Name of This Book?”)

I have the following issue #26 from What Is the Name of This Book? of R. Smullyan: There is a wide variety of puzzles about an island in which certain inhabitants called "knights" always ...