# Tag Info

Accepted

### Are there eighteen or twenty bars in my castle?

I think I have a faster solution than Rubio. (Or I did, when Rubio's solution took one day longer than mine; he's since incorporated my solution into his answer). The answer: The explanation: Let's ...
Accepted

### A Logician, three students and three initials

I think the correct combination is If we go through the conversation: So that’s it right?

### Are there eighteen or twenty bars in my castle?

The answer Assumptions We assume both have at least one bar on their window (or the window couldn't be said to be barred, and they're told their windows are the only barred ones). We further assume ...
Accepted

### 6 prisoners, 2 colors, one mute

It will be Both A and B can see, what C sees, and that's why they both know that From there, the problem reverts to the earlier one:
Accepted

### A game of multiplication and addition

The numbers are Alice: You can't know my sum. Bob: Thanks to you, I know your sum. Alice: Then I know your product. EDIT: While I show the consistency of the two numbers with the provided ...
Accepted

### Mastermind: Win in two

This is an attempt to prove that there is only one possible setup, namely the one that Beastly Gerbil describes in their answer. First, a couple of observations: That leaves us with Two colors AABB: ...
Accepted

### Abby and Bobby and three numbers on the blackboard

The following table gives the numbers of one person and the corresponding possible numbers of the other person. ...
Accepted

### A 3-person hat puzzle (no, not that one) (no, not that one either!)

The crucial fact here (which I think makes the question kinda unfair since it's not exactly common knowledge) is that And we had better Now, So And in this case
Accepted

### 3 Numbers on Hats, A = B + C

Answer: First, some observations Alright. Now, let's take a look at different possibilities: Generalizing this, we get the rule above: Do note however that the actual answer is actually slightly ...

### Mastermind: Win in two

The code is of the format Bob first guessed To which Alice responded with So Bob knows for certain See @Christoph’s answer for proof this is the only solution!

### 6 prisoners, 2 colors, one mute

I'll try another explanation(with same result): Here are the steps: Next step: So: Who talks?
Accepted

### Sum of secret numbers is 101

Alice: I know we have different numbers. Bob: Aha, I got it. I found all the numbers. Charlie: Me, too. I know our numbers, now. Alice: Alas, I still don't know.
Accepted

Reasoning:

### Three people wearing hats

This was trickier than it looked. I have a feeling that there should be a quicker way to find the answer than the list of cases I worked through. Note: I interpret "two of which are factors of the ...
Accepted

### Three secret numbers and sum

I think this works, although it results in two possible solutions that I believe meet all the criteria... The first student says that he knows that the two other students have different numbers, ...

### What are the three numbers in this puzzle?

The Answer: My reasoning: How I got the numbers:
Accepted

Accepted

### Meta Knights and Knaves Puzzle with Hats

If the Blue hat guy answered YES (Raymond is a knight), then there were many compatible scenarios: Raymond indeed was a knight, and Blue=knight=Raymond Raymond indeed was a knight, and Blue=knight=...
Accepted

### Another sum and product puzzle

The fact $3z\geq x+y+z>xyz$ implies that $3>xy$, so $x=1$ and $y=1$ or $x=1$ and $y=2$. In the former one, we get $2+z>z$. Otherwise we get $3+z>2z$, so $z<3$ and then in fact $z=2$. ...
Accepted

### Constructing interesting "Don't Know - Don't Know - Now I know!" type puzzles

The professor says: I have written on Alice's paper an even ordinal and on Bob's paper an odd ordinal. Who has the lesser ordinal? Then, after $\lambda$ iterations of the game, it is common ...
Accepted

### Yet Another What am I? Puzzle

You are 1) From my birth I want to rise But I shall fall, its no surprise I should display approval from afar But pedantic snobs is what you are. 2) I could produce a rise in rank But not if my ...

I'm no mathematician, but I think both Deusovi and Gareth can say: I'm not sure about making it into a proof, but by the extreme example: Basically (maybe/hopefully):

### A game of multiplication and addition

Riley's answer proves that the numbers are consistent with the conversation. I will prove that these are the only possible numbers. After Alice's first statement, After Bob's statement: After ...

### Liar and the Truth teller with 6 inhabitants

We have five statements to process: "Two of us are truth tellers". "None of us are truth tellers". "Three of us are truth tellers". "Only one of us is a truth teller". "Three of us are truth tellers"....

### Are there eighteen or twenty bars in my castle?

Along the lines of Glen O's answer, this answer attempts to explain the solvability of the problem, rather than provide the answer, which has already been given. Instead of using the meta-knowledge ...

### 3 travelers and 9 diamonds

I think it isn't possible and here is my reasoning.

### Blue eyes riddle: a counter-argument to accepted solution

Say I'm one of the residents of this island, and the Guru hasn't shown up yet. I'm a perfect logician, like all the rest of the residents... but I'm very forgetful. So, to help me remember things, I ...