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48 votes
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 ...
Joe's user avatar
  • 596
42 votes
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?
Beastly Gerbil's user avatar
40 votes

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 ...
Rubio's user avatar
  • 41.7k
33 votes
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:
Bass's user avatar
  • 77.7k
27 votes
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 ...
Riley's user avatar
  • 14.4k
24 votes
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: ...
Christoph's user avatar
  • 3,901
21 votes
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
Gareth McCaughan's user avatar
21 votes
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 ...
votbear's user avatar
  • 4,637
19 votes

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!
Beastly Gerbil's user avatar
18 votes

6 prisoners, 2 colors, one mute

I'll try another explanation(with same result): Here are the steps: Next step: So: Who talks?
Tode's user avatar
  • 420
17 votes
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.
Wen1now's user avatar
  • 9,253
17 votes
Accepted

Again! 6 prisoners, 2 colors, one mute

Reasoning:
EightAndAHalfTails's user avatar
17 votes

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 ...
Jaap Scherphuis's user avatar
17 votes
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, ...
Stiv's user avatar
  • 145k
16 votes

What are the three numbers in this puzzle?

The Answer: My reasoning: How I got the numbers:
Acerfire37's user avatar
15 votes

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 ...
Deusovi's user avatar
  • 147k
14 votes
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 ...
Milo Brandt's user avatar
  • 7,891
14 votes

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 ...
Gabriel Burns's user avatar
14 votes
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 ...
Hellion's user avatar
  • 2,204
14 votes

Communicating Information about Cards

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):
Alconja's user avatar
  • 37.3k
14 votes

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 ...
Mike Earnest's user avatar
  • 32.5k
13 votes

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"....
Rand al'Thor's user avatar
13 votes

3 travelers and 9 diamonds

I think it isn't possible and here is my reasoning.
Bennett Bernardoni's user avatar
12 votes

In the 100 blue eyes problem - why is the oracle necessary?

The oracle disproves a nested hypothetical. I'll try to prove this from the top down without using induction. First, a definition: Person(n) is the n'th blue-eyed person. We number the blue-eyed ...
Tim C's user avatar
  • 2,564
12 votes
Accepted

Star Puzzle: Determine which circles are True and which circles are False

The following truth values should solve the puzzle: Steps I used to find the solution:
w l's user avatar
  • 4,992
12 votes

Sum of secret numbers is 101

The answer is: Alice: I know we have different numbers. So no one can have the same number as Alice, it must be 51 or over. Also, so Bob and Charlie cannot have the same number, the remainder must ...
Angkor's user avatar
  • 1,347
12 votes
Accepted

Origin of the "Ages of Three Children" puzzle (Census-taker problem)

After doing a lot of (possibly not quite legal) digging, I think I've found the rough birth of the problem. The problem seems to have evolved in around 1940, from the M.I.T campus during World War II. ...
Beastly Gerbil's user avatar
11 votes

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

Here is an extension of Julian Rosen's method which works for all ordinals up to and including $\omega^2$. In what follows, I will write some numbers in "base-$\omega$", so that $23_\omega$ refers to $...
Mike Earnest's user avatar
  • 32.5k
11 votes

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

Here is an example of a situation in which Alice and Bob will never learn the value of $C$, but if they are told this they can work out the value. $$ \begin{array}{c|cc} &0&1&2&3&4&...
Julian Rosen's user avatar
  • 14.3k

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