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 ...
- 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?
- 60.6k
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 ...
- 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:
- 77.9k
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 ...
- 14.5k
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:
...
- 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
- 120k
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 ...
- 4,647
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!
- 60.6k
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?
- 420
18
votes
Accepted
Finding a mystery number from a sum and product, with a twist
Era chose:
There are two cases:
Now
But
So, the perfect logician overhearing everything deduces all this and works out that
- 60.6k
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.
- 9,253
17
votes
Accepted
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 ...
- 53.9k
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, ...
- 146k
16
votes
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 ...
- 148k
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 ...
- 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 ...
- 619
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 ...
- 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):
- 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 ...
- 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"....
- 117k
13
votes
13
votes
Finding a mystery number from a sum and product, with a twist
Era has:
We can analyze this bit by bit:
- 551
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:
- 4,992
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 ...
- 2,564
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 ...
- 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.
...
- 60.6k
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