82
votes
Accepted
68
votes
Accepted
48
votes
48
votes
Accepted
47
votes
Accepted
47
votes
Accepted
Who robbed the store?
Two questions?
The truth tellers that are not the criminal will simply answer "no". The liars that are not the criminal will know their answer would be "yes", so they also answer &...
- 76k
44
votes
Accepted
43
votes
Accepted
The Second Hardest Logic Puzzle in the World
This solution works no matter what happens in the case of paradoxes or questions with ambiguous answers.
First, ask:
With this,
A note: this problem is actually easier than it seems, because
- 145k
40
votes
Accepted
Who committed the crime?
Answer:
Reasoning:
And it fits the requirement of one truthful answer and one lie for each.
- 17.9k
40
votes
Accepted
Out of these 20 Doors, Which One Leads You to the Jackpot?
Plotting every answer's truth combinations would take a lot of room, so let's take a couple of shortcuts first:
Assistant 2 is speaking the truth. There are no square numbers with 6 distinct divisors ...
- 76k
38
votes
The Knight never lies, the knave always lies, and the spy either lies or tells the truth
To start, A must be:
Then, B must
The means that C must
- 8,071
37
votes
Batman vs 4 villains
This answer is kind of cheap and relies on some technicalities, but here goes:
First round, ask everyone:
Next, ask everyone:
Now, we have one person we know is either always lying or always ...
- 8,071
37
votes
Accepted
Ask one verbal question to figure out who is blind and who is mute among three persons
I think this could be an answer:
- 1,135
36
votes
Accepted
XKCD inspired logic puzzle
With two questions, you can ask for the first question:
Based on the answer you'll know if they speak the truth or lies.
If they're lying:
If the they're telling the truth:
- 1,347
36
votes
33
votes
Batman vs 4 villains
The answer is
The reason is
This will also work if
And just for kicks,
However,
- 579
33
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Knights and Knaves: What does C say?
A shortcut to get the correct answer, assuming that one exists, is to simply assume that A, B and C are all knights, and thus speak the truth. In this case, C will obviously answer "Yes." And since ...
- 3,199
32
votes
30
votes
Accepted
Find the identity of the four troll brothers
The mathematically minimum possible solution is:
Credit to supercat and user1540815! I overlooked an important fact in my first draft.
If the trolls stand in one line, there are 4 possible ...
- 2,181
30
votes
Accepted
You trolls, get out of my party!
Solution:
This was about the same thing I said before.
But now...
See Trenin's answer for a different formulation of the same approach, in case that one is easier to understand.
Previous attempt at ...
- 17.9k
28
votes
28
votes
Accepted
Knights and knaves in Landilandia
Ask the man that spoke to you:
Reasoning:
For the follow-up question:
Reasoning behind this:
- 10.5k
28
votes
Accepted
27
votes
Accepted
Batman vs 4 villains
At least half the time, Batman can get the order correct in only 4 questions. For certain sequences, it will take 5 questions.
The Riddler's future answer would be "Yes", and since he answers ...
- 385
27
votes
Accepted
27
votes
Accepted
An Infinitude of Deceptive Devourers
Answer:
Explanation:
Consider two possible cases.
Case 1 - the children used the "at least" convention:
Let's consider two subcases.
Case 1a - only a finite number of people ate cake
Case ...
26
votes
Accepted
26
votes
How many liars are in the room?
This is the same answer as others have already found, but I would like to provide what I see as a better-worded explanation:
(Note that the puzzle doesn't actually require knights who always tell the ...
- 632
25
votes
Accepted
Ten Tricky Mathematicians
By case distinction on the value $g$:
If $g=1$, then the unique truth teller Mx must claim that $h=x$; contradiction.
If $g=2$, then M5 tells the truth ($g=2$). The other truth teller Mx must claim ...
- 45.4k
Only top scored, non community-wiki answers of a minimum length are eligible