I’m posting all these puzzles because Yat said he thought that logic puzzles are becoming stale, and I’m trying to prove him otherwise.
There are two types of inhabitants in the world: humans and vampires. Humans always tell the truth and vampires always lie. Also, inhabitants can either be sane or insane. Someone who is insane has all of their beliefs backwards; everything true they believe to be false, and everything false they believe to be true.
For example, if you ask an insane vampire, “Is the sky blue?” he will insanely think that it isn’t and then lie and say that it is. He will answer, “Yes.”
Here’s the problem: insane vampires and sane humans will give the exact same answer to any question (as will sane vampires and insane humans), so how are you supposed to protect yourself from vampires in this world if you can’t tell them apart?
Ask any inhabitant if 2 + 2 = 4. If the answer is yes, is he a sane human or an insane vampire? If he answers no, is he an insane human or a sane vampire? There’s no way to tell!
…or is there?…
What is a single yes or no question that you could ask to any inhabitant to determine if he is a human or a vampire?
Please use rot13 to encode your answers so as not to ruin the puzzle for anybody else.
You can find more puzzles in my blog, and you should try playing the game of Munch as well.
Tags: logic, Raymond Smullyan, sanity, vampires
Wow, I certainly did not say that logic puzzles were getting stale. I just think that the type of question used in the earlier problem made trivial most of the problem for every puzzle of this type, when it is a purely logic puzzle. I suspect the problem with the perfect logician unable to find out something we could (the article before this one), to be very out-of-the-box, because it would need to find information that both the reader and the inhabitant have, but not the logician… I am curious to know the answer, but I would be surprised if this were a solution involving only logic.
For this puzzle, the problem is the concept of insanity, which I am not sure I understand well. But you seem to say that insanity and lie work the same way, so here is my solution :
“Vs V nfxrq lbh vs lbh ner n inzcver, jung jbhyq lbh fnl ?”
N fnar uhzna jbhyq anghenyl nafjre ab
N fnar inzcver jbhyq yvr nobhg gur snpg gung ur jbhyq yvr, naq nafjre lrf
Na vafnar uhzna jbhyq guvax ur vf n inzcver, fb fnl lrf va uvf ulcbgurgvpny fvghngvba, ohg or jebat nobhg vg naq fnl ab.
Svanyyl, na vafnar inzcver jbhyq guvax ur vf uhzna, ohg yvr nobhg vg va uvf ulcbgurgvpny fvghngvba naq fnl lrf, or jebat nobhg guvf naq guvax ur jbhyq fnl ab, gura yvr naq nafjre lrf.
I may be wrong about the way insanity works, but as getting both humans and vampires a sincere answer is already solved, any difference between the insanity and the lie would be easy to use to make difference between vampires and humans.
Rkpryyrag! “Vs V nfxrq lbh vs” vf gur xrl gb guvf fbeg bs chmmyr. Vafnar crbcyr ner jebat nobhg rirelguvat, rira gurve bja oryvrsf. Nfxvat gurz jung gurl jbhyq fnl vs lbh npghnyyl nfxrq gurz trgf nebhaq guvf.
Bu, gur bgure xrl vf hfvat gur cuenfr “lbh” va gur dhrfgvba, orpnhfr gung nfxf n qvssrerag dhrfgvba qrcraqvat ba jurgure be abg gurl ner n inzcver. Gung’f jung V ybir nobhg guvf evqqyr. Rira gubhtu gur jbeqf ner gur fnzr, gur dhrfgvba vf qvssrerag sbe rnpu crefba.
“Wow, I certainly did not say that logic puzzles were getting stale. I just think that the type of question used in the earlier problem made trivial most of the problem for every puzzle of this type, when it is a purely logic puzzle.”
I know, but that’s what I love about it! It’s like taking puzzles to the “next level”. We’ve moved beyond the simple true/false puzzles
Hey,
Great puzzle. I used to do these and the Knights and Knave puzzles in logic classes in college. I’ve been looking for them in book form, but cant find them collected in anyone place (book or online). Any suggestions?
Thanks,
Tim
Lbh whfg nfx “Ner lbh vafnar?”
Gur gehyl vafnar qb abg xabj gurl ner vafnar fb..
Gur fnar uhzna jvyy nafjre “Ab”
Gur vafnar uhzna jvyy nafjre “Ab”
Gur fnar inzcver jvyy yvr naq gryy lbh “Lrf”
Gur vafnar inzcver jvyy guvax ur vf fnar ohg yvr naq gryy lbh “Lrf”
Are you sane? Vampires will always say no and humans will always say yes.
Oh shoot. I mean “Ner lbh fnar? Inzcverf jvyy nyjnlf fnl ab naq uhznaf jvyy nyjnlf fnl lrf.”
An insane vampire would say yes Tyler.