Author |
Topic: Doorway to Salvation (Read 2261 times) |
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender: 
Posts: 4489
|
 |
Doorway to Salvation
« on: Jun 13th, 2003, 2:53pm » |
 Quote  Modify
|
One morning you inexplcably wake up to find yourself in a large room with three identical exits,
numbered 1, 2, and 3. However, there is also a violent-looking guard barring your departure.
You meekly ask him if it's OK for you to leave now. The guard, who fancies himself a poet, replies:
"One of these doors leads to salvation,
the other two lead to damnation.
Three questions you will get to try,
But be forewarned, on two I'll lie.
Don't ask why, for I just will.
You'll have to use your wits and skill."
Which three 'Yes or No' questions will ensure you safe passage to the outside world?
|
| « Last Edit: Jun 13th, 2003, 5:26pm by ThudnBlunder » |
 IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
Lightboxes
Full Member
Gender:
Posts: 203
|
|
Re: Doorway to Salvation
« Reply #1 on: Jun 13th, 2003, 11:52pm » |
Quote Modify
|
Would it work if I just used those double negative questions?:
If I were to ask you if door #1 leads to damnation, would you say "yes"?
If I were to ask you if door #2 leads to damnation, would you say "yes"?
If I were to ask you if door #3 leads to damnation, would you say "yes"?
|
|
IP Logged |
A job is not worth doing unless it's worth doing well.
|
|
|
Chronos
Full Member
 
Gender:
Posts: 288
|
|
Re: Doorway to Salvation
« Reply #2 on: Jun 14th, 2003, 12:09am » |
Quote Modify
|
Simple double negative questions won't do the trick, since the guard can choose to put his two lies on whichever question he wants. You can't be sure he's going to lie unless you know he's already used up his true answer, and if you know that, then why do you need more questions?
I'm not convinced there is an answer. At the very least, I know you can't always determine which answer the guard gave was true: To know which answer was true and to also know which exit is correct would be two trits of information, but you can only get three bits of information, and three bits is less than two trits.
But I also don't see how, once you know which exit is correct, you would be unable to determine which answer was correct. So it looks like you can't determine the exit without knowing which answer was true, and you can't determine the exit with knowing which answer was true, either. So you can't determine the exit.
|
|
IP Logged |
|
|
|
redPEPPER
Full Member
Posts: 160
|
|
Re: Doorway to Salvation
« Reply #3 on: Jun 14th, 2003, 5:35am » |
Quote Modify
|
I believe Lightboxes has got something. With each of these questions, it doesn't matter if the guard is lying or not, you get the same answer.
Let's say door 1 leads to damnation.
If the guard tells the truth, he would answer "yes" to the question "does door 1 lead to damnation?" (let's call this the imaginary question). He would therefore also answer yes to the question "If I were to ask you if door #1 leads to damnation, would you say yes?" (let's call that the real question)
If the guard lies, he would answer "no" to the question "does door 1 lead to damnation?". So, to the question "If I were to ask you if door #1 leads to damnation, would you say yes?" he has to answer yes if he wants to be lying.
The only problem I see with this is that it expects the guard to be consistent, and pretend he would lie for the imaginary question if he chose to lie for the real question.
As you can see, with these questions you know which door leads where, but you don't know when the guard lied. You're getting only one trit out of your three bits.
Actually two questions would be enough, as you can deduce the third door based on the two first doors.
|
|
IP Logged |
|
|
|
LZJ
Junior Member
Gender:
Posts: 82
|
|
Re: Doorway to Salvation
« Reply #4 on: Jun 14th, 2003, 5:46am » |
Quote Modify
|
Ah, but perhaps you only have 2 questions left:
Quote:However, there is also a violent-looking guard barring your departure.
You meekly ask him if it's OK for you to leave now. |
|
See? Wasted 1 question already. 
|
| « Last Edit: Jun 14th, 2003, 5:55am by LZJ » |
IP Logged |
|
|
|
tohuvabohu
Guest
|
|
Re: Doorway to Salvation
« Reply #5 on: Jun 14th, 2003, 11:39am » |
Quote Modify
 Remove
|
Asking the question, "If I were to ask you..." won't work because the guard doesn't have to decide whether to lie or not until he's heard the question. Maybe he'd lie if you ask is this the right door, but he'll tell the truth if you ask what his answer would be to that other question.
The only time you can force a true answer is on the third question, when he no longer has a choice. That may be the key.
Suppose I ask the guard, Is it door A, and then Is it door B.
No, no means it can't be C. (that would have been 2 true statements)
No, yes, means it can't be B.
Yes, no, means it can't be A.
Any of those can be solved with the third question. You don't even need to make use of the forced truthfulness if he said no twice, since the third answer would definitely be a lie.
The problem is Yes, yes.
So is there some way to optimize the first two questions so that, in the event that both were going to be no, you manage to extract a bit of information about the Yes, Yes case?
|
|
IP Logged |
|
|
|
Lightboxes
Full Member
Gender:
Posts: 203
|
|
Re: Doorway to Salvation
« Reply #6 on: Jun 14th, 2003, 8:23pm » |
Quote Modify
|
Just in case this is a play on words...I will guess that the gaurd will only lie on question #two:
Quote:
however, I will be back to modify this message and give some alternatives...
K...here is what I have:
I can only get a 7/9 probability of surviving but I'm sure 8/9 (I think, not sure about the math) probability is possible. (T=True, L=Lie, Y=Yes, N=No, S=Salvation, d=Damnation, D1=Door 1..., #1=Question #1...)
#1 Does either door 1 or 2 lead to Salvation?
#2 Does either door 1 or 3 lead to Salvation?
#3 Did you lie on question 1 or will you tell the truth on 3?
Possible Combonations:
D1 D2 D3 D1 D2 D3 D1 D2 D3
S d d d S d d d S
#1 #2 #3 #1 #2 #3 #1 #2 #3
(TLL) Y Y Y Y N Y N Y Y
(LTL) N N N N Y N Y N N
(LLT) N Y Y N N N Y N Y This is only a 7/9 probability of surviving...I think.
The problem is that there are only 8 possible formations of a Yes or No answer in sets of three. BUT 9 possible formations of Truths and Lies with Salvation and Damnations.
I don't know where to go from here...Maybe something more clever!
|
| « Last Edit: Jun 15th, 2003, 6:45pm by Lightboxes » |
IP Logged |
A job is not worth doing unless it's worth doing well.
|
|
|
btiboy
Guest
|
|
Re: Doorway to Salvation
« Reply #7 on: Jun 16th, 2003, 12:19pm » |
Quote Modify
Remove
|
Ths is my first time trying the hide tags, so I hope this works...
Hint 1:You can ask if the guard is lying on a question
Hint 2:Use XOR with Hint #1 to manipulate his answers
Here's my solution, using Lightboxes' notation:
XOR = exclusive OR ((a OR b) AND NOT (a AND b)) - my logic is rusty, so please correct me if I'm using the wrong operator
#1 Is D1 Salvation XOR will you lie on #2?
if the answer to #1 is yes,
#2 is D1 Salvation XOR will you lie on #2?
if the answer to #2 is no, leave through D1
if the answer to #2 is yes, we know he's going to lie, so ask
#3 is D3 Salvation?
if the answer to #3 is yes, leave through D2
if the answer to #3 is no, leave through D3
if the answer to #1 is no,
#2 is D1 Salvation?
if the answer to #2 is no, leave through D1
if the answer to #2 is yes, we know he's going to tell the truth, so ask
#3 is D2 Salvation?
if the answer to #3 is yes, leave through D2
if the answer to #3 is no, leave through D3
The solution above gives a chart of:
D1 D2 D3 D1 D2 D3 D1 D2 D3
S d d d S d d d S
#1 #2 #3 #1 #2 #3 #1 #2 #3
(TLL) N N - Y Y Y Y Y N
(LTL) N N - Y Y Y Y Y N
(LLT) Y N - N Y Y N Y N
Notice with the above solution, we can't always determine on which question he tells the truth.
ADDENDUM: I think there's a way to eliminate the "future" stuff, when we ask if he's going to lie on a future question. The first question would be a normal one (eg. is D1 Salvation?) and subsequently ask him if he lied on a previous question, to manipulate his answer. However, I can't work on this right now...
|
|
IP Logged |
|
|
|
Lightboxes
Full Member
Gender:
Posts: 203
|
|
Re: Doorway to Salvation
« Reply #8 on: Jun 16th, 2003, 7:35pm » |
Quote Modify
|
Quote:| I think there's a way to eliminate the "future" stuff, |
|
I agree with no future stuff. I only used it for the third answer because the gaurd will know whether or not he/she will lie or tell the truth...as chronos said:
Quote:| You can't be sure he's going to lie unless you know he's already used up his true answer |
|
Thanks btiboy. Looks like as long as you can get varations of Yes, No answers that are different from each other in the different collumns (of three) and not worry about the rows.
|
| « Last Edit: Jun 16th, 2003, 7:36pm by Lightboxes » |
IP Logged |
A job is not worth doing unless it's worth doing well.
|
|
|
James Fingas
Uberpuzzler
Gender:
Posts: 949
|
|
Re: Doorway to Salvation
« Reply #9 on: Jun 17th, 2003, 6:07am » |
Quote Modify
|
After you're done this one, try my Door to Salvation II.
|
|
IP Logged |
Doc, I'm addicted to advice! What should I do?
|
|
|
Dante
Newbie
Gender:
Posts: 7
|
|
Re: Doorway to Salvation
« Reply #10 on: Jun 17th, 2003, 9:25am » |
Quote Modify
|
I'm not very happy about using XORs in the question, but I can't of a nicer way right now. Anyway, my solution:
1. Is D1 salvation
2. (Is D2 salvation) XOR (did you lie on 1)
3. (Is D2 salvation) XOR (did you lie on both 1&2)
FFx -> C
TTF -> B
TTT -> C
TFT -> A
TFF -> B
FTT -> A
FTF -> B
I'm fairly sure that will work, but I haven't been rigorous in checking the answer.
|
|
IP Logged |
|
|
|
James Fingas
Uberpuzzler
Gender:
Posts: 949
|
|
Re: Doorway to Salvation
« Reply #11 on: Jun 17th, 2003, 9:52am » |
Quote Modify
|
Using my Method of Solving Who's Who Questions I have determined that the best you can do asking questions of the type "Does door 1 lead to salvation?" is 8/9 (actually, 7/9 guaranteed with a 50/50 shot guess in the last two cases).
Adding a single question of another type somewhere in the question tree (but it can't be the last question) lets you find the correct door every time.
Leonid suggested a method of solving the "Door to Salvation II" that is applicable here, but there is a more elegant way to do it (well I think it's more elegant anyways) that achieves the same performance.
|
|
IP Logged |
Doc, I'm addicted to advice! What should I do?
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print