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anthonynow12
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Riddles  
« on: Dec 20th, 2006, 12:32pm »
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You approach two talking doors. One door leads to the City of Truth, while the other door leads to the City of Liars. You do not know which door is which. You are able to ask only one question to determine which door is which. The door that leads to the City of Liars always speaks lies, while the door that leads to the City of Truth always speaks the truth. You want to go to the City of Truth. What question do you ask to determine which door leads to the City of Truth?
 
1. What row of numbers comes next in this series?
 
 
1
11
21
1211
111221
312211
13112221
 
2. A man was to be sentenced, and the judge told him, "You may make a statement. If it is true, I'll sentence you to four years in prison. If it is false, I'll sentence you to six years in prison." After the man made his statement, the judge decided to let him go free. What did the man say?
 
3. You have a barrel of oil, and you need to measure out just one gallon. How do you do this if you only have a three-gallon container and a five-gallon container?
 
4. If your sock drawer has 6 black socks, 4 brown socks, 8 white socks, and 2 tan socks, how many socks would you have to pull out in the dark to be sure you had a matching pair?
 
5. What is broken every time it's spoken?
 
6. How did Mark legally marry three women in Michigan, without divorcing any of them, becoming legally separated, or any of them dying?
 
7. Mom and Dad have four daughters, and each daughter has one brother. How many people are in the family?
 
8. What English word retains the same pronunciation, even after you take away four of its five letters?
 
9. If I say "Everything I tell you is a lie," am I telling you the truth or a lie?
 
10. What work can a painter never quite finish?
 
11. Why wasn't Bertha put in jail after killing dozens of people?
 
12. Why wasn't John able to take a photo of his mother with curlers?
 
13. If there are three cups of sugar and you take one away, how many do you have?
 
14. What has a mouth but can't chew?
 
15. How many letters are in the alphabet?
 
16. What gets wetter and wetter the more it dries?
 
17. What can travel around the world while staying in a corner?
 
18. Food can help me survive, but water will kill me. What am I?
 
19. Take away the whole and some still remains. What is it?
 
20. What stinks when living and smells good when dead?
 
21. When is it bad luck to meet a white cat?
 
22. If it has a quart capacity, how many pennies can you put into a empty piggy bank?
 
And One More Hard Riddle
23. Which of the following statements are true?
 
1. At least one of these ten statements is false.
2. At least two of these ten statements are false.
3. At least three of these ten statements are false.
4. At least four of these ten statements are false.
5. At least five of these ten statements are false.
6. At least six of these ten statements are false.
7. At least seven of these ten statements are false.
8. At least eight of these ten statements are false.
9. At least nine of these ten statements are false.
10. At least ten of these ten statements are false.
 
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Re: Riddles  
« Reply #1 on: Dec 20th, 2006, 2:37pm »
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on Dec 20th, 2006, 12:32pm, anthonynow12 wrote:
You approach two talking doors. One door leads to the City of Truth, while the other door leads to the City of Liars. You do not know which door is which. You are able to ask only one question to determine which door is which. The door that leads to the City of Liars always speaks lies, while the door that leads to the City of Truth always speaks the truth. You want to go to the City of Truth. What question do you ask to determine which door leads to the City of Truth?

Am I a pizza?
 
Quote:
2. A man was to be sentenced, and the judge told him, "You may make a statement. If it is true, I'll sentence you to four years in prison. If it is false, I'll sentence you to six years in prison." After the man made his statement, the judge decided to let him go free. What did the man say?
The goldbach conjecture is true.
 
Quote:
3. You have a barrel of oil, and you need to measure out just one gallon. How do you do this if you only have a three-gallon container and a five-gallon container?
If they're perfectly cylindrical, hold the 5 gallon container tilted, and fill it such that the surface divides the container diagonally in two. Then fill from the 5G container (with 2.5 G) the 3G container in the same way (it will then have 1.5G in it, and 1 G thus remains in the 5G one).
 
Quote:
4. If your sock drawer has 6 black socks, 4 brown socks, 8 white socks, and 2 tan socks, how many socks would you have to pull out in the dark to be sure you had a matching pair?
It's never that dark in my room, unfortunately, and all my socks are white. But I can also grab a flashlight or put on the main light.
Having a matching pair distributed among numerous other socks I pulled out wouldn't help me anyway.
Besides which, if you're smart, you fold your socks up in pairs, so that you always get a matching pair in one grab.
 
Quote:
5. What is broken every time it's spoken?
'broken'
 
Quote:
6. How did Mark legally marry three women in Michigan, without divorcing any of them, becoming legally separated, or any of them dying?
It's 2098 and Islam conquered the US.
 
Quote:
7. Mom and Dad have four daughters, and each daughter has one brother. How many people are in the family?
At least 7. But they might have pets that we could count, or cousins, aunts, uncles, grandparents, etc.
 
Quote:
9. If I say "Everything I tell you is a lie," am I telling you the truth or a lie?
No.
 
Quote:
10. What work can a painter never quite finish?
housework (ask any mother, there's always more to be done)
 
Quote:
11. Why wasn't Bertha put in jail after killing dozens of people?
She was a cannon.
 
Quote:
12. Why wasn't John able to take a photo of his mother with curlers?
He was a kitten.
 
Quote:
13. If there are three cups of sugar and you take one away, how many do you have?
Depends on how many I already had; but at least one.  
 
Quote:
14. What has a mouth but can't chew?
Ply
 
Quote:
15. How many letters are in the alphabet?
26, 11 or 7, or something else entirely, depending on the interpretation.
 
Quote:
17. What can travel around the world while staying in a corner?
Anything that fits in a corner; the earth spins, after all.
 
Quote:
21. When is it bad luck to meet a white cat?
When you're violently allergic.
 
Quote:
22. If it has a quart capacity, how many pennies can you put into a empty piggy bank?
None, I don't have pennies.
 
Quote:
And One More Hard Riddle
23. Which of the following statements are true?
 
1. At least one of these ten statements is false.
2. At least two of these ten statements are false.
3. At least three of these ten statements are false.
4. At least four of these ten statements are false.
5. At least five of these ten statements are false.
6. At least six of these ten statements are false.
7. At least seven of these ten statements are false.
8. At least eight of these ten statements are false.
9. At least nine of these ten statements are false.
10. At least ten of these ten statements are false.
None. And they're not false either. They have absolutely no bearing on reality and hence no truthvalue. There are no facts being described you could check them against.
« Last Edit: Dec 20th, 2006, 2:46pm by towr » IP Logged

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Re: Riddles  
« Reply #2 on: Dec 20th, 2006, 3:04pm »
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Haha.  Funny, towr.  I'm surprised you went through all those, even if you did it flippantly.
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Re: Riddles  
« Reply #3 on: Dec 20th, 2006, 3:08pm »
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Well, I skipped a few that were either new, or for which I could only think of the intended answer.
 
I liked my 2 container solution though, my memory is bad enough not to remember it being on here before (if it has).
« Last Edit: Dec 20th, 2006, 3:09pm by towr » IP Logged

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Re: Riddles  
« Reply #4 on: Dec 20th, 2006, 4:22pm »
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Quote:

1. What row of numbers comes next in this series?  
 
 
1  
11  
21  
1211  
111221  
312211  
13112221  
 

 
I have seen this one around here on forum somewhere..
 
Answer: 1113213211
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Re: Riddles  
« Reply #5 on: Dec 20th, 2006, 6:11pm »
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0. Which way leads to the city of truth tomorrow?
 
2. I will be sentenced to six years in prison.
 
3. Fill 3 gallon bucket, dump in 5 gallon bucket, fill 3 gallon bucket, dumb in 5 gallon bucket 'till is full. There is one gallon in the 3 gallon bucket.
 
4. None, u know at least two of the socks in there are matching already.
 
5. Silence
 
7. At least seven.
 
9. A lie
 
13. Three
 
16. Towel
 
21. Friday the 13th on Opposite day.  Roll Eyes
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Re: Riddles  
« Reply #6 on: Dec 21st, 2006, 1:37am »
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on Dec 20th, 2006, 6:11pm, flamingdragon wrote:
0. Which way leads to the city of truth tomorrow?
How will this help? Each door may reply "this door".
 
Quote:
9. A lie
If he never said anything before, and promptly dies after uttering his sentence, how can this be a lie? It would become true if it were a lie, and a lie if it were true.
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Re: Riddles  
« Reply #7 on: Dec 21st, 2006, 8:26am »
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2. "1000 years from now, a comet will hit the planet Neptune"
 
6. He officiated at 3 weddings
 
8. QUEUE or AITCH (that's how some of us say "H" in the UK, don't know about those of you in the colonies).
 
11. A hurricane
 
12. Because you take photos with a camera (groan)
 
14. River / cave / dead animal
 
17. News?
 
21. When you're a mouse.
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Re: Riddles  
« Reply #8 on: Dec 21st, 2006, 8:55am »
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Green readers in favour of recycling should also see
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_eas y;action=display;num=1053630445
and
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_eas y;action=display;num=1049661852
 
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_eas y;action=display;num=1120600713
 
 Smiley
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Re: Riddles  
« Reply #9 on: Jan 1st, 2007, 12:12am »
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on Dec 21st, 2006, 1:37am, towr wrote:

How will this help? Each door may reply "this door".
 
If he never said anything before, and promptly dies after uttering his sentence, how can this be a lie? It would become true if it were a lie, and a lie if it were true.

 
No, the truthfull door would say "this door", and the lying one, knowing that tomorrow he would say "this door" must lie and say the correct door, "the other door".
 
And for the second one, if that is the only sentence he ever said then there is no answer to that riddle.
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Re: Riddles  
« Reply #10 on: Jan 1st, 2007, 5:04am »
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on Jan 1st, 2007, 12:12am, flamingdragon wrote:
No, the truthfull door would say "this door", and the lying one, knowing that tomorrow he would say "this door" must lie and say the correct door, "the other door".
You didn't ask him what he'd say tomorrow, but only where it would lead tomorrow.
Besides which, even if you asked that, tomorrow he might have said "neither", in which case "this door" would still be a lie today.
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Re: Riddles  
« Reply #11 on: Jan 1st, 2007, 10:52am »
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Oh oops!
 
That was totally wrong, must be an answer to some other path question.
 
 You ask one of the doors if the other door would tell you if this path leads to the city of safety.
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Re: Riddles  
« Reply #12 on: Jan 5th, 2007, 6:49pm »
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You approach two talking doors. One door leads to the City of Truth, while the other door leads to the City of Liars. You do not know which door is which. You are able to ask only one question to determine which door is which. The door that leads to the City of Liars always speaks lies, while the door that leads to the City of Truth always speaks the truth. You want to go to the City of Truth. What question do you ask to determine which door leads to the City of Truth?
 
I'd ask one of them "Which city would the other door say it leads to?", then I'd through the door that supposedly leads to the City of Liars.
[e]or
"Which city would you say you lead to tomorrow?" and if it says the city of truth, go through that door.  If it says the city of liars, go through the other door.[/e]
 
1. What row of numbers comes next in this series?
 
 
1
11
21
1211
111221
312211
13112221
 
IDK
 
 
2. A man was to be sentenced, and the judge told him, "You may make a statement. If it is true, I'll sentence you to four years in prison. If it is false, I'll sentence you to six years in prison." After the man made his statement, the judge decided to let him go free. What did the man say?
 
lol this is just about the exact one that I have in my sig! XD "You will sentence me to six years in prison." -it's a paradox.
[e]or
any other unprovable statement like "in 1532 years, a meteorite will hit the very spot that you were buried."[/e]
 
3. You have a barrel of oil, and you need to measure out just one gallon. How do you do this if you only have a three-gallon container and a five-gallon container?
 
Oh, I hate these ones. Fill the 3-gallon container, put that in the 5-gallon container, fill the 3-gallon container again, dump out what's left in the barrel, put the 5-gallon container (with 3 gallons of oil) above the barrel and pour the 3-gallon container's contents into the 5-gallon container.  The overflow that lands in the barrel is one gallon.  -I know that's wrong. :P
[e]right: same as before, but instead of emptying out the barrel (that would be wasteful ;)) and letting the 5-gallon container overflow, just stop when it's filled and there will be 1 gallon left in the 3-gallon  container.[/e]
 
 
4. If your sock drawer has 6 black socks, 4 brown socks, 8 white socks, and 2 tan socks, how many socks would you have to pull out in the dark to be sure you had a matching pair?
 
14?
 
 
5. What is broken every time it's spoken?
 
The "Don't speak" rule lol
[e]or
'broken'
or
silence[/e]
 
 
6. How did Mark legally marry three women in Michigan, without divorcing any of them, becoming legally separated, or any of them dying?
 
He was a priest, marrying them to other men.
 
 
7. Mom and Dad have four daughters, and each daughter has one brother. How many people are in the family?
 
7
 
 
8. What English word retains the same pronunciation, even after you take away four of its five letters?
 
queue, even though 'q' isn't technically a word?
 
 
9. If I say "Everything I tell you is a lie," am I telling you the truth or a lie?
 
WTHeck?!?  Are you stealing all these things from me?!?  It's another paradox!
[e]The answer is yes. :P[/e]
 
10. What work can a painter never quite finish?
 
Now this could be anything.
 
 
11. Why wasn't Bertha put in jail after killing dozens of people?
 
She was an animal?
[e]or
a tool used to kill dozens of ppl[/e]
 
12. Why wasn't John able to take a photo of his mother with curlers?
 
Because curlers can't take photos, duh! :P
 
 
13. If there are three cups of sugar and you take one away, how many do you have?
 
One
 
 
14. What has a mouth but can't chew?
 
A river
[e]or
a cave
or
anything that has a mouth and is dead (animal, human)[/e]
 
 
15. How many letters are in the alphabet?
 
Well, 26, but that' can't be it, so I'd have to say 11.  [e]Or just 8 if you aren't including 'the'.[/e]
 
 
16. What gets wetter and wetter the more it dries?
 
A towel
 
 
17. What can travel around the world while staying in a corner?
 
Anything that you put in a corner of a plane, etc.
 
 
18. Food can help me survive, but water will kill me. What am I?
 
fire
 
 
19. Take away the whole and some still remains. What is it?
 
The word 'wholesome'.
 
 
20. What stinks when living and smells good when dead?
 
A fish?
 
 
21. When is it bad luck to meet a white cat?
 
IDK
[e]when you're a mouse[e]
 
 
22. If it has a quart capacity, how many pennies can you put into a empty piggy bank?
 
None, because as soon as you put one in, it is empty again...
 
 
And One More Hard Riddle
23. Which of the following statements are true?
 
1. At least one of these ten statements is false.
2. At least two of these ten statements are false.
3. At least three of these ten statements are false.
4. At least four of these ten statements are false.
5. At least five of these ten statements are false.
6. At least six of these ten statements are false.
7. At least seven of these ten statements are false.
8. At least eight of these ten statements are false.
9. At least nine of these ten statements are false.
10. At least ten of these ten statements are false.
 
If you're looking for the one that's always true, then it's one.  Otherwise it could be any of them but 10.
 
How many did I get right?  I'm guessing somewhere around 13/24, looking on the bright side. :)
 
 
EDIT:  statements surrounded by [e] [/e] were added after reading all the replies.
« Last Edit: Jan 5th, 2007, 7:07pm by Locke64 » IP Logged

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Re: Riddles  
« Reply #13 on: Jan 5th, 2007, 9:11pm »
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on Jan 5th, 2007, 6:49pm, Locke64 wrote:
How many did I get right?  I'm guessing somewhere around 13/24, looking on the bright side. :)

 
Counting only your original answers,
 
Cities: You have one solution. I like towr's better.
1. Sameer has this one right. Just ask John Conway.
2. You answer is the traditional one for this old saw. Personally I favor towr's more creative approach.
3. Your original answer is an environmental disaster! I'm glad you've cleaned-up your dastardly ways with the edited answer... ;)
4. There are only 4 colors. Why in the world would you need 14 socks to get two of the same color?
5. Your original answer is nice, but doesn't apply universally (most places don't have such a rule), so I have to go with the intended answer of silence.
6. Unless Mark is a Justice of the Peace.
7. But what about little Kimmy, the hermaphrodite? (Okay - 7 is the intended answer).
8. I have to go with you on this one, since you have even included my objection to this riddle.
9. Sorry, but you are wrong. This statement is almost certainly nothing more than a lie. It would only be paradoxical if everything else that the speaker said was a lie.
10. Housework might even be the intended answer, but I'm not sure.
11. I believe towr's answer was the intended one.
12. There are so many answers to this one, it's hard to guess which one the author was after. I like towr's again.
13. Nah. Too much of a sweet tooth. I've already eaten it. (Yes, "one" is the correct answer.)
14. "River" is probably the intended answer, but "cave" also works quite well. Or Ply, if you don't mind  a pilgrimage.
15. I count only 7, even with the "the". Though "11" is probably the answer being looked for.
16. Another standard answer to an old saw.
17. "Stamp" is the intended answer.
18. yep.
19. "
20. Fish stink bad when they are dead. Not sure of the intended answer here, but "fish" isn't it.
21. Birds and baby rabbits also don't find the experience enjoyable.
22. I assume you meant "it is no longer empty". But your answer is still wrong: it should be one. The first penny goes into an empty bank. The remainder are put into banks that are not empty.
23. The truth values of all the statements are fully defined by the information at hand, so there is no difference between "true" and "always true". More than just the first are true.
 
For your original answers, I would say that 15 out of the 25 are correct.
 
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Re: Riddles  
« Reply #14 on: Jan 5th, 2007, 9:19pm »
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on Jan 5th, 2007, 9:11pm, Icarus wrote:

 
For your original answers, I would say that 15 out of the 25 are correct.
 

Yay!  More than I thought! :)
« Last Edit: Jan 5th, 2007, 9:20pm by Locke64 » IP Logged

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Re: Riddles  
« Reply #15 on: Jan 6th, 2007, 3:32am »
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on Jan 5th, 2007, 9:11pm, Icarus wrote:
10. Housework might even be the intended answer, but I'm not sure.
The one I thought was intended was a self portrait. (It'd have to be continually change as (s)he changes with aging)
His/her life's work might also fit. Although, I suppose dying finishes it.
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Re: Riddles  
« Reply #16 on: Jan 6th, 2007, 6:45am »
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on Jan 6th, 2007, 3:32am, towr wrote:

The one I thought was intended was a self portrait. (It'd have to be continually change as (s)he changes with aging)
His/her life's work might also fit. Although, I suppose dying finishes it.

The Forth (Rail) Bridge in Scotland is popularly supposed to require continuous re-painting - having to start again at one end by the time you finish at the other...
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Re: Riddles  
« Reply #17 on: Jan 6th, 2007, 10:50am »
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on Jan 5th, 2007, 6:49pm, Locke64 wrote:

 
1. What row of numbers comes next in this series?
 
 
1
11
21
1211
111221
312211
13112221
 
IDK
 
 

 
Say every digit of every number aloud to yourself. e.g. one, one one, two one, one two one, one, etc. if the answer doesn't make sense.
 
I still think it's funny that you became a JM in 2 days.
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Re: Riddles  
« Reply #18 on: Jan 6th, 2007, 12:21pm »
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on Jan 6th, 2007, 10:50am, hiyathere wrote:

 
Say every digit of every number aloud to yourself. e.g. one, one one, two one, one two one, one, etc. if the answer doesn't make sense.
 
I still think it's funny that you became a JM in 2 days.

I still don't get it. :(
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Re: Riddles  
« Reply #19 on: Jan 6th, 2007, 1:49pm »
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Door riddle: What will the other one say if I ask it which door is the correct one?
 
1. 1113213211
 
2. I will be sentenced for six years
 
3. Fill 3, pour in 5, fill 3, pour in five until full, empty five and you are left with 1 gallon in the 3 gallon
 
4. 5
 
5.  
 
6. He is the priest
 
7.
 
8.
 
9. Both/Neither. Infinite
 
12. Because you take pictures with a camera, not with curlers.
 
14. A tap
 
15. 11
 
16. a towel
 
23. #9
« Last Edit: Jan 6th, 2007, 1:51pm by Roy42 » IP Logged

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Re: Riddles  
« Reply #20 on: Jan 6th, 2007, 4:20pm »
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The wording on the truth/Lie door riddle is flawed:
 
1) You do not know which door is which.
 
2) The door that leads to the City of Liars always speaks lies, while the door that leads to the City of Truth always speaks the truth.
 
1) contradicts 2)
 
It's also the reason Towr's answer (Am I a Pizza?) would lead you to the correct city since 2) implies you take the door that answers "no".
« Last Edit: Jan 6th, 2007, 4:21pm by denis » IP Logged
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Re: Riddles  
« Reply #21 on: Jan 6th, 2007, 4:26pm »
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on Jan 6th, 2007, 4:20pm, denis wrote:

The wording on the truth/Lie door riddle is flawed:
 
1) You do not know which door is which.
 
2) The door that leads to the City of Liars always speaks lies, while the door that leads to the City of Truth always speaks the truth.
 
1) contradicts 2)
 
It's also the reason Towr's answer (Am I a Pizza?) would lead you to the correct city since 2) implies you take the door that answers "no".

You don't know which door speaks the truth and which door tells lies either.  He meant that you don't know if the door to the right leads to the city of truth or the door on the left, not the truth-telling one and the lie-telling one.
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Re: Riddles  
« Reply #22 on: Jan 7th, 2007, 7:19am »
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on Jan 6th, 2007, 4:20pm, denis wrote:
It's also the reason Towr's answer (Am I a Pizza?) would lead you to the correct city since 2) implies you take the door that answers "no".
I should perhaps caution, that if you are ever confronted with magic doors, joke answers like this (although they are a correct solution), might have unexpected consequences if the doors have an awkward sense of humour. For example, the truthfull door might turn you into a pizza, and then answer "yes".
After all, if a door can talk, who knows what other magic powers they have.
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Re: Riddles  
« Reply #23 on: Jan 7th, 2007, 8:47pm »
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Locke64 - the point of the "Am I a pizza" response is that the way this riddle is stated, all you need to know is which door lies and which one tells the truth. Therefore practically any question to which you know the answer will do: Ask "is 1 = 1?" If the door you ask says "yes", enter it. If it says "no", enter the other.
 
This is what happens when someone repeats a riddle from memory that they did not adequately understand themselves: they leave out or change critical parts with the result of rendering the puzzle trivial (as here), or unsolvable (as is usually done with the GRY puzzle). In this case, the puzzle was ruined by making the doors themselves the responders. In correct versions of this puzzle, there are two things you could find out: Which responder is the one telling the truth, and which door leads to the desired end. To know both requires gathering two bits of information. But you are allowed only one yes or no question - so you can only gain 1 bit of information. The trick to the puzzle is to realize that you don't actually need to know which responder is telling the truth, so you should just spend your question on finding out which door is the one you want. But in this version, by making the doors the responders, you have only one bit of information to track. Finding out which responder is which is the same as finding out which door is which. Thus the problem becomes trivial.
 
Probably, in the uncorrupted puzzle, it was not given that the truthtelling door was the desired one. Instead one door led somewhere you wanted to go (heaven is a common choice), while the other led somewhere you didn't (hell). Your question to the doors needed to find out which door led to heaven, without worrying about which was telling the truth.
 
 
Concerning #1, John Conway (a name you will become familiar with if you hang around here long enough, and are not familiar with it already) calls this the self-describing sequence. Each entry describes the entry before.
1  
11 (the previous entry consists of one 1)
21 (the previous entry consists of two 1s)
1211 (the previous entry consists of one 2, and then one 1).
etc.
« Last Edit: Jan 7th, 2007, 8:49pm by Icarus » IP Logged

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Re: Riddles  
« Reply #24 on: Jan 8th, 2007, 3:43am »
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on Jan 7th, 2007, 8:47pm, Icarus wrote:
Locke64 - the point of the "Am I a pizza" response is that the way this riddle is stated, all you need to know is which door lies and which one tells the truth. Therefore practically any question to which you know the answer will do: Ask "is 1 = 1?" If the door you ask says "yes", enter it. If it says "no", enter the other.
 
This is what happens when someone repeats a riddle from memory that they did not adequately understand themselves: they leave out or change critical parts with the result of rendering the puzzle trivial (as here), or unsolvable (as is usually done with the GRY puzzle). In this case, the puzzle was ruined by making the doors themselves the responders. In correct versions of this puzzle, there are two things you could find out: Which responder is the one telling the truth, and which door leads to the desired end. To know both requires gathering two bits of information. But you are allowed only one yes or no question - so you can only gain 1 bit of information. The trick to the puzzle is to realize that you don't actually need to know which responder is telling the truth, so you should just spend your question on finding out which door is the one you want. But in this version, by making the doors the responders, you have only one bit of information to track. Finding out which responder is which is the same as finding out which door is which. Thus the problem becomes trivial.
 
Probably, in the uncorrupted puzzle, it was not given that the truthtelling door was the desired one. Instead one door led somewhere you wanted to go (heaven is a common choice), while the other led somewhere you didn't (hell). Your question to the doors needed to find out which door led to heaven, without worrying about which was telling the truth.
 
 
Concerning #1, John Conway (a name you will become familiar with if you hang around here long enough, and are not familiar with it already) calls this the self-describing sequence. Each entry describes the entry before.
1  
11 (the previous entry consists of one 1)
21 (the previous entry consists of two 1s)
1211 (the previous entry consists of one 2, and then one 1).
etc.

Ah.  Now I understand both.  Thanks. ;)
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