NationStates Jolt Archive

Greetings Forum goers! Good news this week, NOBODY DIES!!! But I can see that my puzzles are FAR too easy for you people, so in addition to the standard puzzle, i'm throwing in a REALLY REALLY hard one.

Last week's answer: The detective ran across the third and fourth floors, feeling the lightbulbs in the rooms. The bulb that was hot would indicate the room he was looking for.

NOTE: If anyone else had turned on their lights in hearing the screams, the ambiguity could be solved by seeing if the windows were open. If they were not, then a 'deaffening scream' could not have been heard across a street, and so the room was wrong.

Results:

Correct Answer: Lots of people (There WERE over 100 posts, and I can only say that I saw it a lot)

Most Imaginitave Answer: Bodies Without Organs (http://forums.jolt.co.uk/showpost.php?p=12727091&postcount=53)

Best Answer: JuNii (http://forums.jolt.co.uk/showpost.php?p=12727078&postcount=50)

Easy Puzzle:

A woman went over to a man in the street. Without either of them saying a word, she kissed him. She did not know him, nor did she find him attractive, nor was she rewarded for her action.

Why did she do it?

Hard Puzzle:

One day a house was robbed. The police later arrested 4 suspects: Alfred, Egbert, Wilfred and Orville. Soon, the men were made to make statements.

As it turned out, any man that was under 30 years of age told the truth, while any man that was over 30 told a lie.

The men stood in a line as follows:

Alfred------Egbert------Wilfred------Orville

The men made the following statements:

Alfred: If the robber was Egbert or Orville, the robber was Egbert.
Egbert: The robber is not standing next to a man who is under 30.
Wilfred: At least two of us are over 30.
Orville: If the robber was Alfred or Wilfred, the robber was Wilfred.

Who was the robber?

This puzzle is an example of a mind-baffler. It can ONLY be solved through reason- or guesswork, if you prefer. I will only reward answers with explanations though. Good luck!

Easy Puzzle:

The man was unconscious and not breathing. She gave him the "kiss" of life.

=
Easy Puzzle:

A woman went over to a man in the street. Without either of them saying a word, she kissed him. She did not know him, nor did she find him attractive, nor was she rewarded for her action.

Why did she do it?



it was VE day, the man was the local catholic cardinal who was wearing a "Kiss me im irish" t-shirt.

Hard puzzle answer: Egbert.

I just typed out a long explanation, then accidentally deleted it...:headbang:

Shorter explanation:
Basically, it's impossible for all four of them to be under 30. Likewise it's impossible for them all to be over 30. If only one of them is under 30, it has to be Wilfred as he'll be telling the truth. Then if you go through the statements, you reach the answer through a process of elimination.

If only one is over 30, it again has to be Wilfred, otherwise his statement conflicts with known facts. Again, you go through a process of elimination, and you reach the same answer.

If two are over 30 and two are under 30, you know Wilfred is telling the truth and is therefore under 30. By going through each combination, you can then deduce that Alfred must also be under 30. If Wilfred and Alfred are telling the truth, you once again go through the elimination process, and again arrive at the same answer.

what with all the spoiler tags?

what with all the spoiler tags?
Didn't want to give away the answer if other people were working on it.

As it turned out, any man that was under 30 years of age told the truth, while any man that was over 30 told a lie.

The men stood in a line as follows:

Alfred------Egbert------Wilfred------Orville

The men made the following statements:

Alfred: If the robber was Egbert or Orville, the robber was Egbert.
Egbert: The robber is not standing next to a man who is under 30.
Wilfred: At least two of us are over 30.
Orville: If the robber was Alfred or Wilfred, the robber was Wilfred.

Who was the robber?

This puzzle is an example of a mind-baffler. It can ONLY be solved through reason- or guesswork, if you prefer. I will only reward answers with explanations though. Good luck!

Possibilities:
4 lying - not possible. If Wilfred is lying, at least two are telling the truth.
3 lying - If Wilfred is telling the truth, then the robber is Albert or Orville. However, Egbert would be lying and the robber would be standing next to a man who is under 30. So it must be Orville.
- If Wilfred is lying, then at least two are telling the truth and this scenario is not possible.
2 lying - Wilfred is automatically telling the truth: Two (or more) are lying. Wilfred is under 30.
Alfred telling the truth: Egbert or Alfred did it. Robber is standing next to a man under 30 (is not standing next to a man over 30). Egbert did it.
Egbert telling the truth: The robber is Alfred or Orville. The robber is not standing next to a man under 30. Alfred and Orville are both standing next to men under 30.
Orville telling the truth: The robber is Wilfred or Orville. The robber is standing next to a man under 30 (is not standing next to a man over 30). Orville did it.
1 lying - If wilfred is lying, then The robber is not standing next to a man under 30. Wilfred is the only one over 30 and it can only be Orville then, but then Alfred would be lying and there would be two liars. Not possible.
- If anyone else is lying, then Wilfred is as well.
0 lying - not possible. If Wilfred is telling the truth, at least two are lying.

I got it narrowed down to:
Wilfred is automatically telling the truth: Two (or more) are lying. Wilfred is under 30.
Alfred telling the truth: Egbert or Alfred did it. Robber is standing next to a man under 30 (is not standing next to a man over 30). Egbert did it.

Alfred------Egbert------Wilfred------Orville
>30, <30, >30, <30.

It definitely works out.

Orville telling the truth: The robber is Wilfred or Orville. The robber is standing next to a man under 30 (is not standing next to a man over 30). Orville did it.


Alfred------Egbert------Wilfred------Orville
<30, <30, >30, >30.

Erm, I get 3 different coherent solutions to the robbery puzzle.:confused:
Solution 1:
Alfred lies so Egbert can not be the robber.
Egbert lies so the robber must stand next to someone who tells the truth.
Wilfred tells the truth since there are 2 or more liars.
Orville lies so Wilfred can not be the robber.
Answer: The robber must be Orville since he must stand next to Wilfred and can't be Egbert.

Solution 2:
Alfred tells the truth so Orville can not be the robber.
Egbert lies so the robber must stand next to someone who tells the truth.
Wilfred tells the truth since there are 2 or more liars.
Orville lies so Wilfred can not be the robber.
Answer: The robber must be Egbert since he must stand next to Albert and/or Wilfred but can't be Orville.

Solution 3:
Alfred lies so Egbert can not be the robber.
Egbert lies so the robber must stand next to someone who tells the truth.
Wilfred tells the truth since there are 2 or more liars.
Orville tells the truth so the robber can not be Alfred.
Answer: The robber is either Orville or Wilfred since he must stand next to one of them and they stand next to each other, Egbert also stands next to Wilfred but it can't be him since Alfred lies.

There are disturbing forces at work in this case.

First of all, robbery is an offence against the person: taking the property of another, with the intent to permanently deprive the person of that property, by means force or fear. This means that for a house to be robbed (not just the scene of a robbery) it must be imbued with some mind. What abomination, what inhuman capacity are these subtle words hinting at? Are we being warned of something?

As the detective ponders these things in the house that was robbed, the answers that suggest themselves become more terrifying by each passing interminable hour. He is lulled into pathetic repose by the promise that this case is hard to solve. Obviously the other inspectors are sent out to find the ages and identities of the suspects. But they will never return (else the case would not be hard).

The realisation comes in a flash: these men, with names of long dead ancestors, Alfred, Egbert, Wilfred and Orville, cannot be under 30. Such names only appear on the tombstones that with primordial power dot the surrounding woods. These men cannot speak one work of truth. But before him, Wilfred mockingly recites, 'At least two of us are over 30.'

What witchery is this, what paradox! Desperate reason grasps at the answer: those were not the words of any man. The creatures before the detective carry no will, no voice of their own, but the command of the spirit of the house. This evil spirit, that promised the detective glory and puzzle, was really playing a cruel game, toying with a terrified mind like dolls in a cot. He realises he has been caught in the house by this game too long, frantically tries to flee in panic. But it is too late.

Months later, search parties came to the old house, only to find a deserted building, and a newly layed gravestone in the swaying woods.

Erm, I get 3 different coherent solutions to the robbery puzzle.:confused:
Solution 1:
Alfred lies so Egbert can not be the robber. (yes)
Egbert lies so the robber must stand next to someone who tells the truth. (yes)
Wilfred tells the truth since there are 2 or more liars. (yes)
Orville lies so Wilfred can not be the robber. (yes)
Answer: The robber must be Orville since he must stand next to Wilfred and can't be Egbert.(yes)

what the... strange. Bolded parts added by me. Also, I didn't notice this for some reason.

Solution 2:
Alfred tells the truth so Orville can not be the robber.
Egbert lies so the robber must stand next to someone who tells the truth.
Wilfred tells the truth since there are 2 or more liars.
Orville lies so Wilfred can not be the robber.
Answer: The robber must be Egbert since he must stand next to Albert and/or Wilfred but can't be Orville.

Solution 3:
Alfred lies so Egbert can not be the robber.
Egbert lies so the robber must stand next to someone who tells the truth.
Wilfred tells the truth since there are 2 or more liars.
Orville tells the truth so the robber can not be Alfred.
Answer: The robber is either Orville or Wilfred since he must stand next to one of them and they stand next to each other, Egbert also stands next to Wilfred but it can't be him since Alfred lies.

Yep, doesn't make sense. I am editing my initial post too.

Easy Puzzle:

A woman went over to a man in the street. Without either of them saying a word, she kissed him. She did not know him, nor did she find him attractive, nor was she rewarded for her action.

Why did she do it?

Could this be any more obvious?

The woman, who was coincidentally a zombie, and liked eating human flesh as all zombies do, decided that she needed to know how that man tasted.

After eating the same old human flesh for a couple of monthes, she decided that she prefered better tasting meet, so she would have to kiss the people before she ate just to make sure the meat met her standard.

She kissed him, he didn't meet her standard, and she took a cab home. End of story.

pfft too easy


1) the road happens to be in Italy and she is greeting someone she met over the net by kissing him on the cheek


2) they where all over 30 and thus lying as such in the eyes of the law they are all innocent due to lack of evidence

Greetings Forum goers! Good news this week, NOBODY DIES!!! But I can see that my puzzles are FAR too easy for you people, so in addition to the standard puzzle, i'm throwing in a REALLY REALLY hard one.

Last week's answer: The detective ran across the third and fourth floors, feeling the lightbulbs in the rooms. The bulb that was hot would indicate the room he was looking for.

NOTE: If anyone else had turned on their lights in hearing the screams, the ambiguity could be solved by seeing if the windows were open. If they were not, then a 'deaffening scream' could not have been heard across a street, and so the room was wrong.

Results:

Correct Answer: Lots of people (There WERE over 100 posts, and I can only say that I saw it a lot)

Most Imaginitave Answer: Bodies Without Organs (http://forums.jolt.co.uk/showpost.php?p=12727091&postcount=53)

Best Answer: JuNii (http://forums.jolt.co.uk/showpost.php?p=12727078&postcount=50)

Easy Puzzle:

A woman went over to a man in the street. Without either of them saying a word, she kissed him. She did not know him, nor did she find him attractive, nor was she rewarded for her action.

Why did she do it?

Hard Puzzle:

One day a house was robbed. The police later arrested 4 suspects: Alfred, Egbert, Wilfred and Orville. Soon, the men were made to make statements.

As it turned out, any man that was under 30 years of age told the truth, while any man that was over 30 told a lie.

The men stood in a line as follows:

Alfred------Egbert------Wilfred------Orville

The men made the following statements:

Alfred: If the robber was Egbert or Orville, the robber was Egbert.
Egbert: The robber is not standing next to a man who is under 30.
Wilfred: At least two of us are over 30.
Orville: If the robber was Alfred or Wilfred, the robber was Wilfred.

Who was the robber?

This puzzle is an example of a mind-baffler. It can ONLY be solved through reason- or guesswork, if you prefer. I will only reward answers with explanations though. Good luck!

I'll take the easy puzzle. The woman was depressed, so she was encouraged to live a little by her friends. One of these friends gave her a highly potent aphrodisiac. She just needed to kiss someone.

Hard puzzle answer: Egbert.

I just typed out a long explanation, then accidentally deleted it...:headbang:

Shorter explanation:
Basically, it's impossible for all four of them to be under 30. Likewise it's impossible for them all to be over 30. If only one of them is under 30, it has to be Wilfred as he'll be telling the truth. Then if you go through the statements, you reach the answer through a process of elimination.

If only one is over 30, it again has to be Wilfred, otherwise his statement conflicts with known facts. Again, you go through a process of elimination, and you reach the same answer.

If two are over 30 and two are under 30, you know Wilfred is telling the truth and is therefore under 30. By going through each combination, you can then deduce that Alfred must also be under 30. If Wilfred and Alfred are telling the truth, you once again go through the elimination process, and again arrive at the same answer.

So who are you saying committed the robbery?

So who are you saying committed the robbery?

It's in white text after the first colon. He said: Egbert.

She was a crazy hippie.

For the easy puzzle, the answer is obvious.

The woman is named Jenny. She used to work as a waitress before getting fired by her asshole boss. She spent several weeks searching for a new job but to no luck. She started drinking and smoking weed more, and because marijuana is a gateway drug, pretty soon she tried some heroin and got hooked. Now she knew she couldn't get a job, even with tips she wouldn't be able to afford more of that good shit. So she decided to whore herself out, but because it's a small town there weren't any pimps she knew of. She decided to hang out in a dark alley and just randomly approach guys to see if they were interested in a quick shag and some hastily exchanged cash. The man she kissed tonight was, but she wasn't rewarded with cash afterwards; he just slapped her, laughing, knowing she didn't have a pimp and couldn't do anything against him. She yelled and screamed anyway, and the man got angry and stabbed her with a broken beer bottle and left her bleeding in the back of his car, which turned out to be his friend's car, and it was his friend that got the rap. The irony being that if only the friend hadn't loaned his car to this guy, Jenny would still be alive. The moral of the story? Don't be a whore unless you get yourself a pimp. Bitch.

Easy puzzle: The woman saw that the man was lying there on the ground. She felt that he looked emaciated and starving. She asked him if he was hungry, and he said yes. But as he did so, she saw that he had no teeth.
She reached into her pocket to give him some money, and she realized that she didn't have any. She was however, holding the leftovers of her dinner, which was roast beef. She couldn't just give him the roast beef, because he couldn't chew it, so she chewed it for him and fed it to him, kissing him in the process.

Hard puzzle:

Wilfred is the robber.

They can't all be lying, because liars are over 30, which would mean that Wilfred is telling the truth. Three of them can't be liars for the same reason. Only one of them can't lie, because either Alfred or Orville must be lying (or both), and the robber would be by default standing next to a man under 30, thus meaning Egbert is telling the truth.
Thus two of them are liars, and Wilfred is telling the truth.
Since Wilfred is telling the truth, only one other person is also telling the truth. It can't be Egbert telling the truth, because Egbert and Wilfred would both be under 30, everyone is standing next to someone who is under 30, and so someone can't be standing next to someone over 30.
Since Egbert is lying, the robber can't be Alfred, since Alfred is only standing next to someone who is over 30, and the robber stands next to someone under 30.
Orville can't be lying, since he said the robber wasn't Alfred, and since the robber isn't Alfred, it must be Wilfred, since that's what Orville said, and he is telling the truth. Thus Alfred is the other liar.

The easy puzzle is obvious. She's on a blind date. >_>

Yeah, I got Egbert the same way I V Stalin got it.
Hope that counts.

*...*

This puzzle is an example of a mind-baffler. It can ONLY be solved through reason- or guesswork, if you prefer. I will only reward answers with explanations though. Good luck!

Don't take Higher Thinking's advice on this one, folks. Get a pencil and paper.

Didn't want to give away the answer if other people were working on it.

okay, that's just rediculocus...

She was a crazy hippie.
It was Ladame?!
okay, that's just rediculocus...

Eh no, not really.

Easy: Clearly the woman's a nymphomaniac.

Hard: Let us examine the case the author assumes: (a) one person is guilty, (b) nobody is exactly 30, (c) nobody had a birthday during these statements.

The only way that Alfred and Orville both lie is if both orville and alfred are guilty, which is impossible given the assumption. Therefore if Wilfred is lying, the other three (inluding Egbert) all tell the truth, but that means EVERYONE is next to an under-30! Therefore Wilfred is telling the truth, so Egbert and either Alfred or Orville is lying. That means the robber DOES stand next to a 30+. In addition, either Orville or Alfred must be guilty (as they make the other a liar), but only Orville is next to Wilfred, so he's guilty!

There are other possibilities, though.

Possibility A: It's NOT the case that only one person is guilty.

It's entirely possible that NONE of them did it and the homeowner faked it. Then Alfred, Egbert, and Orville are all telling the truth, and therefore wilfred lies.
Possibility B: One (or more) of them is/are exactly 30, not 29, 31, or whatever. In fact, they can all be 30. Therefore all of them could be either lying or telling the truth without violating the puzzle's defined rules. Thus any of the sixteen combinations (form "everyone did it" to "everyone is innocent") are valid.
Possibility C: The lineup was late at night and the clock struck midnight (causin someone's birthday) between the first and final statements. Again, every combination is valid. It's possible, for example, that all four are quadruplets and celebrated a brithday between Egbert's statement and wilfred's

CONCLUSION: The intended solution is that Alfred did it, but the rules are vague enough that any combination is possible. Also Atma reads Raymond Smullyan books too often.

Easy Puzzle:

A woman went over to a man in the street. Without either of them saying a word, she kissed him. She did not know him, nor did she find him attractive, nor was she rewarded for her action.

Why did she do it?

The woman was deaf, blind and insensate. She would just get really bored and fat if she didn't go around kissing people.
It was sheer luck she kissed a man, it could easily have been a grizzly bear wearing a nice aftershave.

EDIT: My solution was utterly wrong, due to a mistake at the very first stage (converting ages to truthfulness.)

Note: an important part of my reasoning here is that a statement "If A or B, then B" cannot be tested for truth if 'neither A nor B.' A person under 30 could make this statement, intending to lie, but it would not be a lie if 'neither A nor B.'
If the statement "If the robber was Egbert or Orville, the robber was Egbert" is considered a lie when the robber is actually e.g. Wilfred, then we have been given yet another stupid broken riddle. I really wasn't going to do another of these after the insultingly faith-based Adam and Eve question.

The easy one is too easy. I'll take the hard one.

First, Wilfred has to be telling the truth. If he were lying, only one of them would be over 30, that person would have to be lying, so Wilfred would be the ONLY person over 30. But then Egbert would be telling the truth in saying that the robber is NOT standing next to someone under 30, which would be impossible. Therefore, Wilfred is telling the truth. Wilfred is under 30, but at least two others are over 30.

Next, Egbert must be lying. If he were telling the truth, then the robber could not be standing next to someone under 30, which rules out Egbert and Orville (standing next to Wilfred). The robber would have to be Alfred AND to satisfy the rule Egbert would have to be over 30--but in that case he would be lying. Thus, he cannot be telling the truth because this results in a contradiction. Therefore he is lying, and he is over 30.

So far we have:

A ..... E ..... W ..... O
? .....>30....<30..... ?

Here is where it gets tricky, and to understand it you have to understand the truth table for a conditional statement, as "If x, then y." The following table explains:

x | y = "Truth of statement"
T | T = T
T | F = F
F | T = T
F | F = T

In other words, an "if-then" statement is ONLY false if the premise is true and the conclusion is false.

As it happens, we can rule out one possibility for these particular statements. Alfred states, "If the robber was Egbert or Orville, the robber was Egbert." But if "the robber was Egbert" = T, then "the robber was Egbert or Orville" = T by addition, so we can NEVER have the third possibility in the truth table (F | T = T). The same logic holds for Orville's statement.

Thus, for each of these statements, the truth table of theoretically possible statements is:

x | y = "Truth of statement"
T | T = T
T | F = F
F | F = T

We also know that at least one of them is lying, because at least one of them must be over 30. But then, we know that EXACTLY one of them is lying, since it is true that EITHER "Egbert or Orville" did it OR "Alfred or Wilfred" did it. One of these must be true, and one of these must be false. Let's set about seeing which is which.

Consider Orville. The ONLY way he could be lying is if his premise is true--"the robber is either Alfred or Wilfred" but his conclusion is false--the robber would NOT be Wilfred. But in that case, the robber would be Alfred, and that's not possible because Alfred is NOT standing next to someone under 30!!

Thus, Orville must be telling the truth, which means he is under 30. But we know that at least two of them are over 30, which means that Alfred is over 30. That also means that Alfred is lying. But if Alfred is lying, then his premise is true but his conclusion is false. Thus, while it is true that the robber was either Egbert or Orville, it is NOT true that the robber was Egbert.

The robber was Orville.

*bow*

The easy one is too easy. I'll take the hard one.

*snip exposition*

*bow*

OMG. I had >30 for truth, <30 for liar. I got tricked by the entirely spurious age thing which I translated into "truthy/liar" as the very first stage ... and got the wrong way around!

Bah.

OMG. I had >30 for truth, <30 for liar. I got tricked by the entirely spurious age thing which I translated into "truthy/liar" as the very first stage ... and got the wrong way around!

Bah.

Ooh, subconscious ageism!

Easy Puzzle:

A woman went over to a man in the street. Without either of them saying a word, she kissed him. She did not know him, nor did she find him attractive, nor was she rewarded for her action.

Why did she do it?

She was a politician running for office, or a beauty queen tryin to win the pageant and kissed the man on the cheek! But he didn't cast his vote for her.


Hard Puzzle:

One day a house was robbed. The police later arrested 4 suspects: Alfred, Egbert, Wilfred and Orville. Soon, the men were made to make statements.

As it turned out, any man that was under 30 years of age told the truth, while any man that was over 30 told a lie.

The men stood in a line as follows:

Alfred------Egbert------Wilfred------Orville

The men made the following statements:

Who was the robber?

Answer pending...

Easy puzzle: she's drunk.

Hmmm...It seems that my hard puzzle is causing tremendous ambiguities...HA HA!

All I can do is confirm that there can only be ONE robber- if you do the reasonning, you'll get the answer.

toodles :D

If the statement "If the robber was Egbert or Orville, the robber was Egbert" is considered a lie when the robber is actually e.g. Wilfred, then we have been given yet another stupid broken riddle. I really wasn't going to do another of these after the insultingly faith-based Adam and Eve question. But I have a very forgiving nature ... until I crack and murder someone with an adze, that is. X-[]

:( There's nothing wrong with this puzzle, the reasonning is there! The statement: "If the robber was Egbert or Orville, the robber was Egbert" is valid IN THE EVENT that the robber is either of the two. If your reasonning deduces that the robber IS one of the two, then by considering the honesty or dishonesty of Alfred's statement, you get the answer.

P.S. The Adam and Eve puzzle, while you may be dissatisfied with the answer, is still valid as an answer. To get it you had to consider religion, and how it is only through myth that eating something causes death.

For the record, "If X, then Y" is only false if X is true and Y is false. I thought they went without syaing, but I guess the board doesn't have enough knight-knave puzzles.

*bow*

Looks pretty solid to me.

:( There's nothing wrong with this puzzle, the reasoning is there! The statement: "If the robber was Egbert or Orville, the robber was Egbert" is valid IN THE EVENT that the robber is either of the two. If your reasonning deduces that the robber IS one of the two, then by considering the honesty or dishonesty of Alfred's statement, you get the answer.

Yes, I had it wrong. As I realized when I saw AnarchyL's answer.
I'm still concerned that IN THE EVENT that the robber is not one of the two, such a statement can't be said to be either truthful or a lie. That makes it hard to assess Wilbur's truthfulness since we need to count liars.

I'll reread Anar's solution in the morning, when I'm a bit clearer. For now, I'll leave my wrong answer there as an example of ... well, wrongness.

Please give consideration to South Lorenya, and in particular the "one or more of the suspects may be neither over nor under 30, being in fact 30" interpretation.

P.S. The Adam and Eve puzzle, while you may be dissatisfied with the answer, is still valid as an answer. To get it you had to consider religion, and how it is only through myth that eating something causes death.

I disagree completely. Any facts which have to be used but aren't provided in the puzzle (assumptions) must be the simplest and most commonly accepted ones.

Genesis is not commonly accepted fact. Sorry, it just isn't.

For that matter, what was the answer? "Eve by giving Adam the forbidden fruit caused him to die" is not an answer to "Why did Adam die?" It may be a partial answer, but if we are to accept Genesis as fact, it is clearly not a full answer.

It is not reasoning or higher thinking which that puzzle tested, but an ability to recognize the kindie version of a Bible story with the names taken out.

However, this puzzle (the hard one) has restored my faith in your puzzles somewhat.

For the record, "If X, then Y" is only false if X is true and Y is false. I thought they went without syaing, but I guess the board doesn't have enough knight-knave puzzles.

I really should shut up until I'm sober, but isn't it possible for a statement to be neither true nor false? Um ... a Boolean null I think? EDIT: Er, probably not. An "undefined state"?

I think what I'm getting at is that a "lie" is not just a matter of assessing the truth or falsity of a statement. If Alfred intended to lie in saying "If one of E or O is the robber, then it is E" then surely we need to know which of the four he believes to be the robber, not just which one is?
If A believes W to be the robber, or knows himself to be, then is he lying, or telling the truth, with his statement? I would say neither.

I have a tip for all of you:

Don't read too much into the technicalities of the puzzle! After all, it's just a puzzle, and the method for obtaining the answer is logical. Try to curb the 'is belief true?' or 'being in fact 30' mallarky.

Still, i suppose it shows imagination. Either that or the ability to tear a perfectly good puzzle down to its bare-bones minimum, leaving nothing but pure conjecture. Ah well.

I have a tip for all of you:

Don't read too much into the technicalities of the puzzle! After all, it's just a puzzle, and the method for obtaining the answer is logical. Try to curb the 'is belief true?' or 'being in fact 30' mallarky.

Still, i suppose it shows imagination. Either that or the ability to tear a perfectly good puzzle down to its bare-bones minimum, leaving nothing but pure conjecture. Ah well.You're hinting that one of them is 30 and thus told neither the truth nor a lie. The problem is that when people say someone is over 30, that includes ages like 30 1/2. The solutions that count the invalid statement as one made by someone over 30 are still correct.

The claim "If one of E or O is the robber, then it is E." is true only if the robber is E and false only if the robber is O. If the robber is neither of them then the turthfulness of the claim must be left undetermined and does not give any hint about A's age so both age cases must be considered.

You can't validate a claim about a situation that doesn't exist. "If the next US presidential election would stand between Hilton and Borat, Borat would win." You can't prove for sure if that is true or false unless it would actually stand between those 2 so you get the real result to compare to. So the truthfulness of that claim is left undetermined.

The claim "If one of E or O is the robber, then it is E." is true only if the robber is E and false only if the robber is O.No. This is basic sentential logic. For an if-then statement of the form x-->y, the statement is TRUE in every circumstance EXCEPT the one in which x is true and y is false.

You can't validate a claim about a situation that doesn't exist.Logic isn't about determining what is actually true so much as it is about determining what statements are logically valid.

"If Hitler was a man, then Bill Clinton is a woman." Not valid, since Hitler was a man but Clinton is not a woman.

"If Hitler was a woman, then Bill Clinton is a woman." Valid. If it helps you, consider that the contrapositive--"If Bill Clinton is not a woman, then Hitler was not a woman"--is obviously valid. To preserve contraposition, we have to take this statement as valid ("true" in logical terms but not empirical terms) even though it has a false premise and a false conclusion.

I hope that helps.

EDIT: Perhaps I should also point out why x-->y is TRUE when x is false and y is true. It's actually quite simple. If y is true, then "it follows that y" no matter what is the case with x: x-->y and ~x-->y are BOTH true, because it is true in either case that "If __, then y," because we already know that y is in fact true. (In other words, as soon as we name the value for y we are treating it as a constant, so you could actually insert any variable you want for x. Consider: "If ____, Earth orbits Sun." It doesn't matter what you put as your premise, your "deduction" will always be logically valid.)

any man that was over 30 told a lie.

So are you saying saying that all old people are dirty liars? shame!

While I agree 100% with AnarchyeL's exposition on propositional logic and material implication (if .. then statements for the uninitiated), I find myself sympathizing with the arguments of Ruby City et al. The OP (Higher Thinking) dis not specify that the problem was to be solved using propositional calculus; he simply said that we would have to think about it.

Now material implication is notoriously counter intuitive in its results, and to have a problem that depends on a technical understanding of this is more than a little restrictive for the majority here.

So, I support AnarchyeL's detailed and complete analysis, as being the "correct" interpretation, but would recognize the efforts made by others such as Nobel Hobos, IV Stalin, Ruby City etc. as being excellent answer obtained with the tools available in common sense reasoning.

So are you saying saying that all old people are dirty liars? shame!

Never trust anyone under 30.

I know the hippies had it the other way round, but they were wrong.

NOTE: for those unfamiliar with propositional logic operators, I provide the following key:
A <==> B : A is logically equivalent to B
A => B : A implies B (i.e. if A, then B)
A ^ B : A and B
A v B : A or B
!A : not A
Vx(P(X)) : For all x, P(x)
∃x(P(x)) : There exists some x for which P(x)

Let
>30(x) = x is over 30 years old
R(x) = x is the robber
S(x, y) = x is standing next to y

(I will assume that none of the suspects are EXACTLY 30 years of age, whatever that may mean)

Alfred: "If the robber was Egbert or Orville, the robber was Egbert."
Egbert: "The robber is not standing next to a man who is under 30."
Wilfred: "At least two of us are over 30."
Orville: "If the robber was Alfred or Wilfred, the robber was Wilfred."

Convert their statements to logical sentences:

A says: [R(E) v R(O)] <==> R(E)
E says: Vx(R(x) => Vy(((x != y) ^ S(x,y)) => >30(y)))
W says: ∃(x,y)(>30(x) ^ >30(y) ^ (x != y))
O says: [R(A) v R(W)] <==> R(W)


E's statement:

!>30(E) <==> ( Vx[R(x) => Vy(S(x,y) => >30(y))] )

!>30(E) <==> Vx[R(x) => [
(S(x,A) => >30(A)) ^
(S(x,O) => >30(O)) ^
(S(x,E) => >30(E)) ^
(S(x,W) => >30(W))
]] (Universal Instantiation)

!>30(E) <==> [
[R(A) => [(S(A,A) => >30(A)) ^
(S(A,O) => >30(O)) ^
(S(A,E) => >30(E)) ^
(S(A,W) => >30(W))]]
^
[R(O) => [(S(O,A) => >30(A)) ^
(S(O,O) => >30(O)) ^
(S(O,E) => >30(E)) ^
(S(O,W) => >30(W))]]
^
[R(E) => [(S(E,A) => >30(A)) ^
(S(E,O) => >30(O)) ^
(S(E,E) => >30(E)) ^
(S(E,W) => >30(W))]]
^
[R(W) => [(S(W,A) => >30(A)) ^
(S(W,O) => >30(O)) ^
(S(W,E) => >30(E)) ^
(S(W,W) => >30(W))]]
] (Universal Instantiation)

!>30(E) <==> [
[R(A) => [(S(A,O) => >30(O)) ^
(S(A,E) => >30(E)) ^
(S(A,W) => >30(W))]]
^
[R(O) => [(S(O,A) => >30(A)) ^
(S(O,E) => >30(E)) ^
(S(O,W) => >30(W))]]
^
[R(E) => [(S(E,A) => >30(A)) ^
(S(E,O) => >30(O)) ^
(S(E,W) => >30(W))]]
^
[R(W) => [(S(W,A) => >30(A)) ^
(S(W,O) => >30(O)) ^
(S(W,E) => >30(E))]]
] (Elements in which a person is standing next to himself may be eliminated, since x != y in the original statement)

!>30(E) <==> [
[R(A) => [(F => >30(O)) ^
(T => >30(E)) ^
(F => >30(W))]]
^
[R(O) => [(F => >30(A)) ^
(F => >30(E)) ^
(T => >30(W))]]
^
[R(E) => [(T => >30(A)) ^
(F => >30(O)) ^
(T => >30(W))]]
^
[R(W) => [(F => >30(A)) ^
(T => >30(O)) ^
(T => >30(E))]]
] (Since the order of the suspects is known [A-E-W-O], S(x,y) can be written as true or false)

!>30(E) <==> (
(R(A) => >30(E))^
(R(O) => >30(W))^
(R(E) => (>30(A) ^ >30(W)))^
(R(W) => (>30(O) ^ >30(E)))
) (Modus Ponens)


W's statement:

!>30(W) <==> ( ∃(x,y)(>30(x) ^ >30(y) ^ (x != y)) )

!>30(W) <==> [
(>30(A) ^ >30(O)) v
(>30(A) ^ >30(E)) v
(>30(A) ^ >30(W)) v
(>30(O) ^ >30(E)) v
(>30(O) ^ >30(W)) v
(>30(E) ^ >30(W))
] (Existential instantiation)


A's and O's statements are similar enough that they may be done concurrently:

!>30(A) <==> ( [R(E) v R(O)] <==> R(E) )
!>30(O) <==> ( [R(A) v R(W)] <==> R(W) )


We are left with the following four logical sentences:

!>30(E) <==> (
(R(A) => >30(E))^
(R(O) => >30(W))^
(R(E) => (>30(A) ^ >30(W)))^
(R(W) => (>30(O) ^ >30(E)))
)

!>30(W) <==> (
(>30(A) ^ >30(O)) v
(>30(A) ^ >30(E)) v
(>30(A) ^ >30(W)) v
(>30(O) ^ >30(E)) v
(>30(O) ^ >30(W)) v
(>30(E) ^ >30(W))
)

!>30(A) <==> ( [R(E) v R(O)] <==> R(E) )

!>30(O) <==> ( [R(A) v R(W)] <==> R(W) )


We may combine them all simply by stipulating that they all be true. i.e.:

!>30(E) <==> (
(R(A) => >30(E))^
(R(O) => >30(W))^
(R(E) => (>30(A) ^ >30(W)))^
(R(W) => (>30(O) ^ >30(E)))
)
^
!>30(W) <==> (
(>30(A) ^ >30(O)) v
(>30(A) ^ >30(E)) v
(>30(A) ^ >30(W)) v
(>30(O) ^ >30(E)) v
(>30(O) ^ >30(W)) v
(>30(E) ^ >30(W))
)
^
!>30(A) <==> ( [R(E) v R(O)] <==> R(E) )
^
!>30(O) <==> ( [R(A) v R(W)] <==> R(W) )


To save time, I used an online propositional logic program (http://www.oursland.net/aima/propositionApplet.html) to evaluate the resulting sentence. If anyone is curious, I can provide the raw data, but from the 256-line truth table it generated, in the following cases was the sentence true:

>30(A) >30(W) >30(E) >30(O) R(A) R(W) R(E) R(O) Result
false true false false false false false false true
true false true false false false false true true
false false true true true false true false true
false false true true true false true true true
true false true true true false false true true
true false true false false true false true true
true false true false true true false true true

I'm assuming that the OP intended only one case, with one robber, in which the conditions were satisfied; under that assumption, the case where R(O) is true (Orville alone is the culprit, and Alfred and Egbert are older than 30) is the desired result. If thought about carefully (which I did for several of them), the other cases could also be solutions. I suspect that their existence is due to the inherent ambiguity of an english sentence's logical meaning (i.e. if Orville is truthful and the robber could be Alfred, Wilfred OR Egbert, does Orville's statement still apply? Or if instead only Alfred and Egbert are possibly the robber?).

If anyone knows propositional logic, I invite them to check my figures ... it is entirely possible that I made a mistake.

To save time, I used an online propositional logic program (http://www.oursland.net/aima/propositionApplet.html) to evaluate the resulting sentence.Whereas I saved time and wrote a thoroughly readable solution by using simple logical proofs (primarily indirect proof) to eliminate possibilities without trying to compute a sentence so complicated that only a computer could handle it in a reasonable amount of time! :p

As for your results, of the first several which I check the ONLY one that works out is the one I provided. At some point I've stopped, but at any rate it would appear that even after all that work you have to go back to check basic deductions. Seems like a waste of time to me!

Observe:

>30(A) ... >30(W) ... >30(E) ... >30(O) ... R(A) ... R(W) ... R(E) ... R(O)
true ....... false ....... true ....... false ..... false ... false ... false ... true
This one checks out. This was my answer.

false ...... false ....... true ....... true ...... true .... false ... true ... false
According to this one, A and E are both robbers, and E is over 30--which means that E is lying when he says the robber is NOT standing next to a man under 30. So any robbers have to be standing next to a man under 30. But A is standing next to E, who is over 30!! Contradiction!

false ...... false ........ true ....... true ...... true ... false ... true ... trueHere E is >30, so he's lying: any robber(s) must be standing next to someone who IS <30. But A is standing next to E, who is over 30. Contradiction.

true ....... false ....... true ........ true ...... true ... false ... false ... trueAgain, if E is >30, then robber(s) must be next to someone <30. But again, A is next to E, who is not <30. Contradiction!
If thought about carefully (which I did for several of them), the other cases could also be solutions.None of the ones I checked, anyway. I suspect that their existence is due to the inherent ambiguity of an english sentence's logical meaning (i.e. if Orville is truthful and the robber could be Alfred, Wilfred OR Egbert, does Orville's statement still apply?In logical terms, there is only one translation--and at any rate, you didn't include any of these alternative interpretations in your translation, so why should they start popping out on their own?

If anyone knows propositional logic, I invite them to check my figures ... it is entirely possible that I made a mistake.With work that complex, it's entirely likely.

In logic as in everything else, simpler is better.

EDIT: I found at least one with multiple robbers that checks out in a narrow sense... narrow in that you have to ignore the meaning of the definite article, as in the frequently repeated phrase "the robber." :)

Whereas I saved time and wrote a thoroughly readable solution by using simple logical proofs (primarily indirect proof) to eliminate possibilities without trying to compute a sentence so complicated that only a computer could handle it in a reasonable amount of time! :p

As for your results, of the first several which I check the ONLY one that works out is the one I provided. At some point I've stopped, but at any rate it would appear that even after all that work you have to go back to check basic deductions. Seems like a waste of time to me!

Actually, I found the process of logically translating it enjoyable ... especially since it took some time to narrow down the results and iron out (admittedly not all) the mistakes in my reasoning. If you like to do it a different way, that's fine with me.


Observe:

This one checks out. This was my answer.

According to this one, A and E are both robbers, and E is over 30--which means that E is lying when he says the robber is NOT standing next to a man under 30. So any robbers have to be standing next to a man under 30. But A is standing next to E, who is over 30!! Contradiction!
Here E is >30, so he's lying: any robber(s) must be standing next to someone who IS <30. But A is standing next to E, who is over 30. Contradiction.
Again, if E is >30, then robber(s) must be next to someone <30. But again, A is next to E, who is not <30. Contradiction!
None of the ones I checked, anyway. In logical terms, there is only one translation--and at any rate, you didn't include any of these alternative interpretations in your translation, so why should they start popping out on their own?

What do you mean? I chose an interpretation for my translation; I have no way of knowing which interpretation will produce which results (which is not to say that isn't apparent in some way, just that I'm not sure how one can be certain). I recognize, some of the solutions appear contradictory; I only tested the first two and the final one, if I remember correctly. It was my intention to arrive at an exhaustive list of possibilities; I expected there to be only one, of course, and the others may merely be the results of mistakes. When I initially set up the translation, there were many more, and every time I corrected a mistake the list was shortened. I couldn't find any more mistakes with my translation, so I posted the list as it was.

With work that complex, it's entirely likely.


EDIT: I found at least one with multiple robbers that checks out in a narrow sense... narrow in that you have to ignore the meaning of the definite article, as in the frequently repeated phrase "the robber." :)

Thanks.

I remember saying that I assumed there was a single robber. My translation came up with those additional results, so I thought I'd post them anyway.

After reviewing the preceding translations more thoroughly, I believe I have isolated the reason that the program produced so many "contradictory" results.

It rests on a (perhaps inevitable) ambiguity that arises as soon as one decides to allow cases with more than one robber.

When one assumes only one robber, the meaning of the definite article "the" is unambiguous. When one allows multiple robbers, however, it is unclear whether "the robber" should be translated in all sentences as "some robber" or "all robbers."

In my critique above I took it to mean "all robbers" or "anyone who is a robber," so that, for instance, ALL robbers must be standing next to someone who is under 30 years old. (Of course, this introduces a further ambiguity, but again one only occurring if one ignores the obvious meaning of "the": does one translate the sentence before or after deducing that Egbert MUST be lying? Depending on which you choose, you get different results in the translation.)

If one takes it to mean, however, not "all robbers" but "some robber," then the above results are valid under that translation. And indeed, if one checks the usage above, one finds that "robber" was plugged in so that the rules would be satisfied as long as some robber satisfied each rule--effectively separating out the rules and making them easier to satisfy.

I maintain that the "one robber" interpretation is the singular "correct" answer to the problem, based at least in part on the fact that this is the only interpretation that satisfyingly disambiguates the word "the." However, I will concede that in the above analysis we saw not so much a "mistake" in propositional logic as an alternate interpretation of the puzzle in which "a" robber satisfies the rule rather than "the" robber. It is, admittedly, a much easier puzzle that way with multiple acceptable answers.

I guess my basic problem with your procedure is that you ignore the meaning of "the." If you go back and introduce a sentence providing that V(x,y)((R(x) ^ (x != y)) => !R(y)) -- or something to that effect -- then I would be satisfied that you had accurately translated the problem. But, you would only get one solution.

OK, I'm going to try again. Again, I am going to test each case for contradictions and see what is left. I'll use the right age catagory to be liars this time!

First to the assumptions.

There is only one robber.
"Tell the truth" means to have correct knowledge and make a true statement.
"Lie" means to have correct knowledge and make a false statement.
(There is no solution if any of the 4 is incorrect in their knowledge.)
There is only one robber, it is one of the four suspects.
The suspects are either over 30 or under 30.

Making a statement which the speaker knows cannot be tested for truth seems pretty dodgy to me. It could be considered lying, so I'll keep track of those.

I will take out the "over or under 30" term right at the beginning. Hereafter, there are only liars and truth-tellers.

Robber is:

Alfred.
A(true): If E or O, then E. Hence not O.
...A(lies): If E or O, then E. Hence, robber is O.
...A(?): (If E or O, then E) can't be called a lie when A or W is the robber.
E(true): Not next to truth-teller. Contradiction, is next to E.
...E(lies): Next to truth-teller. Contradiction, is next to E.
This possibility is excluded.
It is excluded by E's statement (as others mentioned), regardless of the truth of A'a statement.
_______________

Egbert. Tells truth.
A(true): If E or O, then E.
...A(lies): If E or O, then E. Contradiction, statement is true.
E(true): Not next to a truth-teller. Contradiction, is next to A.
This possibility is excluded.

Egbert. Lies.
A(true): If E or O, then E.
...A(lies): If E or O, then E. Contradiction, statement is true.
E(lies): Not next to a truth-teller. A is one, so this is a lie. OK.
W(true): At least two are liars. O must be a liar.
...W(lies): At least two are liars. But E + W are liars. Contradiction.
O(lies): If robber is A or W, it is W.
If an untestable statement is considered a lie, we have one possibility: Egbert, liar and thieving scrote. Lock 'im up!
___________

Wilbur. (Liar or truth-teller)
A(?): If robber is E or O, then it is E. If null=lie, A is a liar. If null=truth, A is telling the truth.
E(true): Not next to a truth-teller. But is next to E. Contradiction.
...E(lies): Not next to a truth-teller. O must be telling the truth.
...W(true): A least two of us are liars. A must be lying.
......W(lies): At least two of us are liars. But E + W are. Contradiction.
...O(true): If robber is A or W, it is W.
This is another possible solution, if an untestable statement is considered a lie. Wilbur, honest housebreaker and schmuck. Give 'im an 'efty fine!
_____________

Orville.
A(true): If robber is E or O, then it is E. Contradiction.
A(lies): If robber is E or O, then it is E. We have 1 liar.
E(true): Not next to a truth-teller. Therefore W lies.
...W(lies): At least two of us are liars. But that's true already. Contradiction.
E(lies): Not next to a truth-teller. Therefore W is telling the truth.
...W(true): At least two of us are liars. True already. OK.
...O(?): If A or W, then W. True or false or null, no matter. We have our liars.

Orville. Dead to rights. Lock 'im up, let 'im get his law degree in some stinking hole.

So here is my result at last. It is probably Orville, and cannot be Alfred.

Implicit in the assumption that "all statements made by a liar are false" is that the liar knows the truth. This last case, Orville the robber, A lies, E lies, W tells truth, and it doesn't matter whether Orvilles statement is true or not, is the most satisfactory answer.