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BS: Mental Workouts without Dilbert
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Subject: Mental Workouts without Dilbert From: Mrrzy Date: 26 Feb 02 - 04:30 PM I was asked, so purists please don't kill me. Feel free to make this as musical as you wish. You die and are sent to a plain, unadorned room, whence you will go either to Heaven or Hell. All you can see are 2 doors and a pair of absolutely identical twins, one guarding each door. You know 2 things: First, that one always tells the truth and one always lies; and second, that one door leads to Heaven and the other to Hell. You may not open either door without going through it, and once through, you cannot come back. You do not know which twin, good (truth) or evil (lies) guards which door. You are allowed ONE question - what do you ask, to find out which is the door to Heaven? |
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Subject: RE: BS: Mental Workouts without Dilbert From: JohnInKansas Date: 26 Feb 02 - 05:42 PM This is a very old one. I think the ancient Greeks used it in their textbooks. Ask either twin if the other twin will tell you that Door A leads to heaven. (Pick either door). If the answer is "YES" go through Door B. If the answer is "NO" go through Door A. (Unless you think that Hell might be more fun.) John |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 26 Feb 02 - 05:47 PM I used to know the answer to this one (or should I say "the question to this one"?).... |
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Subject: RE: BS: Mental Workouts without Dilbert From: mack/misophist Date: 26 Feb 02 - 05:59 PM If I were smart, I would explain the logic of it. It's been explained to me at least twice. All I can remember's that the logic is iron clad. Would somebody explain it again? |
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Subject: RE: BS: Mental Workouts without Dilbert From: gnu Date: 26 Feb 02 - 06:03 PM A hoops B, then C. That's all I remember from my only philosophy course. Does that help ? |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 26 Feb 02 - 06:19 PM What if he answers, "You'll have to ask him yourself"? |
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Subject: RE: BS: Mental Workouts without Dilbert From: JohnInKansas Date: 26 Feb 02 - 06:26 PM SharonA In this case, you're s.o.l. because you've already asked the ONE QUESTION you were permitted. Purists normally include the condition that the angels can only answer "YES" or "NO" since any other answer takes this out of the realm of LOGIC, which is where the question originates. John |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST,petr Date: 26 Feb 02 - 06:28 PM I have another one. There are two knights vying for the hand of a princess. Although she would be happy to marry either one, her father on the other hand doesnt want to let her go. So he suggests that they have a horserace with one twist. The one whose horse is last wins the princess' hand. Now at this point the two suitors dont want to start the race they just stay put and it looks like the king wont have to give away his daughter. WHereupon the princess comes over to the knights and whispers something in their ears. THey do something and the race is on. What did she tell them to do? |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 26 Feb 02 - 06:31 PM John n Kansas: Exactly my point!! *BG* |
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Subject: RE: BS: Mental Workouts without Dilbert From: JohnInKansas Date: 26 Feb 02 - 06:44 PM A complete "truth table" for the "DOORS" problem requires a rather lengthy construction, and since it's 3-dimensional, is a little tough to describe in text. Assume that door A is GOOD. Assume Angel 1 is TRUE Assume angel 2 is FALSE If you ask Angel 1 "Is door A the way to Heaven?" he will answer YES. If you ask Angel 2 "Is door A the way to Heaven?" he will answer NO. If you ask Angel 1 "Would your brother say door A is the way to heaven?" Brother Angel 2 is a liar so he would say "NO," and Angel 1 tells the truth so the answer is "NO" If you as Angel 2 "Would your brother say door A is the way to heaven?" Angel 1 would tell the truth, and would answer "YES" but Angel 2 lies so he would say "NO" Repeat for door A is GOOD Angel 1 is FALSE Angel 2 is TRUE Repeat for door A is BAD Angel 1 is TRUE Angel 2 is FALSE Repeat for door A is BAD Angel 1 is FALSE Angel 2 is TRUE In every case, when you ask either angel "Would your brother say Door A is the way to Heaven?" a "NO" reply means door A is the way to heaven and a "YES" answer means that it is NOT. (Attempts to introduce artificial postulates and possibilities (even when the question is only partially formed in the original statement) merely indicates a reply from someone not really interested in the logic. This is a well known, and not totally trite, classic of formal logic. John |
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Subject: RE: BS: Mental Workouts without Dilbert From: Hilary Date: 26 Feb 02 - 06:47 PM It's been a long day, so this may not come out right. BUT The person you ask is A telling the truth B lying The other person guards C the door to hell D to heaven And you can pick either person to ask, this gives 4 possible combinations. What you do know, by asking what the 'other one' would say you are getting a two layered answer BUT Exactly one layer is a lie. And You are thinking about going into Door A, bt asking about door B Option A, Door A, To heaven, honest answer. Door B is to hell, but is guarded by a liar, so first layer of answer is Yes -this is the door to heaven. The person you are speaking to will not alter the reply - so will say - Yes You are at the door to heaven & heard yes - go in. Option B Door A, To heaven, speaking to the liar. Door B - Hell - honest twin. First layer of answer - No-this isn't the door to heaven. But the liar at door A lies & says Yes. You are at the door to heaven, you've heard yes - go in. Option C Door A- Hell, with the liar. Door B, Heaven & honest twin who would say Yes, but the liar you actually spoke to says No. You're at the door to heel, heard NO, don't go in. Option D Door A -Hell with the honest twin, Door B - Heaven with the liar - who would say No- you're not at the gate to heaven. The honest twin you are speaking to reports it accurately as NO, so don't go in. Like JohninKansas said Ask - would the person at the OTHER door tell me if I asked them if that was the door to heaven. If they said YES - go in If the said NO - don't If you only ask about your own door, you can't know if it's true or a lie. But by putting the answer through BOTH twins you know you are getting exactly one lie, invert that you get the truth, guaranteed. Hope that makes some sense ! What's next Mrzzy ???
Hilary |
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Subject: RE: BS: Mental Workouts without Dilbert From: Hilary Date: 26 Feb 02 - 06:55 PM Hi Petr, Is it something like hey go round the the wrong way (anti versus clockwise) or they race backwards ???? Interesting one Hilary |
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Subject: RE: BS: Mental Workouts without Dilbert From: gnu Date: 26 Feb 02 - 06:59 PM Thread drift alert... Male engineer and mathematician are set at the start line. Naked woman at finish line. Rules are that each time starter blows whistle, racers can advance one half the distance to the finish line and whistle will blow again as soon as first racer reaches his half distance and comes to a complete stop. First whistle blows and engineer makes a mad dash. Mathemetician stands at start line and laughs. Starter asks why and he replies, "If you only go half the distance each time, you'll never arrive." Starter tells this to engineer and he replies, "Yeah, I know. But for all practical purposes, I'll get close enough." |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 26 Feb 02 - 07:01 PM JohnInKansas says, "Attempts to introduce artificial postulates and possibilities (even when the question is only partially formed in the original statement) merely indicates a reply from someone not really interested in the logic." I disagree. The question must be completely formed in the original statement; otherwise it is logical to introduce postulates and possibilities not forbidden by the original statement. If, in this case, you mean to say that one must assume that the twins may only answer one question by saying "yes" or "no", even though the original statement does not include this information, I'd have to respond that that in itself is faulty logic. |
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Subject: RE: BS: Mental Workouts without Dilbert From: JohnInKansas Date: 26 Feb 02 - 07:36 PM Sharon Since this is a well known "riddle" it is probably appropriate to assume the "standard conditions." If you wish to do "what-ifs" about other ways that the question could be posed, that's allright; but if you do that, then there's no real "answer" because someone else can always "repose" the question. By all means, have fun with it. Hilary - I think you've pretty much got it, but there's an extra "OTHER" that confuses me a little. The "classic" problem is used to demonstrate the use of the boolian - "The AND of two inputs where one is TRUE and the other is FALSE is FALSE." Since you know that one of the answers will always be FALSE, you state a question that depends on BOTH answers, and then you know that the answer will be FALSE. John |
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Subject: RE: BS: Mental Workouts without Dilbert From: dick greenhaus Date: 26 Feb 02 - 11:34 PM ..and as for the horse race, the maid's suggestion is "swap horses" |
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Subject: RE: BS: Mental Workouts without Dilbert From: Hilary Date: 27 Feb 02 - 03:41 AM Nice one Petr & Dick. Looking though old old threads a minute ago and saw 'shortest joke' thread ..... which reminded of the (supposedly) shortest clue in a crossword..... gge (9,3) To confirm, it says gge. Jonhinkansas, I'm surprised that I only confused you a bit !!!!
A simpler variation on the original scenario : Plain room, two doors & two twins as before. You know The liar guards the door to hell, the truth-teller guards the door to heaven. You have only one question, 'they' only answer yes/no. So what question do you ask ??? Personally rather than go through all the what if's/nand/nors etc I would ask a question all 3 of you KNOW the answer to eg Is he(she) your twin ? Have I asked you a question ? Can I get to heaven if I ask the right question ? But that's pobably deemed cheating. Hilary
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Subject: RE: BS: Mental Workouts without Dilbert From: Hrothgar Date: 27 Feb 02 - 03:54 AM I thought the solution in the horse race problem was that the winner married the king, because after all, it is a fairy story. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Fibula Mattock Date: 27 Feb 02 - 04:54 AM Okay, here's my favourite: Two mathematicians are sitting in a restaurant. One says "I've got three daughters, and if you multiply their ages together you get 36." The second one says: "Give me another clue." First one "If you add their ages together, you get the same number as the number of tables in this restaurant." Second one: "Give me another clue." First one: "The eldest one is blonde." Now the second mathematician replies with the correct ages. What are the ages of the three daughters? There's no trick to this, just some logical deduction is required. |
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Subject: RE: BS: Mental Workouts without Dilbert From: gnu Date: 27 Feb 02 - 07:03 AM 2x2x9=36, 2x3x6=36 ? Okay... spill it Fibula !!! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Fibula Mattock Date: 27 Feb 02 - 07:08 AM heh heh heh! I'll PM you. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 27 Feb 02 - 07:14 AM Don't need Fibula to answer this, (only to wear shin pads). Obviously looking for two solutions which would give 3 numbers multiplied to give 36, and when added both give same answer, so second mathematician needs more data. The fact their is an eldest means that if there are two the same age they are the two youngest. I'll leave it there as it's obvious |
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Subject: RE: BS: Mental Workouts without Dilbert From: Fibula Mattock Date: 27 Feb 02 - 07:26 AM There are a number of ways you can multiply 3 numbers together to get 36. The mathmematician works out all the possible values and, even though he can count the number of tables in the restaurant, still can't get the ages. And if you look at the combinations you will see that 2 of them add to the same number meaning it must be one of those two because the mathematician says he needs more info - he can't work it out from a table count alone. 9 2 2 =13 6 6 1 =13 The other mathematician says the eldest has blond hair, therefore it's the 9 2 2 combo because there actually is an eldest one! |
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Subject: RE: BS: Mental Workouts without Dilbert From: gnu Date: 27 Feb 02 - 07:32 AM More tea is required. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 27 Feb 02 - 08:28 AM The information that there is an eldest daughter shouldn't have helped the mathematician. Both daughters could have been born 11 months apart. This month they both are 6 years old, next month one is seven and the other still six. In this case you'd speak about an eldest daughter though both have the same age during one month each year. Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: Fibula Mattock Date: 27 Feb 02 - 08:52 AM Now, now Wolfgang! No trickery involved! I take it that it's for that given moment in time and we're dealing with whole numbers. Or something. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 27 Feb 02 - 08:59 AM Even with TWINS one is elder, even if (in our case) by 9 mn. But still. I still don't see about the horses... maybe one horse will learn to sing? And does anybody remember the classic setup to What Color Is The Bear? |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 27 Feb 02 - 09:05 AM But if you had two daughters 11 months apart and in that particular moment of time both were six years old and you were asked 'How old is you eldest daughter' would you respond 'I have no eldest daughter this month?'I bet you wouldn't. However, John's response to Sharon also applies here. Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 27 Feb 02 - 09:25 AM JohnInKansas says, "Since this is a well known "riddle" it is probably appropriate to assume the "standard conditions." If you wish to do "what-ifs" about other ways that the question could be posed, that's allright; but if you do that, then there's no real "answer" because someone else can always "repose" the question." John, I wasn't trying to pose the Heaven-Hell riddle's question in another way, I was trying to say that Mrrzy's original question did not include all of the conditions of that particular riddle. I was trying to say that just because a riddle is "well known", one shouldn't assume that everyone knows it and that, therefore, one may exclude some of the conditions of the riddle from the original statement without making it impossible for those who do not know (or, in my case, remember) the entire riddle to arrive at the correct answer. You say there's no "real" answer without assuming the "standard conditions"; I say that there's no "real" question if the conditions are not STATED in the question. In other words, if one poses the problem A + B + C = ? to Herman and gives Herman the value of A and B but not C, how can Herman possibly solve the equation? It does no good to tell Herman "other people already know what C's value is, so I don't have to tell you". There is no reason why Herman should know C's value if no one has ever told him. Even if he was told 30 years ago and has since forgotten, it's still unfair not to remind him! Sharon |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 27 Feb 02 - 10:42 AM It is not necessary in Mrrzy's original problem to assume additionally that only 'yes' or 'no' are allowed as responses. You walk to either of them and ask: "If I ask your brother where this door leads to what will he respond?" If I get the response "To Hell" I walk through this door, if I get the response "To Heaven" I take the other door. So the problem as stated by Mrrzy was complete for all practical purposes. Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: gnu Date: 27 Feb 02 - 10:54 AM Kinda puts in mind of the philosophy exam with one question : Why ? Which led me to recall this one... A thermodynamics professor had written a take home exam for his graduate students. It had one question: "Is Hell exothermic (gives off heat) or endothermic (absorbs heat)? Support your answer with a proof." Most of the students wrote proofs of their beliefs using Boyle's Law (gas cools off when it expands and heats up when it is compressed) or some variant. One student, however, wrote the following: "First, we need to know how the mass of Hell is changing in time. So, we need to know the rate that souls are moving into Hell and the rate they are leaving. I think that we can safely assume that once a soul gets to Hell, it will not leave. Therefore, no souls are leaving. As for how many souls are entering Hell, let's look at the different religions that exist in the world today. Some of these religions state that if you are not a member of their religion, you will go to Hell. Since there are more than one of these religions and since people do not belong to more than one religion, we can project that all people and all souls go to Hell. With birth and death rates as they are, we can expect the number of souls in Hell to increase exponentially. Now, we look at the rate of change of the volume in Hell because Boyle's Law states that in order for the temperature and pressure in Hell to stay the same, the volume of Hell has to expand as souls are added. This gives two possibilities: 1. If Hell is expanding at a slower rate than the rate at which souls enter Hell, then the temperature and pressure in Hell will increase until all Hell breaks loose. 2. Of course, if Hell is expanding at a rate faster than the increase of souls in Hell, then the temperature and pressure will drop until Hell freezes over. So which is it? If we accept the postulate given to me by Ms. Therese Banyan during my Freshman year, 'That it will be a cold night in Hell before I sleep with you', and take into account the fact that I still have not succeeded in having sexual relations with her, then 2 cannot be true, and so Hell is exothermic." This student got the only A.
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Subject: RE: BS: Mental Workouts without Dilbert From: Trevor Date: 27 Feb 02 - 10:59 AM The simplest response to the original posting is to say to either guardian 'If I were to ask you which door to go through, what would you say?' and then go through that door. Work it out! Even shorter crossword clue: E (13) The one that always gets me: Three people have a meal in a restaurant and get a bill for £30.00. They decide to split it evenly and so pay £10.00 each. The waiter takes the money but when he adds the bill up on the register realises that it actually only comes to £25.00. He takes 5 £1 coins from the till, puts 2 in his pocket, tells the customers that he made a mistake and gives them each £1.00 back. They have now paid £9.00 each. As there are three of them this means they have paid a total of £27.00. The waiter has £2.00 in his pocket, making £29.00. Where's the other quid gone? Duh! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Bill D Date: 27 Feb 02 - 11:16 AM similar: A farmer dies...he has 3 sons, and at the reading of the will, it states that 1/2 of his horses go to his eldest son. 1/3 to his 2nd son, and 1/9 to his youngest son... the boys look at the lawyer and say. "but Father had 17 horses. We can't do that!" The lawyer thinks a bit and says, "I have a solution!" How did he manage it? |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 27 Feb 02 - 11:29 AM Wolfgang: Not necessarily. Without the "yes" or "no" restriction, the liar could respond by saying, "He [the truthful twin] won't respond because he's deaf"! The truthful twin could respond by saying, "He'll tell you to go to hell!" You also must be careful when using the phrase "your brother"; perhaps these two have other brothers! Better be careful with the word "respond", too; without the "yes" or "no" restriction, the liar could respond by giving you the finger. Your question would have to be more specific: "If I ask the other guard in this room to tell me only whether door 'A' leads to Heaven or Hell, and to give me no other responses, will he say 'Heaven' or will he say 'Hell'?" That might work.... except that either twin could answer that one with "yes"! Besides, doesn't that "and" clause constitute a second question?*G* I guess the question would have to be: "If I ask the other guard in this room to tell me only whether door 'A' leads to Heaven by giving me no other response except to say 'yes' or 'no', will he say 'yes'?" Anybody see any loopholes there? So is this supposed to be a riddle of logic, or semantics? Both? |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 27 Feb 02 - 11:51 AM Sharon, as John has already said you always can argue that any problem statement is incomplete if you want. What if the guard you asked was deaf (and not his brother). What if he didn't understand English (that was not stated explicitely!), what if he did understand and did understand English but your question was to difficult for him to find out how to respond with a lie. And so on. You just have to stop stating conditions at one point and hope for the problem solvers to think a bit. What is the response to A + B + C = ? with A = 2, B = 4 and C = 5? You think it is 11? I say You're wrong. Nowhere did I state explicitely that I was talking about base 10 addition. And by the way who did tell you that the + sign signifies what you consider addition. I forgot to state that too. There is no end to this game if someone is willing to question everything. Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 27 Feb 02 - 11:53 AM This is why I'm no good at riddles! |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 27 Feb 02 - 11:59 AM But, really now, if your eternal soul was at stake, wouldn't you want to be thorough in your examination of the problem? *G* |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 27 Feb 02 - 12:23 PM It is NOT enough to ask "What would YOU say if I asked you if this is the door to Hell?". If it were the door to hell, the liar would say Heaven and the truthteller would say Hell; if heaven, their answers would be reversed, so from that one question, you get no info. They don't have to say Only Yes Or No, but they DO have to answer the question as asked and intended. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 27 Feb 02 - 12:23 PM Oh, and I know where the missing dollar is (ok, pound, as phrased)... |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 27 Feb 02 - 12:31 PM Now to Bill's problem: The lawyer says: "See, your father also left you a little sum of money, just enough to buy one more horse. You have eighteen horses then. The oldest gets 1/2 that is nine horses, the next gets 1/3 that is six horses, the youngest gets 1/9 that is 2 horses." "But, say one brother, that only adds to 17 horses" "Right, says the lawyer, the last horse is for me for my advice how to divide the 17 horses. And by the way, we don't need to buy the 18th horse, you can give me the money alright..." Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 27 Feb 02 - 12:37 PM Try these, y'all... |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 27 Feb 02 - 12:57 PM Short (but not shortest) crossword clues "hijklmno (5)" |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 27 Feb 02 - 01:07 PM Sharon, yes, there are still loopholes, is the liar a "perfect liar" or a "pathological liar". I.e, does he always state the opposite to the truth; or does he make the statement most likely to decieve. The "pathological liar" will give the same answer as the truth teller, as this is the answer most likely to decieve. At this stage the whole question becomes too complex to resolve, Unless... you force one of the guards to precede you through the door. Presumably even the liar does not wish to go to Hell, or will his principles make him go in order to mislead you ???......... This thread could run and run. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 27 Feb 02 - 01:31 PM OK, I'm going to stop after this gets explained to me: Four Men Crossing a Bridge (from Microsoft interview process) I can't come up with less than 19 mn - how do they get 17 mn? |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 27 Feb 02 - 01:40 PM As for the "missing" quid (or dollar), I didn't think there was one. The total payment is no longer 30 units, it's 27, of which 25 are in the till and 2 are in the pocket. Yes? Assuming, of course, that we're calculating in base 10! :^) |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 27 Feb 02 - 01:57 PM 'Scuse me, I should have said "base ten", since every base is base 10! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 27 Feb 02 - 04:25 PM SharonA, I must have missed something, but you at least have found the missing dollar/pound... Oh, I get it! Complex, aincha! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mark Cohen Date: 27 Feb 02 - 04:50 PM Steven's parents have three children. One girl is seven years old, has blonde hair, and is named May. Another child is five years old, four feet three inches tall, and is named June. What is the name of the third child? Aloha, Mark |
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Subject: RE: BS: Mental Workouts without Dilbert From: gnu Date: 27 Feb 02 - 05:11 PM Which minds me of the fellow that didn't know which girl to marry. He gave each of three $5000 to do with it what they may. #1 got a makeover, breast implants, sexy wardrobe, the works, so as to please him. #2 got sporting goods of all types and and a big screen TV. #3 got an investment portfolio with excellent returns so that they would have a nest egg. Who did he pick ? The one with the big tits. |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST Date: 27 Feb 02 - 05:43 PM Mrrzy, Regarding your 'bridge' problem:
Man 1 takes 1 minute Therefore:
First man 1 and man 2 walk across the bridge. This takes 2 minutes. In total: 2+1+10+2+2=17 minutes.
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