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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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Subject: RE: BS: Mental Workouts without Dilbert From: Bill D Date: 27 Feb 02 - 06:42 PM Mark...*grin*....seems like I'd just ask Steven. (remember that "read everything before doing anything" test? |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST Date: 27 Feb 02 - 09:17 PM Hi Mark, the answer is STEVEN. Still thinkin' about the rest, though. Hilary |
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Subject: RE: BS: Mental Workouts without Dilbert From: Hilary Date: 27 Feb 02 - 09:27 PM Hi Nigel Hijkl = H to O = H2O= WATER ! Sorry Bill, your answer was a bit too subtle for me at this time of the morning. Just don't tell me someone has already posted 'water'. Hilary |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mark Cohen Date: 27 Feb 02 - 09:34 PM Bill, I did one of those tests when I was a 6th grader. Must have been a psychology grad student using our class as guinea pigs. I remember that item #23 or so said, "If you have followed all the instructions up to this point, say 'I have.'" And all around me the voices piped up, "I have!" "I have!" For those of you unfamiliar with this, every student was given a piece of paper. At the top of the page it said, in large letters, "FOLLOW ALL INSTRUCTIONS EXACTLY AS WRITTEN". Item #1 said, "Be sure to read the entire test all the way through before completing any of the items", and item #30 said, "Now that you have read through the entire test, go back to the beginning and do item #2 only, and then you are finished." The interesting thing about that problem is that it was in a kids' magazine published by Highlights called MathMania, so all the other problems in the magazine had solutions that used math--that context made it a little more tricky! Aloha, Mark |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 05:40 AM Mark: when you were a Psych grad student, did anyone complain about the wording of the paper ? item 23 gives instructions (which must be followed). item 1 instructs that item 23 must only be read until the whole paper has been read. The Instruction at the top of the paper makes these two instructions self contradictory. It seems impossible for anyone to have obtained full marks as they must have ignored some part of the paper! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 05:58 AM Following on. If this test were set by the armed forces then those responding "I Have" to item #23 would be correct. "Always obey the most recent command received, even if it is at odds with an earlier command" |
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Subject: RE: BS: Mental Workouts without Dilbert From: Trevor Date: 28 Feb 02 - 05:59 AM Mrrzy, '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.' If the question is 'What WOULD you say....' the liar must also give an untruth as his answer. If he said 'I WOULD say heaven....' at that point he would be telling the truth. As he must always lie, his answer to 'What WOULD you say....' must also be a lie. Gettit? And 'cos I can't stand the tension any more and want to be a smartarse, the answer to my crossword clue: E (13) = Senselessness
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 06:07 AM Crosswords, how about: A rag man (7) |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 06:12 AM Mrrzy requested "What colour was the bear?" A man walks out of his house, walks 2 miles South, walks 2 miles East, shoots a bear, then walks two miles North, back to his house. What colour is the bear.
And before the pedants get in, it doesn't require a house to be 2 miles wide with a door at each end!! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Fibula Mattock Date: 28 Feb 02 - 06:21 AM white |
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Subject: RE: BS: Mental Workouts without Dilbert From: Fibula Mattock Date: 28 Feb 02 - 06:35 AM ...although this is subjective and depends on perception (just to join the pedants who had issue with the ages in my puzzle!). |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 06:47 AM Fibula, I realise Mrzzy probably knew the bear's colour before requesting a reiteration of the question, but you could have delayed posting your response slightly, so that it did not show immediately below the question! Also, can you (correctly) justify your answer ?. And I don't mean move it to the right or left margin! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Hilary Date: 28 Feb 02 - 06:48 AM Nigel's last clue .. ANAGRAM, I like the 'E' clue, very surreal. A few letters put in for gge (9,3) S _ R_ _ _ _ _ _ , _ G _ Hilary
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 06:50 AM Hilary, yes, I liked that one, but left it for others. See my recent post for Fibula about immediate responses. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Fibula Mattock Date: 28 Feb 02 - 06:53 AM Nigel - likewise your answer to mine when I was PM-ing clues to people! *BG* The house is at the North Pole? |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 07:10 AM To help (or hinder) people with the 'Bear' question, A man leaves his house, walks 2 miles North, walks 2 miles East, relieves himself in the snow, and walks 2 miles South, back to his house, Where is his house ? |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 07:38 AM No apologies for this Crossword clue today: Continue? Milligan (4) |
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Subject: RE: BS: Mental Workouts without Dilbert From: donal Date: 28 Feb 02 - 07:39 AM Back to the original question (I hope it hasn't been answered already) The question to be asked is - "If I asked your twin which door to go through, which would he say ?" Then go through the other door. The truth teller would say what his twin would say (ie. a lie) and the liar would NOT say what his twin would say (ie. again a lie). Therefore use the other door ! Donal |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST Date: 28 Feb 02 - 07:40 AM North Pole |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 28 Feb 02 - 07:46 AM There is an infinite number of correct responses to Nigel's version of the 'where is the house' puzzle. One of them is: At any point that has a distance of 2121 m from the North Pole. Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 28 Feb 02 - 07:48 AM Blame my pocket calculator: roughly 3730 m from the North Pole Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 07:53 AM Wolfgang, North Pole, Any point at a distance (no calculator with me so I'll take your word) X metres from N Pole, But... Where else ?? |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST Date: 28 Feb 02 - 07:54 AM South Pole? |
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Subject: RE: BS: Mental Workouts without Dilbert From: Trevor Date: 28 Feb 02 - 07:55 AM Donal, that's more or less what I said , except I said 'What would YOUR answer be....' and went through that door. Cuts out a stage in the reasoning. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 28 Feb 02 - 07:57 AM Guest, with an answer of just "South Pole?" Should you not have signed in as Guessed ? |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 28 Feb 02 - 08:21 AM Nigel, look back at your question. The answer you had in mind to be correct is 'North Pole'. The trivial answer that actually is correct is 'South Pole'. My answer is part the many nontrivial responses. To make it easier: My house is 2 ml + 512 m away from the North pole. What happens if you are 512 m from any of the two poles and walk east for 2 ml? Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST Date: 28 Feb 02 - 08:26 AM your legs feel tired? |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST,Hilary, not logged in Date: 28 Feb 02 - 09:30 AM Hi, Nigel Interesting point about not responding immediately, though you posted just before I did so I hadn't read your post. What does everyone think is an appropriate time-lag ? As we seem to be getting an excellent supply of conundrums it strike me as necessary at the time. Ok, calculators ready ? Though you've probably all heard this one before.... I've dug a hole 3feet+2inches long X 4feet+5inches wide X 2foot deep. How much soil is there in the hole ? NB for the non-imperialists : one foot=12inches Last guest - too true.
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 28 Feb 02 - 09:41 AM GUEST: Mine would! *G* Wolfgang's right; the answer to the question as posted is the South Pole... and I don't believe there are any bears (polar or otherwise) at the South Pole. As for the color of the polar bear, it is not white, contrary to popular belief. Here's an excerpt from this page: http://www.polarbearsalive.org/facts3.htm (probably more than anyone wanted to know, but here it is anyway).... POLAR BEAR FUR * Despite what our eyes tell us, a polar bear's fur is not white. Each hair shaft is pigment-free and transparent with a hollow core. * Polar bears look white because the hollow core scatters and reflects visable light, much like ice and snow does. * When photographed with film sensitive to ultraviolet light, polar bears appear black. Early speculation over this discrepancy produced a theory, now widely repeated as fact, that polar bear hair acts like a fiber optic guide to conduct ultraviolet light to the skin. In 1998, Daniel W. Koon, a physicist at St. Lawrence University in Canton, New York, decided to actually test whether or not polar bear hair could efficiently conduct ultraviolet light. Koon and a graduate assistant, Reid Hutchins, obtained polar bear hair from the Seneca Park Zoo in Rochester. Their experiments showed that a one-fifth inch strand of polar bear hair was able to conduct less than a thousandth of a percent of the applied ultraviolet light. With such a high loss rate, meaningful amounts of ultraviolet light cannot be reaching a polar bear's skin. Instead, Koon believes the ultraviolet light is absorbed by the keratin making up the hair. * In 1979, three polar bears at the San Diego Zoo turned green. Scientists discovered that colonies of algae were growing in the bears' hollow hair shafts. * Although the algae in no way harmed the animals, zoo veterinarian Phillip Robinson restored the bears' "white" fur by killing the algae with a salt solution. * The fur on a polar bear cub [appears] whiter than that of adult bears. In older bears, [apparent] fur colors range from white to almost yellow. * Hybrid cubs born to captive polar bears and their close relative, the brown bear, are "white" at birth but later turn blue-brown or yellow-white [I wonder if this means that some pigment enters the hair shaft?]. * A polar bear is so well-insulated that it experiences almost no heat loss. In addition to its insulating fur, the bear's blubber layer can measure 4.5 inches thick. * So effective is the polar bear's insulation that adult males quickly overheat when they run [All the same, I wouldn't try to outrun one if I were you]. * Because polar bears give off no detectable heat, they do not show up in infrared photographs. (Infrared film measures heat.) When a scientist attempted to photograph a bear with such film, he produced a print with a single spot -- the puff of air caused by the animal's breath. Sources: Lords of the Arctic by Richard C. Davids (Macmillan Publishing, 1982); Polar Bears by Ian Stirling (University of Michigan Press, Ann Arbor, 1988); Daniel W. Koon, "Is Polar Bear Hair Fiber Optic?", Applied Optics, Vol 37, page 3198. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 28 Feb 02 - 10:23 AM Still no takers (except: cold feet, tired feet) for my challenge? 'South pole' is just one possible answer to Nigel's question (in the last posted version; in an earlier it is 'North pole'). What are the other responses? Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST Date: 28 Feb 02 - 11:00 AM Wolfgang: 'Back where you started', is I assume the required response to your question? It's a little confusing as you mix metric and imperial measurements. Or is that part of the 'challenge?' |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 28 Feb 02 - 11:04 AM Sorry, Nigel, I got confused between your "bear" question (North Pole) and your "taking a leak" question (South Pole). Wolfgang, I don't understand the question "What happens?" in your challenge. You'd be east of where you were but the same distance from the pole. But what's supposed to "happen"? If it's the North Pole, I suppose what would happen is that you'd get wet, since I've read that, with global warning, the polar ice cap has melted at the pole (so you wouldn't be walking east, you'd be rowing... or swimming). |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 28 Feb 02 - 11:08 AM Can one swim a distance of milliliters? *G* |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST Date: 28 Feb 02 - 11:12 AM But what's supposed to "happen"? You might meet a 'pretty fair maid' That's what normally happens when you 'walk out'
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 28 Feb 02 - 11:12 AM Thanks about the 17 mn! It was really bugging me. Also, never eat polar bear liver. It contains enough Vitamin A to kill a human. And from a psychological point of view, if a polar bear LOOKS white in its natural habitat, it IS white to our perceptual systems, and explaining how that illusion is created doesn't change the perception, although it is fascinating! Wonder if they ever turn green in the wild? Remember the green monkey experiment? Wonder what polar bears would do with a green one... What happened in the zoo, did it bollix their social interactions? And Trevor, no, I don't. Do you get mine? |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 28 Feb 02 - 11:33 AM I agree that my bad wording of 'what happens' instead of e.g. 'where are you' is to blame for all those funny responses I got beside the one response (GUEST Date: 28-Feb-02 - 11:00 AM) I had expected in that context. Still, there are more correct responses to Nigel's 'taking a leak' question than just 'South Pole' and my '3730 m from the North Pole' response is just one of them. Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST,RedCelt(not signed in) Date: 28 Feb 02 - 12:03 PM Wolfgang, If I'm correct, at that distance from the pole, with that distance traveled, you would be back at your startpoint, having circumnavigated your wee part of the globe. And the answer to the 'How much dirt question above would of course, be NONE, for if oyu had dirt in there, it wouldn;t be a hole. |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 28 Feb 02 - 01:54 PM Mrrzy: I'd thought of that point (that color can be defined by our perception of it), but I wanted to clarify that there is no white pigment in the bear's fur and that the bear's coloration appears differently depending on the circumstances. So we can agree, I think, that a polar bear "is" white sometimes. So to answer the question "What color is the bear?" in the riddle by saying "white", we'd have to assume that the conditions were such that he would appear to be white. Again, one of those assumed standard conditions that irritate me about riddles!!! |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 28 Feb 02 - 02:04 PM Wolfgang: Is that '3730 m from the North Pole' measurement the distance from pole to pole as measured by the diameter of the earth, or the circumference? I forget what each of those measurements is, in miles. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 28 Feb 02 - 02:58 PM Yeah, I know, I just felt nitpicky! |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 28 Feb 02 - 04:25 PM Nitpicky? Ah, a kindred spirit! :^) |
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Subject: RE: BS: Mental Workouts without Dilbert From: Hilary Date: 28 Feb 02 - 08:48 PM Red Celt is quite right about the earth/hole & Walrus has cracked the GGE (9,3). So the yolk isn't on them ! If you want picky......... are we talking magnetic north or due north ...... Hilary |
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Subject: RE: BS: Mental Workouts without Dilbert From: Trevor Date: 01 Mar 02 - 03:15 AM My brain hurts! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 01 Mar 02 - 04:28 AM The classic "Bear" problem requires the answer "White", which most people have heard enough times that they do not bother to reason why, The house in this case is clearly at the North Pole, so that going 2 mls S then 2mls E leaves one at a position that is still 2 mls S of the pole. Similar cases close to the pole permit one to travel along an arc of longitude where ones return journey N converges with ones outward journey. Shooting the bear makes any answer about the S Pole wrong, as there would be no bears there. But once the bear is out of the question (hence "taking a leak") then positions near the S pole are possible. If, after walking 2 miles S the man is on a circle (centred on S pole) of radius 1/(2ð) then walking 2 mls E will take him in a circle once around the pole. So any start point on a circle 2 mls N of this circle is suitable to build a home to fit the question. Similarly, moving closer to the S Pole, we can find positions where the man wals 2 mls E and circles the pole twice. Giving another set of answers, and we can continue inwards for more answers. However, his house cannot be closer than 2 mls from the S pole, as then he would be unable to start by walking 2 mls S. Hope this clarifies the situation. Why don't polar bears eat penguins ?? |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 01 Mar 02 - 04:34 AM Sorry, character set difference, previous post should say a"a circle (centred on S Pole) of radius 1/2*Pi) Alt27 gave that on screen, but it seems to have mutated in crossing the big pond) |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 01 Mar 02 - 07:27 AM As Sharon has alluded to in her question (diameter or circumference) Nigel's formula to come to all other solutions is strictly speaking wrong (though correct for all practical purposes). His formular comes from the planar geometry and the correct formula (which I don't know) would have to come from spherical geometry. The 'error' he makes is to treat the earth as if it was flat. Since we all know that this error (centimetres?, millimeters?)is very small for walks of up to two miles and certainly smaller than any random deviation in our walking, for all practical purposes Nigel has given all possible solutions for all practical purposes . Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST Date: 01 Mar 02 - 07:30 AM They don't eat Penguins 'cos they can't get the wrappers off! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Fibula Mattock Date: 01 Mar 02 - 07:57 AM or because they live at opposite poles! *g* |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 01 Mar 02 - 08:59 AM Penguins aren't eaten by a lot of things, including humans. They apparently taste just awful, like cod liver oil. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Fibula Mattock Date: 01 Mar 02 - 09:09 AM Maybe they'd be okay in orange juice then! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 01 Mar 02 - 09:37 AM ...schrieb sie uns grinste hamish. Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 01 Mar 02 - 09:47 AM ¿En Inglés, por favor? No hablo Aleman. ¡Muchas gracias! |
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Subject: RE: BS: Mental Workouts without Dilbert From: Wolfgang Date: 01 Mar 02 - 10:16 AM How would you feel, Sharon, if you had to explain a stupid joke based upon two different meanings of the same string of phonemes in two languages with an explanation that is in the very least ten times as long as the joke? Fibula did allude to the song 'Cod liver oil and the orange juice' in her last post, a song made know by the late Hamish Imlach. 'Hamish' sounds similar to the German word 'hämisch' which in English means 'maliciously' and so on... Wolfgang |
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Subject: RE: BS: Mental Workouts without Dilbert From: SharonA Date: 01 Mar 02 - 10:35 AM Ah, a bilingual pun! I love 'em when I can understand 'em. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Mrrzy Date: 01 Mar 02 - 01:29 PM I ws thinking it was time for a Continued thread, but we seem to be descending into silliness, so I'm not, yet. If new brainteasers maybe? Anybody got any MUSICAL ones? |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST,petr Date: 01 Mar 02 - 08:17 PM re the mathematicians daughters why not 2x3x6=36 am I missing something? |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 02 Mar 02 - 11:28 AM Guest petr. yes, you are missing the fact that it was a discussion between to mathematicians, so each could be expected to understand the logical processes. So, once the product of the three ages had been set at 36, the total of the ages was equal to the number of tables in the restaurant. The other mathematician was still unable to solve this, and so the idea of three numbers with a product of 36, and a sum of "X" had to have more than 1 solution. Once we have found all the sets of 3 digits with a product of 36, we find there are only two sets with the same sum. Mathematician No 2 is unable to choose between these until he also knows that there is an "Eldest" daughter. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Nigel Parsons Date: 03 Mar 02 - 12:26 PM Anyone still tracing this might like "Song Quiz" posted today! Nothing like blowing your own trumpet, tomorrow I move up to a Sousaphone! |
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Subject: RE: BS: Mental Workouts without Dilbert From: GUEST,petr Date: 05 Mar 02 - 12:26 PM thanks Nigel, good puzzle. |
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Subject: RE: BS: Mental Workouts without Dilbert From: Grab Date: 06 Mar 02 - 08:35 AM Mrzzy, that's a good reason not to work at Microsoft. Any company which considers a good co-worker to be one who knows a particular riddle/trick/useless fact is by definition the place you most want to avoid working in, since the company is obviously populated with total pillocks! It's about as valid as only employing ppl who can pat their head and rub their stomach at the same time or who can recite the alphabet backwards. So if you see this kind of thing at an interview, leave and don't come back. Graham. |