# What's the answer to these logic puzzles: **URL:** \ **Category:** Factual Questions\ **Created:** [September 25, 2009, 2:57am UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465 "2009-09-25T02:57:32Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![gigi](https://avatars.discourse-cdn.com/v4/letter/g/a587f6/32.png) [@gigi](https://boards.straightdope.com/u/gigi)\ **Post date:** [September 25, 2009, 9:32pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/41 "2009-09-25T21:32:59Z")
> [@Skammer](#): > > The “9,2,2” solution doesn’t depend on the differnce between “older” and “oldest.” It’s only important that the clue indicate that the non-twin is older than the twins. I like the riddle better when it makes it clear that the additional information allowed the student to solve the riddle - then you know that he knew the teacher’s house address already, and the fact that one daughter was older than the other two is necessary to distinguish the correct answer from the other possible math solution (9,2,2 vs. 6,6,1). I took it as the student missing a detail, meaning what the house number is. That’s why the comment about piano seems like such a non-sequitur. I still think 4,3,3 should be in the running, especially since I wouldn’t have talked to my teacher outside of school and wouldn’t know anything about their house. ---
**Author:** ![Heart\_of\_Dorkness](https://avatars.discourse-cdn.com/v4/letter/h/4bbf92/32.png) [@Heart\_of\_Dorkness](https://boards.straightdope.com/u/Heart_of_Dorkness)\ **Post date:** [September 25, 2009, 9:37pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/42 "2009-09-25T21:37:02Z")
> [@Superhal](#): > > The sixth enigma is a Knights and Knaves puzzle. Two doors are guarded by two men, one of whom always lies and one of whom always tells the truth; however, the puzzle solver does not know which man is which. One of the doors leads to freedom and one to captivity. The enigma is to determine a single question that, if asked of one of the guards, would reveal the door to freedom with certainty. > [@treis](#): > > You ask what the other guy would say, and then go through the opposite door. > > If you talk to the honest one, he will honestly tell you which door the liar would call the safe passage, i.e. the bad door. > > If you talk to the liar, he will lie and give you the opposite answer of the truthful guy, i.e. the bad door. > > Thus, no matter who you are talking to you will get the “bad door” as the answer. That allows you to choose the good door by doing the opposite. A friend once told me a variation on this one, but he had never heard the answer, only the puzzle. I came up with an answer that works, but I don’t know if it’s the “correct” solution. The variation was simply this: there are more than two guards. My solution: [Spoiler]Ask: “If someone were to ask you which door they should choose, what would your answer be?” The truth teller thinks, “I always tell the truth, and since the good door is A, I would say door A”, and responds, truthfully, “I would say door A.” The liar thinks, “I always lie, and since the good door is A, I would say door B”, and responds, falsely, “I would say door A.” Either way, you choose the door they answer. [/Spoiler] ---
**Author:** ![Superhal](https://avatars.discourse-cdn.com/v4/letter/s/b4bc9f/32.png) [@Superhal](https://boards.straightdope.com/u/Superhal)\ **Post date:** [September 25, 2009, 9:46pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/43 "2009-09-25T21:46:50Z")
> [@gigi](#): > > I took it as the student missing a detail, meaning what the house number is. That’s why the comment about piano seems like such a non-sequitur. I still think 4,3,3 should be in the running, especially since I wouldn’t have talked to my teacher outside of school and wouldn’t know anything about their house. It’s a logic problem mixed with a math problem. The clues are: 1. 3 children 2. 2 are twins, 1 is older 3. Sum of their ages = X 4. Product of their ages = 36 5. The student must know that one child is older than the other two to solve the problem. The factors of 36 = 1, 2, 2, 3, 3 Possible combinations of the above (including rule #2) are: 6, 6, 1 9, 2, 2 4, 3, 3 36, 1, 1 The key clue is that the student says he does not have enough information to solve the puzzle, even if he knows X (the teacher’s house number.) That means there are two sets of numbers that have the same sum. Of the list, only 6, 6, 1 and 9, 2, 2, qualify. It doesn’t matter that we don’t know what the house number is, \*\*as long as we know the student is unable to solve the problem because two sets have the same sum. \*\* Therefore, the last clue (the non-twin is the older one) leaves only one possible solution, 9, 2, 2. ---
**Author:** ![Superhal](https://avatars.discourse-cdn.com/v4/letter/s/b4bc9f/32.png) [@Superhal](https://boards.straightdope.com/u/Superhal)\ **Post date:** [September 25, 2009, 9:50pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/44 "2009-09-25T21:50:37Z")
> [@Heart\_of\_Dorkness](#): > > A friend once told me a variation on this one, but he had never heard the answer, only the puzzle. I came up with an answer that works, but I don’t know if it’s the “correct” solution. The variation was simply this: there are more than two guards. > [/Spoiler] It was famously in Lewis Carroll’s Alice in Wonderland (or Through the Looking Glass?) and copied many times since. I saw it myself first in Games magazine in the 80’s. ---
**Author:** ![Superhal](https://avatars.discourse-cdn.com/v4/letter/s/b4bc9f/32.png) [@Superhal](https://boards.straightdope.com/u/Superhal)\ **Post date:** [September 25, 2009, 9:53pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/45 "2009-09-25T21:53:19Z")
I agree that the unborn baby one is very badly presented, but the solution is quite elegant. ---
**Author:** ![Heart\_of\_Dorkness](https://avatars.discourse-cdn.com/v4/letter/h/4bbf92/32.png) [@Heart\_of\_Dorkness](https://boards.straightdope.com/u/Heart_of_Dorkness)\ **Post date:** [September 25, 2009, 10:04pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/46 "2009-09-25T22:04:23Z")
> [@Superhal](#): > > I agree that the unborn baby one is very badly presented, but the solution is quite elegant. Actually, I thought that presentation was fine. If it asked “How old is the son?”, then you’d have to give a negative age as the answer, which would be silly, but it doesn’t. It only says that in six years, he will be a certain age, and it will indeed be a positive number by that time. My issue was with the lightbulb puzzle, because you’d need to know whether the bulb was on or off to begin with, and it doesn’t specify. ---
**Author:** ![Superhal](https://avatars.discourse-cdn.com/v4/letter/s/b4bc9f/32.png) [@Superhal](https://boards.straightdope.com/u/Superhal)\ **Post date:** [September 25, 2009, 10:06pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/47 "2009-09-25T22:06:56Z")
> [@Heart\_of\_Dorkness](#): > > My issue was with the lightbulb puzzle, because you’d need to know whether the bulb was on or off to begin with, and it doesn’t specify. Imho, one necessary aspect of the puzzle is that the switches must be marked “on/off.” Without that, the puzzle is unsolvable, so I just assumed that was the case. ---
**Author:** ![Fear\_the\_Turtle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fear_the_turtle/32/2926_2.png) [@Fear\_the\_Turtle](https://boards.straightdope.com/u/Fear_the_Turtle)\ **Post date:** [September 25, 2009, 10:20pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/48 "2009-09-25T22:20:05Z")
> [@Superhal](#): > > It’s a logic problem mixed with a math problem… > Therefore, the last clue (the non-twin is the older one) leaves only one possible solution, 9, 2, 2. Just thought of a different interpretation. I agree that referring to a 3rd entity as being older is a bit stilted. So maybe when he said older he was referring to the older twin? Picture someone saying that with a wink as it dawns on the other person that twins are involved. People often refer to one of their twins as being older. In this case, since 2 year olds (typically) don’t play piano, the professor was hinting the older 6 year old plays piano? And the answer is 6,6,1? Was the answer they were looking for given in the movie? ---
**Author:** ![SCSimmons](https://avatars.discourse-cdn.com/v4/letter/s/e495f1/32.png) [@SCSimmons](https://boards.straightdope.com/u/SCSimmons)\ **Post date:** [September 25, 2009, 10:25pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/49 "2009-09-25T22:25:25Z")
> [@jtgain](#): > > IPlus if you want to be technical about it, pregancies don’t last exactly nine months. It could have been shortly before or after the nine month period, and the father could have been doing whatever. He could have even been dead at that time. Maybe the father doesn’t smoke. > > Also, the way these cute little riddles are worded, there are about 5 other interpretations that can be gathered (like with the above candy example) and those are simply dismissed as incorrect because it isn’t what the riddle’s author was thinking. See, my answer was, “Calling his lawyer to sue the fucking condom company.” But I had a feeling that wasn’t what I’d find when I turned to the secret answers page. ---
**Author:** ![Superhal](https://avatars.discourse-cdn.com/v4/letter/s/b4bc9f/32.png) [@Superhal](https://boards.straightdope.com/u/Superhal)\ **Post date:** [September 25, 2009, 10:36pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/50 "2009-09-25T22:36:50Z")
> [@Fear\_the\_Turtle](#): > > Was the answer they were looking for given in the movie? As far as I can tell, this movie is Spanish from 2007, and not released in the US yet. I couldn’t locate a script either. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 25, 2009, 10:52pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/51 "2009-09-25T22:52:51Z")
> [@](#): > > I still think 4,3,3 should be in the running, especially since I wouldn’t have talked to my teacher outside of school and wouldn’t know anything about their house. Most piano teachers teach out of their own homes. Besides, the puzzle tells us (or should, at least) that after the extra piece of information, the student is able to solve the puzzle. If the student doesn’t know the house number, there’s no way he can solve it, so the puzzle itself implies that he does know the house number, no matter how implausible that might be. ---
**Author:** ![Fear\_the\_Turtle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fear_the_turtle/32/2926_2.png) [@Fear\_the\_Turtle](https://boards.straightdope.com/u/Fear_the_Turtle)\ **Post date:** [September 25, 2009, 10:56pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/52 "2009-09-25T22:56:56Z")
> [@Superhal](#): > > As far as I can tell, this movie is Spanish from 2007, and not released in the US yet. I couldn’t locate a script either. Damn. I TiVo’d this movie a while back but I deleted it before I could watch it when I saw it was a subtitled foreign movie (my drug addled, post shoulder surgery body couldn’t handle reading a movie as I kept drifiting in and out of sleep). I’ll check listings to see if it is being shown again (IFC or Sundance I believe). ---
**Author:** ![Superhal](https://avatars.discourse-cdn.com/v4/letter/s/b4bc9f/32.png) [@Superhal](https://boards.straightdope.com/u/Superhal)\ **Post date:** [September 26, 2009, 12:36am UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/53 "2009-09-26T00:36:19Z")
> [@Chronos](#): > > Most piano teachers teach out of their own homes. Besides, the puzzle tells us (or should, at least) that after the extra piece of information, the student is able to solve the puzzle. If the student doesn’t know the house number, there’s no way he can solve it, so the puzzle itself implies that he does know the house number, no matter how implausible that might be. Yep, that’s the “key” in this puzzle: the house number itself is unnecessary, simply that two sets of answers have the same sum. ---
**Author:** ![Chimi](https://avatars.discourse-cdn.com/v4/letter/c/73ab20/32.png) [@Chimi](https://boards.straightdope.com/u/Chimi)\ **Post date:** [September 28, 2009, 12:25am UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/54 "2009-09-28T00:25:41Z")
> [@Superhal](#): > > As far as I can tell, this movie is Spanish from 2007, and not released in the US yet. I couldn’t locate a script either. Blockbuster register-monkey here. My store carries it, so it’s been released in America. I rented it, but the price you pay for free rentals is that you don’t value them much, so they sit by your movie-watching device for a week and then go home unopened. ---
**Author:** ![MysterMenace](https://avatars.discourse-cdn.com/v4/letter/m/71c47a/32.png) [@MysterMenace](https://boards.straightdope.com/u/MysterMenace)\ **Post date:** [January 6, 2010, 7:00pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/55 "2010-01-06T19:00:56Z")
Referring to the logic problem of the Mother and Son: A badly presented puzzle is not “elegant”. If the son is -9 months old, implying “just conceived”, then how is it known that the embryo is a male? If the answer involves a -9 month old child then this is not an elegant puzzle. The other problems can be considered elegant, in that once you understand the solution it is obvious that the solution is correct. There is no such thing as a riddle that cannot be nitpicked to aversion. (e.g. Is she a mother by fact of an embryo, Are other children involved in this puzzle, Is this puzzle about humans or other species? It can get ridiculous.) Read each puzzle for the secret it is trying to reveal. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [January 6, 2010, 9:53pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/56 "2010-01-06T21:53:23Z")
> [@Superhal](#): > > The seventh enigma is an elementary algebra problem with a twist. A mother is 21 years older than her son. In 6 years, the son will be one-fifth his mother’s age. The enigma asks what the father is currently doing. For those who claim that this puzzle is badly presented because it’s silly to talk about negative ages, or because “mother” is not well defined, first, I think you’re a bunch of sourpusses. It’s a clever puzzle, and silliness like claiming that it’s not stated that the mother is human, or that not all pregnancies last 9 months are missing the point. But the problem can easily be restated as something like: “There’s a woman. In one year, she will be 21 years older than her son. In 6 years, she will be 5 times his age. What is she doing right now?” ---
**Author:** ![EdwardLost](https://avatars.discourse-cdn.com/v4/letter/e/bbe5ce/32.png) [@EdwardLost](https://boards.straightdope.com/u/EdwardLost)\ **Post date:** [January 6, 2010, 10:14pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/57 "2010-01-06T22:14:18Z")
A puzzle (or word problem) requires the asker and askee to have a common set of assumptions surrounding the puzzle - and does not break those assumptions. A riddle on the other hand often hinges on breaking an assumption that the askee has made (“Oh, Dorothy is a parakeet!”). If I’m presenting you with puzzles or word problems, I don’t want to keep repeating, “Yes, you’re on Earth. You’re human. Ignore wind resistance, ignore friction, ignore the Coriolis effect, ignore the gravitational pull of Saturn…”. The rule is, in general, if I don’t mention it don’t consider it. People who are familiar with puzzles know the rules of the game and know when to make the proper assumptions. When a puzzle or riddle gets a lot of argument it’s often because the asker has not made clear which of the two he is presenting. Or, if it’s clearly a puzzle, the readers may not make the correct assumptions because of inexperience with those types of puzzles. Sometimes the puzzle itself is not well-posed, i.e. the assumptions and conditions to be used are not clear. The Monty Hall problem is an example of a problem that is often not well-posed. The asker may not make clear whether Monty always reveals a door or sometimes reveals a door. The embryo problem is borderline. If you just plug in the numbers without making any assumptions you get the answer and have a good laugh. On the other hand, the typical assumptions for age problems is that negative ages are not allowed. It’s really a joke in the form of a puzzle. ---
**Author:** ![needscoffee](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/needscoffee/32/1076_2.png) [@needscoffee](https://boards.straightdope.com/u/needscoffee)\ **Post date:** [January 6, 2010, 10:32pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/58 "2010-01-06T22:32:08Z")
Here’s the math: ## A mother is 21 years older than her son. In 6 years, the son will be one-fifth his mother’s age. ## Let Kid’s age = K Then Mother’s age = K + 21 Kid’s age in 6 Years = K + 6 Mother’s age in 6 Years = K + 21 + 6 Kid’s age in 6 Years = 1/5 x Mother’s age in 6 Years K + 6 = 1/5 x (K + 21 + 6) K + 6 = 1/5 x (K + 27) K + 6 = (1/5 x K) + (1/5 x 27) K + 6 = 1/5 x K + 5.4 Now subtract 6 from each side and you get… K = 1/5 x K - .6 Now multiply each side by 5 and you get… 5 x K = 5 x (1/5 x K - .6) Do the math… 5K = 1K x (5 x -.6) 5K = K - 3 Now subtract a K from each side and you get… 4K = -3 Now divide each side by 4 and you get… ## K = -3/4 Ta-da! I say the father was passed out cold. Odds are against him smoking nowadays. ---
**Author:** ![Rysto](https://avatars.discourse-cdn.com/v4/letter/r/ecccb3/32.png) [@Rysto](https://boards.straightdope.com/u/Rysto)\ **Post date:** [January 7, 2010, 12:12am UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/59 "2010-01-07T00:12:28Z")
> [@Superhal](#): > > I agree that the unborn baby one is very badly presented, but the solution is quite elegant. I disagree, because as soon as I read it I knew that the solution had to be “having sex with the mother” without even doing the math. It’s the only possible answer to the question that knowing the son’s age could give me. ---
**Author:** ![AWB](https://avatars.discourse-cdn.com/v4/letter/a/bb73d2/32.png) [@AWB](https://boards.straightdope.com/u/AWB)\ **Post date:** [January 7, 2010, 3:56am UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/60 "2010-01-07T03:56:19Z")
> [@Aspidistra](#): > > Clearly the key to the question is that _the student knows_ the piano teacher’s house number … otherwise he would say “I don’t know your house number”. The fact that he says “I’m missing one piece of information” tells us that he does know the house number and that there are two possible sums of 36-factors that add up to it. The teacher’s answer about his oldest tells us that the differentiating factor between these two is that one has a single “oldest” and one doesn’t. The problem doesn’t state that the teacher is a _piano_ teacher. I’m a teacher, and I hope to God none of my students know my address. 😛 And even if he were the student’s piano teacher, the teacher might be visiting the student’s house. [Previous page](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465.md?page=2) [Next page](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465.md?page=4)