# 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:** 19\ **Page:** 4
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [January 7, 2010, 1:53pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/61 "2010-01-07T13:53:17Z")
> [@bengangmo](#): > > Mine DOES play the piano My one-year-old can play piano, for certain definitions of play.😉 ---
**Author:** ![SGT42](https://avatars.discourse-cdn.com/v4/letter/s/b9e5f3/32.png) [@SGT42](https://boards.straightdope.com/u/SGT42)\ **Post date:** [January 7, 2010, 2:41pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/62 "2010-01-07T14:41:19Z")
> [@treis](#): > > Well 4 year olds don’t play the piano really either. Instead of 9, 2, and 2 I see no reason why it couldn’t be 9, 4, and 1. Or 6, 3, and 2. You are all missing the information that the sum of the ages is the number of the house. From all the combinations of ages possible, only two have the same sum: 6,6,1 and 9,2,2, both sum 13. So you need an extra information: there is an older daughter. ---
**Author:** ![muttrox](https://avatars.discourse-cdn.com/v4/letter/m/a8b319/32.png) [@muttrox](https://boards.straightdope.com/u/muttrox)\ **Post date:** [January 7, 2010, 2:57pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/63 "2010-01-07T14:57:56Z")
> [@Rysto](#): > > 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. I tend to agree. Much like the twins puzzle, you don’t need to know the age - only that knowing the age would tell you the answer. There is really only one age that can lead to an inference. (Well I suppose the son could have been age zero - the father would be passing out cigars.) ---
**Author:** ![XanderCrews](https://avatars.discourse-cdn.com/v4/letter/x/ee59a6/32.png) [@XanderCrews](https://boards.straightdope.com/u/XanderCrews)\ **Post date:** [January 8, 2010, 4:03am UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/64 "2010-01-08T04:03:20Z")
Saw this movie this summer. Before the characters got to the room with the puzzles they had to complete a challange that involved finding what order a series of numbers were in. The correct response was alphabetical order, so the characters (mathematicians) were already expecting to be thinking outside of the box. ---
**Author:** ![MysterMenace](https://avatars.discourse-cdn.com/v4/letter/m/71c47a/32.png) [@MysterMenace](https://boards.straightdope.com/u/MysterMenace)\ **Post date:** [January 12, 2010, 7:38pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/65 "2010-01-12T19:38:29Z")
In the Mother-Son puzzle there isn’t only one age that can lead to an inference. If the son’s age had worked out to be even less, say -6, then the mother would be about 15 and the father would be doing time. ---
**Author:** ![MysterMenace](https://avatars.discourse-cdn.com/v4/letter/m/71c47a/32.png) [@MysterMenace](https://boards.straightdope.com/u/MysterMenace)\ **Post date:** [January 12, 2010, 7:41pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/66 "2010-01-12T19:41:38Z")
Now that we know the answer to the Mother-Son puzzle, I am still trying to figure out what it is. Is the father: going to sleep, asking her if the she is sure about her cycle, wondering if they just created a girl or a boy, wondering how she already knows it’s a boy, getting up to go to work, or church, or shower, or class, sneaking out to go back to his own dorm room, or wondering how his life has become a “puzzle inside a riddle wrapped in an enigma.” ---
**Author:** ![Mama\_Zappa](https://avatars.discourse-cdn.com/v4/letter/m/71e660/32.png) [@Mama\_Zappa](https://boards.straightdope.com/u/Mama_Zappa)\ **Post date:** [January 14, 2010, 8:23pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/67 "2010-01-14T20:23:47Z")
> [@bouv](#): > > As someone upthread suggested, couldn’t you have “3, 3, and 4”? > > This still leaves toy with just one “older” daughter, and while it’s unlikely that a four year old can play the piano, it’s not outside the realm of possibility. Or 9, 4 and 1. Or 18, 2 and 1. Lots of possibilities. ---
**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:** [January 14, 2010, 9:43pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/68 "2010-01-14T21:43:48Z")
But if it were any of those other possibilities, the student could have solved the puzzle quicker. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [January 14, 2010, 11:45pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/69 "2010-01-14T23:45:40Z")
For the candy puzzle again, the answer is zero: 1. The merchant can simply smell all the candies he needs, no tasting necessary. 2. The merchant could, if he felt it necessary, determine the chemical composition of the candies. 3. The merchant could simply dump all the candies into one super box and label it “mixed.” 4. The question never states that the candies are identical in appearance, mint candies are often died greenish, anise is often red. Simply looking at the candies with this knowledge could give the answer. 5. If we want to go with the tasting route, he could simply feed them to an outside observer (i.e. his son, his wife, his friend, random passerby) and determine it by their feedback. 6. He could send it back to the company with a stern letter about his dissatisfaction with the company’s organizational skills and demand them to send him correctly labeled boxes. I also do parties, weddings, and physics questions about barometers. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [January 14, 2010, 11:51pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/70 "2010-01-14T23:51:45Z")
> [@Jragon](#): > > For the candy puzzle again, the answer is zero: > > 1. The merchant can simply smell all the candies he needs, no tasting necessary. > > 2. The merchant could, if he felt it necessary, determine the chemical composition of the candies. > > 3. The merchant could simply dump all the candies into one super box and label it “mixed.” > > 4. The question never states that the candies are identical in appearance, mint candies are often died greenish, anise is often red. Simply looking at the candies with this knowledge could give the answer. > > 5. If we want to go with the tasting route, he could simply feed them to an outside observer (i.e. his son, his wife, his friend, random passerby) and determine it by their feedback. > > 6. He could send it back to the company with a stern letter about his dissatisfaction with the company’s organizational skills and demand them to send him correctly labeled boxes. > > I also do parties, weddings, and physics questions about barometers. Hmmm… It states sample, which may invalidate 1 and 2. For the sufficiently pedantic if could also invalidate 4 and 5 as well. 3 and 6 are completely valid whichever way you read it. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [January 15, 2010, 12:34am UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/71 "2010-01-15T00:34:35Z")
The main problem with the first one is the idea that, if you have a set of twins, one of them won’t be older. Every twin I’ve ever met knows exactly which one of them was born first, and refers to that one as the older sibling. And this would be data they’d have to have learned from their parents. ---
**Author:** ![MysterMenace](https://avatars.discourse-cdn.com/v4/letter/m/71c47a/32.png) [@MysterMenace](https://boards.straightdope.com/u/MysterMenace)\ **Post date:** [January 18, 2010, 10:33pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/72 "2010-01-18T22:33:07Z")
… ---
**Author:** ![MysterMenace](https://avatars.discourse-cdn.com/v4/letter/m/71c47a/32.png) [@MysterMenace](https://boards.straightdope.com/u/MysterMenace)\ **Post date:** [January 18, 2010, 10:35pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/73 "2010-01-18T22:35:16Z")
> [@Jragon](#): > > For the candy puzzle again, the answer is zero: > > 1. The merchant can simply smell all the candies he needs, no tasting necessary. > > 2. The merchant could, if he felt it necessary, determine the chemical composition of the candies. > > 3. The merchant could simply dump all the candies into one super box and label it “mixed.” > > 4. The question never states that the candies are identical in appearance, mint candies are often died greenish, anise is often red. Simply looking at the candies with this knowledge could give the answer. > > 5. If we want to go with the tasting route, he could simply feed them to an outside observer (i.e. his son, his wife, his friend, random passerby) and determine it by their feedback. > > 6. He could send it back to the company with a stern letter about his dissatisfaction with the company’s organizational skills and demand them to send him correctly labeled boxes. > > I also do parties, weddings, and physics questions about barometers. 1, 2, 4,and 5 are types of sampling, so the puzzle conditions still apply and you still need to solve it. 3 and 6 don’t even attempt to respond to the question of labeling each of the boxes. If you are going for the trick answer at least have an answer. A better trick answer given elsewhere in The Straight Dope is zero samples. The merchant could just guess the correct labels, although there has to be at least one sampling done to verify that this guess is correct. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [January 18, 2010, 10:49pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/74 "2010-01-18T22:49:37Z")
> [@MysterMenace](#): > > 1, 2, 4,and 5 are types of sampling, so the puzzle conditions still apply and you still need to solve it. 3 and 6 don’t even attempt to respond to the question of labeling each of the boxes. > If you are going for the trick answer at least have an answer. A better trick answer given elsewhere in The Straight Dope is zero samples. The merchant could just guess the correct labels, although there has to be at least one sampling done to verify that this guess is correct. 1. I’d been up for 36 hours when I’d wrote that. To be perfectly honest I barely even remember doing so. 2. I addressed most of those in the post one after it. 3. I disagree about 4 and 5. For 5 the MERCHANT still isn’t sampling them, he’s requesting someone else to sample them, still perfectly within the bounds of the wording. Looking at them also wouldn’t fit most definitions of “sampling” as it pertains to candy that I’ve heard, however this is probably a difference of opinion. I’ll grant you the smell one though. 4. 3 & 6 both answer the question perfectly. If you want to get technical he’d also have to remove the labels on the boxes that no longer contain any candies. He could also dump them all on the floor and remove the labels and it’s within the wording which simply posits that he has to label the boxes correctly, with no modifier stating that the box has to contain relatively the same thing. Hell, within the bounds of the question he could dump them on the floor, put rocks in one and label it “obsidian” and it still answers the question as worded with an answer of zero. As for 6, again, it still results in correctly labeled boxes once he gets the corrected ones shipped back. Since the company would most likely sample the candies it may fall victim to the same quibble as 5 in a more abstract sense, but it still completely answers the riddle in wording, even if not quite in spirit. ---
**Author:** ![MysterMenace](https://avatars.discourse-cdn.com/v4/letter/m/71c47a/32.png) [@MysterMenace](https://boards.straightdope.com/u/MysterMenace)\ **Post date:** [January 19, 2010, 6:01pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/75 "2010-01-19T18:01:15Z")
> [@Jragon](#): > > 1. I’d been up for 36 hours when I’d wrote that. To be perfectly honest I barely even remember doing so. > > 2. I addressed most of those in the post one after it. > > 3. I disagree about 4 and 5. For 5 the MERCHANT still isn’t sampling them, he’s requesting someone else to sample them, still perfectly within the bounds of the wording. Looking at them also wouldn’t fit most definitions of “sampling” as it pertains to candy that I’ve heard, however this is probably a difference of opinion. I’ll grant you the smell one though. > > 4. 3 & 6 both answer the question perfectly. If you want to get technical he’d also have to remove the labels on the boxes that no longer contain any candies. He could also dump them all on the floor and remove the labels and it’s within the wording which simply posits that he has to label the boxes correctly, with no modifier stating that the box has to contain relatively the same thing. Hell, within the bounds of the question he could dump them on the floor, put rocks in one and label it “obsidian” and it still answers the question as worded with an answer of zero. As for 6, again, it still results in correctly labeled boxes once he gets the corrected ones shipped back. Since the company would most likely sample the candies it may fall victim to the same quibble as 5 in a more abstract sense, but it still completely answers the riddle in wording, even if not quite in spirit. If you modify conditions, by adding, deleting, or changing them, then you essentially are working a different problem. If the merchant or any of his cohorts identify the type of candy then the merchant, even if by proxy, has sampled. If you dump a box, it is no longer a box containing candy. If a label is removed, then it is no longer a labeled box, as all boxes in the problem are described. The best way to achieve a zero samplings solution is to change the dictionary entries for “mint”, “anise”, and “mixed”. And you might find that this method will go a long way to solving just about any puzzle anyone can conjure up. ---
**Author:** ![Keweenaw](https://avatars.discourse-cdn.com/v4/letter/k/da6949/32.png) [@Keweenaw](https://boards.straightdope.com/u/Keweenaw)\ **Post date:** [January 19, 2010, 6:34pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/76 "2010-01-19T18:34:09Z")
The piano teacher puzzle is a version of one I got in an email last June. Only it was somewhat simplified. > [@](#): > > Person x and y have the following conversation: > x: I forgot how old your three kids are. > y: The product of their ages is 36. > x: I still don’t know their ages. > y: The sum of their ages is the same as your house number. > x: I still don’t know their ages. > y: The oldest one has red hair. > x: Now I know their ages! > How old are they? This version removed the some of the ambiguity around knowning where someone else lives, and at what age someone can play the piano. I kinda perfer it and offer it as an alternative to those who wish to try it on others. ---
**Author:** ![grimpixie](https://avatars.discourse-cdn.com/v4/letter/g/ecb155/32.png) [@grimpixie](https://boards.straightdope.com/u/grimpixie)\ **Post date:** [January 19, 2010, 6:43pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/77 "2010-01-19T18:43:05Z")
> [@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. The actual real-world solution is to ask “Did you know that behind the door to Freedom, they are giving away FREE BEER!!!” - the truth teller will say No and run through the door to Freedom while the liar will say Yes and go through the same door… ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [January 19, 2010, 7:59pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/78 "2010-01-19T19:59:04Z")
> [@MysterMenace](#): > > If you modify conditions, by adding, deleting, or changing them, then you essentially are working a different problem. If the merchant or any of his cohorts identify the type of candy then the merchant, even if by proxy, has sampled. If you dump a box, it is no longer a box containing candy. If a label is removed, then it is no longer a labeled box, as all boxes in the problem are described. > The best way to achieve a zero samplings solution is to change the dictionary entries for “mint”, “anise”, and “mixed”. And you might find that this method will go a long way to solving just about any puzzle anyone can conjure up. That was sort of… the point? I would’ve put the dictionary one in there too if I had thought of it. ---
**Author:** ![panamajack](https://avatars.discourse-cdn.com/v4/letter/p/47e85d/32.png) [@panamajack](https://boards.straightdope.com/u/panamajack)\ **Post date:** [January 19, 2010, 8:18pm UTC](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465/79 "2010-01-19T20:18:11Z")
Without giving away too much of the movie’s plot (I saw it on TV too, I think IFC), they’re trapped in the classic room with shrinking walls (see movie poster), have only a minute to send back an answer to each puzzle, and generally expect that they’ll all be smashed anyway because the guy is crazy. So simply trying the ‘obvious’ answers like the gestating baby is something they may as well do. Nitpicking doesn’t help them. I also wonder if the Spanish phrasing refers to the ‘older one’ or not. Most of the time each person who gives an answer explains it, but I don’t recall what they all were. [Previous page](https://boards.straightdope.com/t/whats-the-answer-to-these-logic-puzzles/511465.md?page=3)