There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly? 47 AnswersAll the three boxes are names incorrectly. SO the bax lebeled Apples+Oranges contains only Oranges or Only Apples. Pick one fruit from it. If it is Orange then lebel the box as Orange. So the box lebeled Oranges contains Apples and the remaining contains both. The key bit is "All the three boxes are names incorrectly" so the label on the box which fruit comes from will need to be changes to one of the other 2 labels. It can only be 1 of them (and it will be obvious when you have the fruit) then the remaining box (that hasnt featured yet)...Just swap that label with fruit box that was originally on the box which you took the fruit out of Thats hard for anybody to understand somebody elses explanation... eaiest way is to just do an example Show More Responses Swaz answer is almost correct however it does not work in all scenarios. lets assume: box 1 is labelled Oranges (O) box 2 is labelled Apples (A) box 3 is labelled Apples and Oranges (A+O) and that ALL THREE BOXES ARE LABELLED INCORRECTLY" Pick a fruit from box 1, 1) if you pick an Orange: - box 1's real label can only be O or A+O - box 1's current label is O - since ALL LABELS ARE INCORRECT then box 1's real label can not be O - box 1's new label should then be A+O by elimination - since ALL LABELS ARE INCORRECT - box 2's label is changed to O - box 3's label is changed to A - SOLVED 2) if you pick an Apple: - box 1's real label can only be A or A+O - box 1's current label is O - since ALL LABELS ARE INCORRECT then box 1's real label can not be O - this still leaves us with the choice between label A and label A+O - which would both be correct - FAILURE Solution: The trick is to actually pick a fruit from the A+O labeled box Pick a fruit from box 3: 1) if you pick an Orange: - box 3's real label can only be O or A - box 3's current label is A+O - since ALL LABELS ARE INCORRECT then box 3's real label can not be A+O - box 3's new label should then be O by elimination - since ALL LABELS ARE INCORRECT - box 1's label is changed to A - box 2's label is changed to A+O - SOLVED 2) if you pick an Apple: - box 3's real label can only be O or A - box 3's current label is A+O - since ALL LABELS ARE INCORRECT then box 3's real label can not be A+O - box 3's new label should then be A by elimination (not O) - since ALL LABELS ARE INCORRECT - box 1's label is changed to A+O - box 2's label is changed to O - SOLVED it only says you can't look, doesn't mean you can't feel around or smell the fruit you picked, easy deduction after you figure the first box out Sagmi is right, but did not give the full reasoning. "the bax lebeled Apples+Oranges contains only Oranges or Only Apples. Pick one fruit from it. If it is Orange then lebel the box as Orange." so far so good Now, the box labelled Apples cannot be the box containing only Oranges, you've just found that box, so it must contain Apples and Oranges. And in that case the other box, labelled Oranges, must contain only Apples. It's easier to draw it out. There are only 2 possible combinations when all labels are tagged incorrectly. All you need to do is pick one fruit from the one marked "Apples + Oranges". If it's Apple, then change "Apple + Orange" to "Apple" The "Apple" one change to "Orange" The "Orange one change to "Apple + Orange" If it's Orange, then change "Apple + Orange" to "Orange" The "Apple" one change to "Apple + Orange" The "Orange" one change to ""Apple" Since all 3 boxes are labled incorectly Start with the box Labled A&O. If Its apples than the box labled apples then the apple one is oranges and the oranges is O&A. Label each box "Apples and/or Oranges" and the all will be correct. This is very simple to resolve. I was asked the same question at FileMaker. Each box is incorrectly labeled. So you go to the box that is labeled "Oranges and Apples" and take one out. It doesn't matter what comes out because all that you know is that it is not AO. If you remove an Apple then move the Apple label to it. Since the Apples are already identified it is easy to resolve the rest. All you know for certain is that the other two boxes remaining are mislabeled. So the AO label goes on the box with the remaining label and that label goes on the Apple box as you have already assigned that. The end result is you only need to remove one piece of fruit to figure out the proper locations of all. Go down the road to HP. Maybe they are hiring. Some of these pseudo-problem solving questions like this are bunk. I was once asked why sewer covers are round and not square. I gave the correct answer without even hesitation and the interviewer seemed put off that I knew the answer. I didn't get the job but, in hindsight, no great loss. I prefer the questions (like the basketballs one from google) where you won't be able to give an accurate numerical answer but by explaining HOW you would go about solving the problem is all you need to do and MAYBE shows your aptitude for problem solving. Smell the box you opened. Step 1: Order the boxes by weight. Either apples weigh more than oranges, or oranges weigh more than apples. The mixed box will always be in the middle. Step 2: Open the first box, take out the fruit and look at it. Step 3: If the fruit is an apple, deduce that the middle is apple and oranges and that the third box is oranges. If the fruit is an orange, then deduce that the last is the box with the apples. Show More Responses Donna is the only one with any common sense. The problem with corporate America, is that it's run by a bunch of Bozos who over complicate things and have a narrow to zero vision on how to solve even the simplest problems. I can imagine that most of you would get a committee, have long meetings where you talk about 'think out of the box', and 'at the end of the day' nonsense. This is an interesting logic question, but I would not want to buy fruit from a company who knew they had a problem and then sampled one out of three boxes to resolve the issue. There are other correct answers posted. I'll just make a comment: "The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels." Nothing in the above statement says the labels are limited to oranges/pears, only that they do not identify the contents. They could say 'nuts', 'bolts', etc. Technically, all answers should be prefaced with: assume that the labels say 'oranges', 'pears', and 'orange/pears'. Ok, the problem does not make sense and is unsolvable if the labels say 'x', 'y', 'z', but someone with (likely with a math proof back ground) may appreciate attention to detail. Q: Why do posters denigrate the interview questions? The questions, however stupid they may be, are a opportunity to show you can build an answer. Even if you pursue an invalid train of thought in the interview, it's a thought. It's what they want to see and what will help you get a job offer. Note: I also would not assume that the questions asked are a reflection on the company, department, or team as a whole. It may just be the interviewer that has chosen poorly. So to say "I don't want to work for company X because they asked me a stupid interview question" is pretty closed minded. To even think I don't want to work with that interviewer just based on questions asked seems extreme. rightly pointed out by Sagmi ... this question was put forward to me at Huawei Technologies and that was the answer I gave So the question was asked at an interview for Apple: Label ALL the boxes apple and charge a ridiculous price for them! Just label all of them "Fruit." Put another way, it is not possible to tell since we don't know how the boxes are mis-labled. What if the Apple box was labeled Oranges and both the other boxes were labeled Apples and no box was labled Apples and Oranges? You might have assumed there are three different labels when their might have only been two different labels. Always pict a piece of fruit from the box labelled Apple&Orange. As we know that this label is wrong, there are two possibilities: If it is apple, then wo know that this box should be labelled Apple, so we switch Apple label with the label Apple&Orange. Then Apple label is correct. We also know that the Orange label is incorrect, so we then switch Orange label and Apple&Orange label. if it is orange, then we know that this box should be labelled Orange, so we switch Orange label with label Apple&Orange. Then Orange label is correct. The same as above, we know that the Apple label is incorrect, so we switch Apple label and Apple&Orange label. If all boxes are labeled incorrectly and u pick a orange out of a box that's labeled apple/oranges change the name to oranges then change the box labeled oranges to apples and the the box labeled apples to apple and oranges... If you pick a apple out of a box labeled apples and oranges change the name to apples and then change the box labeled apples to oranges and the last to apples and oranges... If u pick a apple out of a box labeled oranges change it to apples and oranges then the box labeled oranges to apples and the box labeled apples to oranges...if you pic a orange out of a box labeled apples change it to apples and oranges and the box labeled oranges to apples and the last to apples and oranges... See the pattern? I think there is a big box and it contain two small boxes and all the labels are incorrect so big one contain two boxes that makes it carrys both orange and apples and in that thwo boxes having orange and apple respectively so if we open any box we can label it correctly Show More Responses if it known already that boxes labeled incorrectly, I would give it back to those who did label them and ask to fix this confusion. it is impossible to tell by opening only one box, so you have to open one more box. As mentioned already, if you start with the A+O bucket, you can solve the puzzle by pulling only one fruit, Bucket: A+O Found: A Bucket A+O > A | A+O, but since A+O label is incorrect, then it must be A Bucket O > since A is taken, the new label must be O | A+O, but since O is incorrect, it must be A+O Bucket A > since A and A+O are taken, it must be O Bucket: A+O Found: O Bucket A+O > O | A+O, but since A+O label is incorrect, then it must be O Bucket A > since O is taken, the new label must be A | A+O, but since A is incorrect it must be A+O Bucket O > since O and A+O are taken, it must be A If you are lucky, you might solve it with just one fruit even if you start with other buckets, Bucket: A Found: A Bucket: A > A | A+O, but since the A label is incorrect, it must be A+O Bucket: O > A | O, but since the O label is incorrect, it must be A Bucket: A+O > since A+O and A are taken, it must be O Bucket: O Found: O Bucket: O > O | A+O, but since the O label is incorrect, it must be A+O Bucket: A > A | O, but since the A label is incorrect, it must be O Bucket: A+O > since A+O and O are taken, it must be A If you start with the A bucket and pull an O or if you start with the O bucket and pull and A, then you are SOL and you need to pull out more fruits to figure it out. 1. Open one box and check its contents. 2. Remove the current label and apply the correct one (by removing it from one of the other boxes) 3. Since all boxes have been labeled incorrectly, switch labels between the other 2 boxes. And Voila you have all the boxes labelled correctly :) In requirement already specify that all three box labels are not correct. A+O A O Step1: First Pick an item A+O Box. If you get an Apple then it is a Apple Box. swap the label . A A+O O AS we already know in the box that label with Orange, does not contain Orange because of wrong label. So It must contain A+O. Just Swap the label A O A+O OK, all 3 boxes are incorrectly labeled. Open the one that says apples and oranges. Whatever is in there is what it is (since it cannot be apples AND oranges). Now, if there was an orange in there, apples must be in the orange box (since they cannot be in the apples box), and apples and oranges in the apples box (due to process of elimination). Get it? I guess questions like these will appear easy if you put them on paper, it is the possible combinations that become relevant, one way to approach is.. One of the key factor is all boxes are labelled incorrectly, this gives rise to only (2) combinations right To label for 1st box incorrectly you will have (2) options, once you label it then you have only choice to label the other two boxes incorrectly so 2 x 1 = 2 combinations possible i.e. Incorrect lablling options { Boxes_with_Oranges, Boxes_with_Apples, Boxes_with_Apples&Oranges } = { A, AO, O} or {AO, O, A} 2. To know for sure the contents of the boxes, you need to pick the box with either Apples or Oranges and avoid box with Apples and Oranges. So from the (2) combinations you could pick a fruit from Box_labeled AO (this will contain either Oranges or Apples) So, if you get a Orange, it means that combination is{AO, O, A} , so that means Box_with_Label_O has Apples, Box_with_Label_A has Apples and Oranges Box_with_label_AO has Oranges or else if you get a Apple that combination is {A, AO, O}. Box_with_Label_AO has Apples, Box_with_Label_O has Apples and Oranges Box_with_label_A has Oranges Then you can correctly label all the 3 boxes. First answer in this post is correct, as its said all boxes doesnt reflect correct items in it, If an apple is picked from a box , then it can be from either A/O box or A box, if the box is names A/O the, the label of the box has to be changed to A, then other two box labels to be accordingly. It is interesting that in 6 years people keep overthinking this. The answer is in the question and the criteria are that the boxes are immediately labeled and they are labeled correctly. ANSWER: FRUIT FYI you don't even need to open one box. Show More Responses Your choice going to be (( 2 apple 1 orange)) or (( 2orange 1apple )) . It can be recognize only one box (x) . U have to chose again until u get another formula then u will named easly . Step 1: Open a box labeled ‘Apples and Oranges’. We know that this box does not contain ‘Mixture’ for sure. If this fruit is an apple, then label this box as ‘Apple’. Step 2: (Very important) If we look at the box labeled as ‘Oranges’, we know that since the label is incorrect, this box either has only apples in it or has Mixture. Since we already know which box contains only apples, we know that the box labeled as ‘Oranges’ contains ‘Mixture’. So label it as ‘Mixture’. Step 3: (Very easy) The 3rd box will be labeled as ‘Oranges’. When you put your hands on the box to pick the fruits by touching every fruits you can feel whether all are apple or oranges or both and just pick one to see.So it is not necessary to pick one fruit and see whether it is orange or apple also it is not said in question that you can touch and feel all the fruits inside the boxes without taking it out .and then you can fix the label correctly on the boxes. I will took a pen and stab the apple. and then ? apple-pen. Smelling the box and writing the correct label on each. :) Just label the boxes correctly. I got this question in a video interview. He verbally read out the question, but either left out the mislabeled part or I not heard it correctly. Without that piece of information, it was impossible to answer the question. Didn't get the job. Open box which is labeled apple+oranges. This box have the wrong label so it cannot have both. Now, -If you pick apple then it is having apples only -if you pick orange it contains orange change the label accordingly if the assumption is all 3 boxes are labeled wrongly; there is solution for sure; exhaust all possibles of combination A33 = 6 eliminate all wrongly labeled 4 possibilities; there are only 2 possibility left; just open the first box, you can tell which case is true among the left 2 cases. Show More Responses Think about you are taking the box1 A/O , you come to know that you are having Apple and orange combined box is box1,paste the label of A/O in the box1 and problem solved however the other two boxes have wrong label in it .... So the apple box will have orange label and orange box will have the apple label Take a fruit out of any box (let’s call this Box #1). Since, as the question states: “The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels.”, you can remove the label from that box and put it aside. The label for the box the you took the fruit from has to come from one of the other two boxes that you did not take the fruit out of, but since you now know what is in Box #1, you can take the correct label from one of those two boxes (call this Box #2) and place it on the box that you picked the fruit from (which we have called Box #1). So now Box #1 is labeled correctly. Box #2 has no label (you took it and placed it on Box #1). The other box (call it Box #3), does not have the contents that the label says, so you can put it on Box #2 with full confidence that this is the correct label for that box. So now Box #2 is labeled correctly. The label that you put aside after taking it off Box #1 then can only go onto Box #3. So now Box #3 is labeled correctly. Only one box has mixed content and all boxes are incorrectly labeled (such that the box marked apples does not have only apples, the box marked oranges does not have only oranges, and the mixed box has either apples exclusively or oranges exclusively, but not mixed contents). Removing a fruit from either box labeled Apples or oranges can yield ambiguous results depending on if you get the mixed box or not (ie. if you pull an orange from the box labeled Apples, then you don't know if the contents are mixed or if they are exclusively oranges). Therefor, the fruit selection needs to come from the box labeled Mixed (Apples & Oranges). Which ever you select (Apple or Orange) will tell you that the contents of 'that' box is exclusively Apples or exclusively Oranges. Case #1, Mixed box has all Apples: In this case, there are 2 remaining boxes, the one marked "Apples" and the one marked "Oranges", since we know that the box labeled "Oranges" cannot contain oranges exclusively, and we now know that it doesn't contain apples exclusively either (those are in the Mixed box), the only remaining option for the box labeled "Oranges" is to contain the "Mixed (Apples & Oranges)", leaving the box containing all Oranges, exclusively, in the box labeled "Apples" Case #2, Mixed box has all Oranges: In this case, there are (still) 2 remaining boxes, the one marked "Apples" and the one marked "Oranges", since we know that the box labeled "Apples" cannot contain apples exclusively, and we now know that it doesn't contain oranges exclusively either (those are in the Mixed box), the only remaining option for the box labeled "Apples" is to contain the "Mixed (Apples & Oranges)", leaving the box containing all Apples, exclusively, in the box labeled "Oranges" as mentioned all boxes are labelled incorrectly. step 1 :Go for box mixed fruits....you will either get apple /orange there n never mixed becoz its labelled incorrectly.suppose you get apple in that box .....change the lable of mixed fruit to apple step 2: As all boxes are labelled wrongly .....interchange the rest boxes lable .... that is orange labled box to |