You have three boxes of fruit. One contains just apples, one contains just oranges, and one contains a mixture of both. Each box is labeled — one says “apples,” one says “oranges,” and one says “apples and oranges.” However, it is known that none of the boxes are labeled correctly.
How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from each of the boxes?
October 18th, 2009 | Category: 
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Reach in to the box labled Apples and Oranges. Whatever you pull out, that’s what it should be labled as (an apple is apples, an orange is oranges). Let’s say it’s apples:
Now reach into the apples box. If you pull out an apple, than that box is apples and oranges and you’re done because the third box will then be oranges, if you pull out an orange then go to the third box marked oranges.
Reach into the third box and if it’s orange than that box should be labled apples and oranges and the 2nd box is oranges, if it’s an apple then that box is apples and the 2nd box is apples and oranges. Remember they’re all mismarked so it’s not as confusing as I am making it.
: )
Frankie is the winner!!
Take a piece of fruit from the box marked “apples and oranges.” Suppose the fruit you take is an apple. Then that box must be the box containing just apples. Therefore, the box marked “oranges” can’t be the box containing just apples, and it can’t be the box containing just oranges either — so it must be the box containing apples and oranges. The remaining box is therefore the box containing just oranges.
If the fruit you take out is an orange, the solution is derived in a similar fashion: the box marked “apples and oranges” is the box containing just oranges; the box marked “apples” is the box containing both apples and oranges; and the box marked “oranges” is the one containing just apples.
If Frankie is correct, you have written the riddle incorrectly.
“How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?” means a single piece of fruit can be examine.
I think you meant to write;
“How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from
just oneeach of the boxes?”Christopher, you are correct and the riddle has been corrected. Thank you for your attention to detail.
The riddle is stil correct even if you only can take one fruit from one box.
Because every box is labeled incorrectly you can ask to see one fruit from the box labeled “apples and oranges” whatever fruit you take out will be what’s in that box.
For example: They take out an apple which will mean that the box labeled with “apples and oranges” is actually “apples” which means that the box labeled with “oranges” will be “apples and oranges” and the box labeled “apples” will be “oranges” and vice versa.
But if they take out an orange it’ll be:
“apples and oranges” –> “oranges”
“oranges” —> “apples”
“Apples” —> “apples and oranges”
The solution is simpler than you can imagine but the key, the only right move which can guide you to the answer, is picking a fruit from the box labeled “Oranges & Apples”.
1. If the fruit you’ve picked is apple then the content of the box should be apples (clearly it can’t contain oranges & apples because this is what the label says).
2.if the fruit ypu picked is an orange then the box should contain oranges (clearly it can’t contain oranges & apples because this is what the label says).
Now that you have identified the contents of this first box remain 2 other boxes: The box labeled “oranges” and the box labeled “apples”. Given that the first box contained oranges, then naturally One of the other 2 boxes must contain apples and the other one apples and oranges. Obviously the box labeled “apple” can’t contain apples. So it must be containing apples and oranges. And clearly the last box (labeled “oranges”) inevitably contains apples!
Obviously if the first fruit you’ve picked have been an apple, the process is like that but opposite.
I have to admit it wasn’t easy and I thought more than 20 minutes to find out the answer. But of course as any other good riddle, it is worth the delicious sense of satisfaction you get after resolving the riddle! Thanks.
It is possible to solve this without looking in the Apples and Oranges box. However it will not always work.
Step 1: Take a piece of fruit from the box marked Oranges.
If it is an Orange, then we know this box must contain Apples and Oranges because the original label is wrong. Because there are only two boxes left and we know that the box labelled Apples is also wrong, we know that it must contain oranges. The box originally marked Apples and Oranges will contain Apples. Problem Solved.
If it is an Apple, then we still have more work to do.
Step 2: Take a piece of fruit from the box marked Apples.
If it is an Apple, then we know that this box must contain Apples and Oranges because it’s original label (apples) is wrong. From this new discovery we can now say that the box from step 1 contains Apples. This leaves one box left (the one originally names Apples and Oranges) which must contain oranges. Problem Solved.
If it is an Orange, we have failed to solve our problem without looking in the box labelled Apples and Oranges and must look inside to solve the problem.
Ultimately though, the best solution which only involves looking inside one box is stated above, by looking inside the apples and oranges box first. Just thought I would share a different method.
The answer is given away because you already know that all the boxes are labeled incorrectly. Open any of the boxes, the content of which will tell you what’s in the rest…
I say you can’t. Clearly if none of the boxes are labeled correctly. So just by taking one piece of fruit from one of the boxes will never let you be able to label the boxes correctly.
What you have to realize is that None of the boxes are labeled correctly….
Take out a fruit from the apples and oranges box.
What ever fruit you get e.g apple then that boxes is that fruit only I. E apples only.
Thus as all labels are wrong then by default the box labeled you selected fruit only I. E apples only must contain the mixed fruit.
And thus the last box is the other fruit only box
if all boxes are labeled incorrectly, go to the one which says mixture and it will give up which single fruit it is, label it what it is. (say apples) Go to the one which says oranges and see if it is an orange. If it is, then its the mixture. Label it that. If it is an apple go to the one which says apple. If it is an apple, label it mixture and label the second one Oranges. If its an orange then the second one was the mixture and last one the oranges.
as the labels are interchanged.so we will go to the box labelled “both apples and oranges” and pick out the fruit.suppose we got apple so the box is of apple as it is wrongly labelled.then we have the box named “apple only” so that will be the box containing oranges and the box having labbeled “oranges only” has both the types of fruits
cool.
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