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In front of you are 3 boxes. One box contains only apples, another box contains only oranges, and the last contains both apples and oranges. The first box has the label "apples," the second "oranges," and the third "apples and oranges." Unfortunately, all of the labels are wrong. Your job is to fix the labels. You are not allowed to peek inside any of the boxes. But you can ask for a sample from any box. You point to a box, and you get a fruit from that box. What is the minimum number of samples you need to label all of the boxes correctly? Thanks for help.

Guest Jun 27, 2017

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 #2
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This is an interesting question!!

 

They told us all of the labels are wrong.

 

That means that the box labeled  " apples and oranges "  does not have both apples and oranges. Instead, it must be all apples or all oranges.

 

So ask for a sample from the box labeled  " apples and oranges ."  If you get an orange, then the box must be all oranges. (If you get an apple, the box is all apples.)

 

So...let's swap the label on the box that was originally labeled  " apples and oranges "  with its correct label that you know now.

 

That leaves one label untouched. We know that it is incorrect, since all the labels were wrong to begin with. So, swap this label with the  " apples and oranges "  label.

 

Now they are all correct! And we only needed one sample. smiley

hectictar  Jun 27, 2017
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5+0 Answers

 #1
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Only one sample is sufficient!. Take a sample from the box labeled "apples and oranges". Whatever the sample is, that is right label for that box, since they are all labeled wrong. For example, if the sample was an apple, then that box contains only apples. The other two boxes are labeled "apples" and " oranges". Now we go to the box labeled "oranges". Since we have labeled the first box correctly as "apples", then that box must be "apples and oranges". And the remaining box labeled "apples" must be "oranges".

Guest Jun 27, 2017
 #2
avatar+5227 
+2
Best Answer

This is an interesting question!!

 

They told us all of the labels are wrong.

 

That means that the box labeled  " apples and oranges "  does not have both apples and oranges. Instead, it must be all apples or all oranges.

 

So ask for a sample from the box labeled  " apples and oranges ."  If you get an orange, then the box must be all oranges. (If you get an apple, the box is all apples.)

 

So...let's swap the label on the box that was originally labeled  " apples and oranges "  with its correct label that you know now.

 

That leaves one label untouched. We know that it is incorrect, since all the labels were wrong to begin with. So, swap this label with the  " apples and oranges "  label.

 

Now they are all correct! And we only needed one sample. smiley

hectictar  Jun 27, 2017
 #3
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Sorry, hectictar! I didn't know you were answering it at the same I was! Otherwise, I wouldn't have touched it.

Guest Jun 27, 2017
 #4
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There's no need to be sorry Guest!! It can be helpful to have more than one answer, in case the questioner doesn't understand one of them!

 

You seem really nice smiley ...Is there a reason why you haven't gotten an account on here? But...I can understand just wanting to be anonymous too.

hectictar  Jun 27, 2017
edited by hectictar  Jun 27, 2017
 #5
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I only show up occasionally. Maybe once or twice a week for about an hour or so. You are very bright young lady, and I know if you are going to answer a question, there isn't much that I can add to it.

Guest Jun 27, 2017

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