Labeling Boxes: Apples, Oranges, or Both?

[bjr_jyd15]

Three boxes are labeled "Apples", "Oranges", and "Apples and Oranges". Each label is incorrect. You may only select one fruit from one box. (No feeling around or peeking permitted.) How can you label each one correctly?

I had to stare at this problem for quite a while. I will only state this: READ THE PROBLEM CAREFULLY.

Good luck.

 

[chroot]

You may only select a single fruit from one box?

- Warren

 

[bjr_jyd15]

You may only select a single fruit from one box?

Yes, Warren. You may select only one single fruit from one box.

 

[chroot]

There are six labelling possibilities, four of which are not allowed if all three labels are initially incorrect. The two remaining possibilites are:

    Actual    |
   Contents   |   Labelling 1       Labelling 2  
 -------------|---------------------------------
      A       |       AO                 O      
      O       |       A                  AO    
      AO      |       O                  A

Notice that since the labels must be wrong, the box labelled AO must contain only apples or only oranges, but not both.

Go draw from the box labelled AO. If you draw an apple, you fix labelling scheme 1, and you know the contents of the other two boxes. If you draw an orange, you fix labelling scheme 2, and know the contents of the other two boxes.

- Warren

 

[Gokul43201]

Chroot, shouldn't you be working or something ?

 

[BobG]

Three boxes are labeled "Apples", "Oranges", and "Apples and Oranges". Each label is incorrect. You may only select one fruit from one box. (No feeling around or peeking permitted.) How can you label each one correctly?

I had to stare at this problem for quite a while. I will only state this: READ THE PROBLEM CAREFULLY.

Good luck.

Answer in white:

Pull one fruit from the Apples and Oranges box.

1) If an apple, the correct label must be Apples. That leaves two possible label combinations for the other two boxes. One of combinations would put Oranges on the original Oranges box, which cannot be. The Oranges box must be Apples and Oranges. That leaves the Oranges label for the original Apple box.

2) If an orange, the correct label must be Oranges. Of the two remaining labels, the original Apple box can't be Apples, so it is Apples and Oranges, leaving Apples for the original Orange box.

 

[bjr_jyd15]

correct

Nice job to BobG and Warren. I'll post some more good ones in the future.