Solve Logic Box Question: Apples, Oranges, Apples & Oranges

[Miike012]

Homework Statement

If there were three boxes, one box is made of apples, the other is made of organes, and the last is made of organes and apples.
You are able to open only one box without looking in, and you are able to look at only one fruit inside the box. By looking at the fruit, how can you ammediatly label all of the boxes correctly?

The Attempt at a Solution

This is my guess...

If I picked an apple out of box one that means
box 1 could be either apples or apples and oranges.
box 2 could be either oranges or apples and oranges
box 3 could be either oranges or apples and oranges.

My odds of apples and oranges seem to be the best choise for box number one.
for box number two I would have to pick oranges
for box number three I would pick apples.

Is my logic flawed somewhere?
What are your guys solutions?

 

[grief]

It seems from the problem statement that you are required to be correct, not just have a good guess. That seems to be impossible, though I do remember a variant of this problem which was possible:

"one box has two black marbles, one with two white marbles, and one with one of each. The boxes were labeled according to their contents but the labels are switched so that all the labels are incorrect. By drawing one marble, figure out the correct contents of each box."

 

[Miike012]

Yeah, I thought about that to... that the problem requires that I am correct and not just a guess... However I do not know how to do it...

 

[eumyang]

Grief is on the right track. I've done a Google search on the original problem and as far as I can tell, there is piece of information missing from the problem:

If there were three boxes, one box is made of apples, the other is made of oranges, and the last is made of oranges and apples.
You are able to open only one box without looking in, and you are able to look at only one fruit inside the box. By looking at the fruit, how can you ammediatly label all of the boxes correctly?

(First off, it's oranges, not organes.)

You also know that the three boxes of fruit were labeled incorrectly. You neglected to say this in your original post. I'm guessing that without this piece of information, it is impossible to solve the problem correctly. Where did you get this problem? Maybe you copied it wrong?

 

[Miike012]

The boxes being labled incorrectly shouldn't matter. The fact is... that you don't know what is in the box, and you are supposed to figure it out... that's what I stated...
The original says... “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?”

 

[Borek]

IMHO the answer is "you can't".

 

[CompuChip]

The fact that they are all labeled incorrectly does give you extra information, and it is precisely the information that is missing*.
For example, suppose you open a box and pick an apple. Without the extra information on the label, it may still be either the box with the apples or the box with the mixed fruit, and you have a 50% probability of guessing correctly.
However, if you know that the box does definitely not contain what it says on the label you know for sure what is in the box if the label reads "apples" (namely, the mixed fruit) or "mixed" (you have picked the box with the apples), and if it reads "oranges" you can guess with probability 50%. This gives you a probability far greater than 50% to label the box correctly.

The question now is, can you think of a scheme which will increase it to 100%?

* I haven't solved it yet, or searched for the solution, but if it is solvable, this is the info you will need. I suspect that the key is to open the box which is labelled as containing both fruits.

 

[eumyang]

The boxes being labled incorrectly shouldn't matter.

As CompuChip stated, it does matter, and I'm a little annoyed that you didn't state it in the original post. Speaking only for myself, I would be less willing to help someone here if the problem is not posted completely or correctly, in its original form.

Unless, your intent was to ask a variation of this problem, where if was possible to solve it if the boxes were not labeled. If that was the case, then this was not made clear to me.

 

[CompuChip]

Well, let this just be a lesson: it can be good to abstract a question to get quicker replies, but be careful never to leave out (what you think are) unimportant details because they may be the key to the solution :-)

 

[Miike012]

Here is the answer...
Open the box that is labeled "Apples and Oranges".

You know that since none of the labels are correct, the box must either contain only apples, or only oranges.

Suppose, w.l.o.g., that you remove an apple from that box. Therefore, that box is the "Apples Only" box.

One of the two remaining boxes must be the "Oranges Only" box. However, one of them is labeled "Apples Only", and the other is labeled "Oranges Only". Therefore, the one labeled "Apples Only" is the box that contains only oranges, and the box labeled "Oranges Only" is the box that has both kinds of fruit.