Solve Fruit Puzzle: Apples & Oranges in 3 Boxes

  • Context: High School 
  • Thread starter Thread starter Jimmy Snyder
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Discussion Overview

The discussion revolves around a puzzle involving three boxes labeled with different types of fruit: apples, oranges, and a mix of both. The boxes are stated to be mislabeled, and participants explore how to determine the correct contents of each box based on the information provided.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants emphasize that the boxes are mislabeled, suggesting that each box cannot contain what its label indicates.
  • There is a question about whether the labels are completely random or if they can contain the fruit indicated on the label, leading to confusion about the assumptions of the puzzle.
  • One participant humorously suggests using smell to identify the fruit, indicating a lack of confidence in their understanding of the problem.
  • A participant notes that recognizing the importance of the boxes being deliberately mislabeled is crucial to solving the puzzle.
  • Another participant confirms that their understanding of the term "mislabeled" aligns with the idea that none of the boxes contain what the label states.

Areas of Agreement / Disagreement

Participants generally agree that the boxes are mislabeled, but there is some uncertainty regarding the implications of this mislabeling and how it affects the contents of the boxes. The discussion remains somewhat unresolved as participants explore different interpretations of the problem.

Contextual Notes

There are limitations in the assumptions made about the labeling and contents of the boxes, and some participants express confusion about the implications of the mislabeling.

Jimmy Snyder
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There are three boxes. One contains apples only, one contains oranges only, and one contains apples and oranges. They are mislabeled. You designate one of the boxes. I will remove a single piece of fruit from it and hand it to you. From that information you will correctly label all three boxes.
 
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Jimmy Snyder said:
They are mislabeled.

They are mislabeled, or they are labeled at random? What I mean is - if the box is labeled "apples" can I be sure it contains either oranges or mix, or can it contain apples as well?
 
Borek said:
They are mislabeled, or they are labeled at random? What I mean is - if the box is labeled "apples" can I be sure it contains either oranges or mix, or can it contain apples as well?
mislabeled
 
give me something from the box labeled apples and oranges, please
 
Wait, it's a prune. Let me get another one.
 
Smell?

If you've got an apple that smells of orange, or vice versa, that should tell you what is in the box with it.

(I have no idea what I'm talking about, only thing I could come up with).

I can see the logic you have to apply, just got to get my head around it.
 
A more serious attempt at the answer. It all comes down to the boxes being deliberately mislabelled and I've taken this to mean they cannot contain what is written.

I choose the Apples/Oranges box.

If you pull an apple, the oranges box must contain the apples/oranges and the apples box must contain the oranges.

If you pull an orange, the oranges box must conatin the apples and the apples box must contain the apples/oranges.

EDIT: corrected my mistake
 
It's a very simple problem. I had trouble with it because it took me a while to see the importance of the
mislabeling
Once that hurdle is passed the rest is easy. Borek focused attention on that detail.
 
So was my assumption regarding it correct?
 
  • #10
jarednjames said:
So was my assumption regarding it correct?
Yes, by mislabeled, I meant that none of the boxes contain what the label says they do.
 
  • #11
That is an easy one.
Take one out from both fruits container. If it is apple then the orange container will have both fruits and apple will have orange. Same method if it is orange
 

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