- Joined
- 10 Dec 06
- Moves
- 8528
24 Mar 21
In front of you are three boxes are filled with fruit ( Apples, Oranges, Mixed Apples and Oranges). The boxes are labeled: Apples, Oranges, Apples & Oranges. All the labels are incorrectly placed.
You cant look in the boxes, but you can as me to give you a sample of fruit from any of the boxes as many times as you'd like.
What is the minimum number of samples required to properly label all the boxes with the fruit they contain?
24 Mar 21
@joe-shmo said1st step get a fruit from the box labeled "apples and Oranges". If it is an apple label it "Apples". (If it is an orange the process is altered accordingly). Since the box "Apples" was labeled wrong it can't be the apple box, so it has to be the "Oranges" box. Puzzle solved. You need one fruit.
In front of you are three boxes are filled with fruit ( Apples, Oranges, Mixed Apples and Oranges). The boxes are labeled: Apples, Oranges, Apples & Oranges. All the labels are incorrectly placed.
You cant look in the boxes, but you can as me to give you a sample of fruit from any of the boxes as many times as you'd like.
What is the minimum number of samples required to properly label all the boxes with the fruit they contain?
- Joined
- 10 Dec 06
- Moves
- 8528
24 Mar 21
@ponderable saidCorrect!
1st step get a fruit from the box labeled "apples and Oranges". If it is an apple label it "Apples". (If it is an orange the process is altered accordingly). Since the box "Apples" was labeled wrong it can't be the apple box, so it has to be the "Oranges" box. Puzzle solved. You need one fruit.
- Joined
- 10 Dec 06
- Moves
- 8528
24 Mar 21
9 edits
Looking what you exactly said closer, It looks like perhaps you've left out a step in your solution ( or you made a lucky logical error ), because it doesn't appear to be logically consistent the way you've wrote it up.
Since the box "Apples" was labeled wrong it can't be the apple box, so it has to be the "Oranges" box.
It does not immediately follow that the box labeled "Apples" must be "Oranges".
Labels of the three boxes:
A , O , A&O
If we take a sample from the box labeled "A&O" ( which must have either "A" or "O" ) and we find "A":
we now know the box initially labeled "O" , must contain "A&O", because before finding "A", it could have only held "A" or "A&O".
It is only now, since we know the location of "A" and "A&O", we know the location of "O".
A similar argument follows if instead we had first found "O".