Thursday, December 13, 2007

You have three boxes of fruit. One contains just apples, one contains just oranges, and one contains a mixture of both. Each box is labeled -- one says "apples," one says "oranges," and one says "apples and oranges." However, it is known that none of the boxes are labeled correctly. How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?

80 Comments:

Anonymous Anonymous said...

Picking from ANY box tells you, by exclusion, what's in the other two boxes, because of the fact that you know from the outset that all the boxes are labelled wrong.

Anon. who said Nora is 72 again.

December 15, 2007 at 5:48 PM  
Blogger steven said...

OK. So say you reach into the box labelled 'oranges' and pick an apple. How do you know whether the 'oranges' box is the box with only apples, or with both apples and oranges?

December 21, 2007 at 1:27 PM  
Blogger steven said...

Pick from the 'apples and oranges' box.
If you pick an orange, then the 'apples'-labelled box contains apples and oranges, and the 'oranges'-labelled box contains apples only.
If you pick an apple, then then 'oranges'-labelled box contains apples and oranges, and the 'apples'-labelled box contains oranges only.

December 22, 2007 at 5:47 PM  
Anonymous Anonymous said...

I sit corrected. I picked from the “apples and oranges” box, which works exactly as you describe, then overgeneralized. Consider me chastened, and beaten about the head with an apple (or orange) box. Thanks for the puzzles. After a Lyme-induced cognitive meltdown, I'm really enjoying being able to even look at logical puzzles without howling in bewildered despair.

January 9, 2008 at 1:04 AM  
Blogger sarika said...

We can solve this problem through grid box.A lot of information give need to read carefully through this information we can arrange
Apple orange Apple&orange
Label
1Apple x
2orange x
3App&orn x
now we can pick any boxes but we decide that which of the column give the more information if we pick box of apple then once again we will confuse because we can't decide in which box orange or app&orn this question is also arise for orange box but if we pick app&orn then we can eaily guess in which box of apple or orange because accroding to the given information labeled has not correct so we can pick app&orn if we pick apple from box then orange box contain app&orn and apple box contain orange then we get

Apple Orange App&Orn
Label
1Apple x x A
2Orange O x x
3App&Orn x A&O x

April 13, 2008 at 7:30 AM  
Anonymous Anonymous said...

What? I'd fuck it off and have a banana!

July 31, 2009 at 6:21 AM  
Anonymous Anonymous said...

I'd love a banana in my box!

I'm well jealous

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