Math Is Fun Forum

mikau

Member

Registered: 2005-08-22

Posts: 1,504

apples and oranges puzzle

I'm not sure but i think the solution of the 'crates of fruit' puzzle isn't quite sound.
http://www.mathsisfun.com/puzzles/crates-of-fruit-solution.html

The solution says if you reach into the crate labeled 'apples and oranges' and pull out an apple, you know it must be the apples basket. Okay, thats fine. But then it says, This means the crate marked "apples" must be "oranges" It does? Why couldn't it be apples and oranges? As far as I can tell, all we can conclude from step 1 was that neither of the other creates is the apples crate. But we knew the crate labeled 'apples' didn't contain apples to begin with! How did the first step reveal additional information about the crate labeled 'apples'?

What I did was, after step 1, consider the crate labeled 'oranges' we know it cannot contain apples since we know they're in the other crate, and it can't be oranges because its incorrectly labeled, so it must be apples and oranges. And THEN we can conclude that the crate labeled 'apples' must contain oranges.

Can someone explain to me how we were able to conclude the 'apples' crate contained oranges before considering the 'oranges' crate? If not, then I think the solution needs editing.

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A logarithm is just a misspelled algorithm.

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: apples and oranges puzzle

The solution says if you reach into the crate labeled 'apples and oranges' and pull out an apple, you know it must be the apples basket. Okay, thats fine. But then it says, This means the crate marked "apples" must be "oranges" It does? Why couldn't it be apples and oranges? As far as I can tell, all we can conclude from step 1 was that neither of the other creates is the apples crate. But we knew the crate labeled 'apples' didn't contain apples to begin with! How did the first step reveal additional information about the crate labeled 'apples'?

The one labeled Apples must be oranges because if it was Apples and Oranges as you suggest , then the crate labeled Oranges would contain oranges and that can't be since we were told that ALL of the labels were wrong.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: apples and oranges puzzle

so wouldn't it make more sense to list them in the opposite order then?

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A logarithm is just a misspelled algorithm.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: apples and oranges puzzle

After you figured out that apples only must be in the “apples & oranges” crate, the next step is to figure out the contents of the “oranges” crate (not the “apples” crate). It can’t have oranges (because it’s wrongly labelled), nor can it have apples only (because apples only are in another crate).

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: apples and oranges puzzle

aye, thats what I said, Jane. But the solution considers the apples crate second.

I vote that the order of the last sentance be reveresed.

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A logarithm is just a misspelled algorithm.