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**bayogang****Member**- Registered: 2007-03-04
- Posts: 1

Three crates all incorrectly labeled "Oranges", "Apples" and "Oranges & Apples" Remove one piece of fruit from one of the crates and then label each crate correctly. We can solve if we take the one piece of fruit from either the crate labeled "Oranges" or the crate labeled "Oranges & Apples." Have not been able to solve if the one piece of fruit is removed from the crate labeled "Apples." Any help?:|

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

The question is not specific enough. You said that *all* of the crates are labeled incorrectly, but not in what way. For all we know, one could contain kiwis and another a monkey in a cage.

Or, if you mean to say that there are only either Apples or Oranges in each crate, then if each is incorrectly labeled, then each contains the fruit opposite its label. However, this makes the simplifying assumption that the crates that are labeled as containing only one kind of fruit really only contain one kind of fruit. If any one of the three could contain both apples and oranges, then I don't see how we could ever tell what contains what by removing only one piece of fruit.

It's possible I'm just dense today, but this looks unsolvable to me.

El que pega primero pega dos veces.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

I think what **bayogang** means is this:

There are three crates. One contains oranges only, one contains apples only, and one contains both oranges and apples. However, the labels Apples, Oranges and Oranges & Apples are all mixed up on the crates. The problem: Take one fruit from one of the crates, see what it is, and then work out which label should go with which crate.

*Last edited by JaneFairfax (2007-03-04 14:37:42)*

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**pi man****Member**- Registered: 2006-07-06
- Posts: 251

Jane's answe is right on the money. More importantly, that's the only way it can be done.

Bayogang, you say you can figure it out if you pull from the crate labeled oranges but I don't think it's possible. Let's say you pulled a orange from the orange crate. That means that crate has to be apples and oranges. The crate labeled apples can't be apples because it's mislabeled so therefore it contains oranges. And the crate labeled apples and oranges must have apples.

But you could also haved pulled an apple from the crate labeled oranges. If that happens then that crate could either have just apples or both apples and oranges. Let's first assume it has apples. Then the crate labeled apples and oranges must have oranges. And the crate labeled apples must have oranges.

Now the second case where the orange crate has apples and oranges. Then the apple crate must have oranges. And the crate labeled apples and oranges must have apples.

So if you pull an orange from the crate labeled oranges, you can figure it out (similarly, you could figure it out if you pulled an apple from the crate labeled apple). But if you pull an apple from the orange crate, there are the 2 possibilities shown above. So picking one from the orange crate won't necessarily enable you to figure out what's in the three crates. You have to draw from the crate labeled "apples and oranges".

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