Three JarsDate: 11/01/2000 at 20:17:51 From: Steven Subject: Logic puzzle We have three jars: one contains red marbles, one contains black, and one contains both, but we don't know which is which. The jars are labeled Red, Black, and Mixed, but each of the labels is wrong. Nancy says she can put the labels on the right jars by picking one marble from one container. How can she do this? I think I know the answer, but it's hard to explain. Can you give me an answer so I can compare? Date: 11/02/2000 at 15:38:33 From: Doctor Ian Subject: Re: Logic puzzle Hi Steven, This kind of question can drive you crazy without a picture to help you keep track of what's going on. Here are the containers: +---+ +---+ +---+ | | | | | | +---+ +---+ +---+ We'll use the letters "r," "b," and "m" to indicate whether a container _actually_ contains red, black, or mixed marbles. Without knowing anything else, we have to assume that each container can contain any kind of marbles: r r r b b b m m m +---+ +---+ +---+ | | | | | | +---+ +---+ +---+ Now let's label the containers: r r r b b b m m m +---+ +---+ +---+ | R | | B | | M | +---+ +---+ +---+ Since we know all the labels are wrong, we can eliminate some possibilities right off the bat: r r b b m m +---+ +---+ +---+ | R | | B | | M | +---+ +---+ +---+ Now, let's say we take a marble out of the container marked "M", and let's say it's red. r r b b m m +---+ +---+ +---+ | R | | B | | M | +---+ +---+ +---+ red Since we know the label is wrong, we know that it must contain _only_ red marbles: r r b m m +---+ +---+ +---+ | R | | B | | M | +---+ +---+ +---+ red And since it contains only red marbles, no other container can contain only red marbles: r b m m +---+ +---+ +---+ | R | | B | | M | +---+ +---+ +---+ red So we know which one is red, and which is mixed. Which means that the other must be black: r b m +---+ +---+ +---+ | R | | B | | M | +---+ +---+ +---+ red Now you need to see whether this still works if you pull a black marble instead of a red one out of the container marked "M"... I hope this helps. Write back if you'd like to discuss this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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