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3rd grade geometry question

  1. Jul 7, 2010 #1
    Here is how I interpreted it.
    INTERPRETATION 1
    Consider only the part of the question colored in orange. The answer to this phrase is obviously all 6 faces of the cube. Then we place an additional constraint on it (the remaining part of the sentence that's not orange). Call the edges of the cube [sideA, sideB, sideC, sideD, sideE, sideF] wlog.
    Consider sideA; does it share an edge with any one other face? Yes (pick any one of the four faces that are adjacent to it).
    Consider sideB; does it share an edge with any one other face? Yes.
    ...
    Consider sideF; does it share an edge with any one other face? Yes.

    Count all the faces that qualify under the constraint the orange part of the sentence is placed under and you will get the original 6 - just if there was no constraint.

    Here's how the solutions interpreted it:
    INTERPRETATION 2
    Consider any one face of a cube (sideA, sideB, sideC, sideD, sideE, or sideF). How many faces are adjacent to it? 4.

    Why is INTERPRETATION 1 fallacious?
     
    Last edited: Jul 7, 2010
  2. jcsd
  3. Jul 7, 2010 #2
    Have you asked a third grader?
     
  4. Jul 7, 2010 #3
    I'm not looking for "obvious" reasoning but rather descrying the logic of the sentence. I still don't see how my interpretation is false.
     
  5. Jul 7, 2010 #4
    Generally, interpretations are not true or false, but are more like opinions. As such, they need to be justified in some way, and then people either accept them, or not, based on the strength of the arguments. Interpretation 2 seems straightforward and correct to me. Interpretation 1 is harder to justify, and your explanation doesn't seem clear to me, but I could be missing your point of view.

    There is also the issue of why would they add a constraint that does not constrain anything. Of couse, it could be a trick question, but that's a mean-spirited trick to play on a third grader. :wink:
     
    Last edited: Jul 7, 2010
  6. Jul 7, 2010 #5
    The trick is that words can often be left out in English, but are still part of the implied meaning.

    "the number of faces that share an edge with any one face" actually means: "the number of faces that share an edge with any one particular face".

    Your interpretation of the meaning of the sentence hinges on a misinterpretation of the phrase "any one". Here are some examples of uses of "any one":

    "Pick any one candy."
    "Give a card to any one person"
    "How many hats can be worn by any one person at a time?"
    "How many people share a name with any one person?"

    In this last sentence, it's very easy to mistakenly assume "any one" means the same as "some other". Needless to say, the wording "any particular" would have been less ambiguous. However, "any one" has a very STRONG connotation that is has been picked in advance (as you can see in the first three examples). Indeed, because of how strong the phrase "any one" is, it can only be used in certain circumstances. For example, you would never say, "How much money does any one person in the U.S. earn?", because "any one" restricts you to addressing only those properties shared by all members of the group which you are referring to (salary not being one of them).

    Now, I also think neither of your answers are correct! The answer is clearly 5. Choose any particular face. Note that there are four adjacent faces (each of which share an edge). Also, however, the face shares an edge with itself. (You certainly wouldn't say is does not share an edge with itself, would you?) This leaves five. :smile:
     
  7. Jul 8, 2010 #6
    After reading through 4 pages of forum posts (I also asked on another forum) I finally found what I was looking for. Thanks.
     
  8. Jul 8, 2010 #7
    A good example of how the blind can indeed lead the blind. The person with an answer of 6 gets an explanation from the person with an answer of 5 (perhaps given with tongue in cheek) and then finally agrees with all third graders that the answer is 4.

    No offense meant to either, given the fair question, and the good response, but that is a little ironic, and very funny. :rofl:
     
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