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A Advanced Challenge of the Week #1 03/19/2017

  1. Mar 3, 2017 #1
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  2. jcsd
  3. Mar 11, 2017 #2

    Erland

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    A rectangle is divided into a finite number of subrectangles. The sides of the subrectangles are all parallell to sides of the large rectangle.
    Each subrectangle has at least one side with integer length.

    Prove that the large rectangle also has at least one side with integer length.
     
  4. Mar 13, 2017 #3

    mfb

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    Do you need advanced mathematics for this?

    A nice puzzle.
    I can see why it fails although I don't find a mathematically sound proof yet that covers all weird cases.
     
  5. Mar 14, 2017 #4

    Erland

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    The only proof I know of uses advanced mathematics. But if you have an elementary proof, it would be interesting to see it :).

    I should add the the "advanced" proof is very short, simple and surprising, if one masters this particular advanced topic.
     
  6. Mar 14, 2017 #5

    mfb

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    I keep running into cases that are completely irrelevant (situations that won't lead to solutions anyway), but keep ruining an elementary approach.
     
  7. Mar 20, 2017 #6

    Erland

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    mfb solved the problem, and should be given the credit!
     
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