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The New Coffee Room

  1. TNCR
  2. General Discussion
  3. Puzzle time - area-perimeter match

Puzzle time - area-perimeter match

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  • jon-nycJ Offline
    jon-nycJ Offline
    jon-nyc
    wrote on last edited by
    #1

    Find all integer-sided rectangles whose area and perimeter happen to be the same number.

    The whole reason we call them illegal aliens is because they’re subject to our laws.

    1 Reply Last reply
    • jon-nycJ Offline
      jon-nycJ Offline
      jon-nyc
      wrote on last edited by
      #2

      Unless I’m missing something, which is far from impossible, this one was pretty easy.

      The whole reason we call them illegal aliens is because they’re subject to our laws.

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      • KlausK Offline
        KlausK Offline
        Klaus
        wrote on last edited by Klaus
        #3

        Hm, let's see.

        :::

        It means we want all integer solutions to

        a*b = 2a+2b

        or

        b = 2a / (a-2)

        That's a hyperbola, so there can only be finitely many solutions.

        a18c1942-5caf-43a1-bc24-6e034f714d2e-image.png

        I'd say it's these four number pairs.

        0,0
        3,6
        4,4
        6,3

        :::

        (I put this into a defunct spoiler (damn lazy forum admin should fix this); if you want to see what I wrote you can push "Quote")

        Yeah, seems to be pretty simple.

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