Math Forum - Project of the Month, October 1996

A Math Forum Project


October POM - Winner

Hayley Tanler, April Price, and Juli Timmony
Redmond High School, Redmond, Oregon

From: LHHK21A@prodigy.com

Here is our solution to the problem of the month:

1.) The twelve possible pentaminoes are . . .

     a.   _
         |_|_ _ _
         |_|_|_|_|    (given)

    
     b. _
       |_|_
       |_|_|
       |_|_|

     c.  _
        |_|
        |_|_ _
        |_|_|_|

     d.     _
           |_|
          _|_|_
         |_|_|_|


     e.   _ _
         |_|_|
           |_|_
           |_|_|


     f.    _ _
          |_|_|_
            |_|_|
            |_| 


     g.  _   _
        |_|_|_|
        |_|_|_|

     
     h.        _
             _|_|_
            |_|_|_|
              |_|



      i.    _ _ _ _ _ 
           |_|_|_|_|_|


      j.   _
         _|_|_ _ 
        |_|_|_|_|



      k.     _ _
            |_|_|_ _
              |_|_|_|



       l.  _ _
          |_|_|_
            |_|_|
              |_|
2.) There are four possibe rectangles with an area of 60 and integer sides greater than two. The sides have to be greater than two because if they weren't not all of the pentanomoes could possibly fit in the rectangle.
     _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
    |  _| |_ _ _ _ _|  _ _| | | |_   _ _| | |
    | |_   _|   | |_ _|_   _| |_  |_|  _ _| |    
    |_ _|_|_ _ _|_ _ _ _|_|_ _ _|_ _|_|_ _ _|

                      3 x 20

    _ _ _ _ _ _ _ _ _ _ _ _
   | |_ _  |  _  |_   _ _| |         
   |  _ _| |_| |_| |_|  _ _|
   |_|  _|_|_  |_   _|_|   |
   |  _|  _ _|_ _|_| |_ _ _|
   |_|_ _|_ _ _ _ _|_ _ _ _|

             5 x 12

   _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
  |  _| |_  |_ _ _ _ _|_  |_ _  |
  | |_   _|  _| |  _| | |_ _ _| |
  | | |_| |_|  _| |   |  _ _| |_|
  |_|_ _ _|_ _|_ _|_ _|_|_ _ _ _|

                4 x 15


    _ _ _ _ _ _ _ _ _ _
   | |_ _ _ _ _|_ _ _  |
   |  _| |_  |_  |   |_|
   | |_   _|_  | |_ _ _|
   |_| |_| | |_|_ _|_  |
   |  _ _| |  _ _|  _| |
   |_|_ _ _|_|_ _ _|_ _|

           6 x 10

Well that's it. I hope that you can understand the diagrams. I wish I could've used some different form of software but it just wasn't possible.

Thanks for your time . . .

Yours truly,

April Price
Hayley Tanler
Juli Timmony

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