Geometry

Rocker1414 · #1 $Old$ 09-01-2008, 03:01 PM

I attatched a figure on dot paper.
I am to divide the region into three congruent parts, but I have no idea how to do this with this strange shape. Thank you all for your time and help.

The picture is a 4 by 4 square with one unit cut out of the bottom right hand corner.

Click on the picture for an enlarged copy of it.

Rocker1414 · #2 $Old$ 09-01-2008, 03:24 PM

haha nevermind came up with the answer, thanks guys

Soroban · #3 $Old$ 09-01-2008, 03:54 PM

Hello, Rocker1414!

I'm delighted that you solved it.

It can be solved with a bit of Thinking.

Code:

      *---*---*---*---*
      |   :   :   :   |
      * - + - + - + - *
      |   :   :   :   |
      * - + - + - + - *
      |   :   :   :   |
      * - + - + - *---* 
      |   :   :   |
      *---*---*---*

We have 15 unit squares, to be divided into three congruent groups.
Hence, each group contains 5 units squares.

There are 12 possible shapes ("Pentominos"),
. . but only one can be used to fill the board.

And there is basically one solution.

Code:

      *-----------*---*
      |           |   |
      |       *---*   |
      |       |       |
      *-------*       |
      |       |       |
      |       *---*---* 
      |           |
      *-----------*