# Geometry

• Sep 1st 2008, 01:01 PM
Rocker1414
Geometry
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.(Cool)

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.
• Sep 1st 2008, 01:24 PM
Rocker1414
haha nevermind came up with the answer, thanks guys
• Sep 1st 2008, 01:54 PM
Soroban
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:

```      *-----------*---*       |          |  |       |      *---*  |       |      |      |       *-------*      |       |      |      |       |      *---*---*       |          |       *-----------*```