# Partition the following graph into 4 parts

Partition the following graph into $4$ parts, each with the same shape-size, and each with one circle in it.

$$\begin{array}{cc} 1& 1& 1& 1& 1& 1\\ 0 &0 &1 &1 &1 &1\\ 1 &1 &0 &1 &1 &1\\ 1 &1 &1 &1 &1 &1\\ 1 &1 &1 &1 &1 &0\\ 1 &1 &1 &1 &1 &1 \end{array}$$

$0$ is circle.

Does each partition have to be the same shape and size? – Ataraxia Jul 29 at 4:58 Do the four partitions have to cover the entire area? – abiessu Jul 29 at 5:01

If possible.

I think there is some general rules/programs to do this kind of exercises?

If not possible to get the right answer under present condition, I'd like to know why. And slightly change of the conditions is also ok, and that is interesting, we do this for fun?

• Does each partition have to be the same shape and size? – Ataraxia Jul 29 '13 at 4:58
• Do the four partitions have to cover the entire area? – abiessu Jul 29 '13 at 5:01
• @Ataraxia If possible, – forlorn Aug 7 '13 at 14:36
• @abiessu If possible, – forlorn Aug 7 '13 at 14:37

Here are four partitions of equal "shape size" which cover the entire area without overlap:

1
0
1
1
1
1 1 1 1

1
0
1
1
1 1 1 1
1

1 1 1
1 1 1
0 1 1

1
1
1
1 1 1 1
0
1

It would not be possible to have all four have the same shape and size unless the area were considered to wrap from top to bottom and from left to right, in which case the four partitions would be 3x3 squares each with common corner in the center of the 2x2 area which appears so:

0 0
1 1