How can I model this puzzle mathematically?
My friend had showed me this puzzle from the game Professor Layton and the Curious Village and I was wondering how it could be solved mathematically rather than using trial and error.
Here's the puzzle:
{
A man who lives in a red house, a man who lives in a yellow house, a man who lives in a blue house and a man who lives in a green house all have their houses built on the same land lot, and want to divide up the property evenly.
They live on a 6 by 6 grid, furthermore each house needs a well on its property.
The land also must be divided up such that the shape surrounding each person's land is the same.
}
Here's a visual representation (wells are grey) :
http://filesmelt.com/dl/squares.JPG
Thanks in advance! Sorry if I didn't make this very clear.