There are many ingenious puzzles involving matchsticks that are arranged as squares, rectangles or triangles, and can be moved under some restrictions (for a lot of examples see http://www.learning-tree.org.uk/phpBB3/viewforum.php?f=1). I wonder if there are any mathematical article about this kind of problems.
Thank you in advance for any suggestion :-)
A quick Google search came up with this paper, although I'm not sure it covers what you are asking for.
And if you're into this kind of puzzles, this book may be something for you :)