The figure below shows Sam Loyd's well known square-dissection
puzzle. It is made by locating the midpoints of all four sides
of the square, drawing the appropriate lines, and dissecting.
The five pieces construct all of the puzzle patterns shown.
Again note the interesting paradox of the two on the right -
one being a solid rectangle and the other a rectangle with a
corner missing, yet both use all five pieces.

Solution:
I've been told by some of you anonymous mathematicians 
that you don't bother with these puzzles if I include the 
solution.  So, no solution was included.