hola artist;

look forward to seeing the product of your puzzle perousals; in the meantime, here are some ideas which are i hope relevant to your problem:

i believe general answers to puzzles of this type are to be found in the maths of tilings, which deal with whether or not a particular repeating unit can 'tile' space (2d in your case), and allows you to calculate the number of repeating units etc.

a good initial link to the subject can be found at http://www.ics.uci.edu/~eppstein/junkyard/tiling.html

i think the type of shapes you are dealing with in particular - the L shape & variants - are 'polyominoes'. good link on this:

http://student.cusu.cam.ac.uk/~jsm28/tiling/

no set of links on tilings would be complete without a reference to beautiful, aperiodic penrose tilings. here is one:

http://www2.spsu.edu/math/tile/aperiodic/

best wishes,

wufnik

-- in the world of the mules there are no rules --