Here's a collection of results that are related to Michael Kleber's nice argument, although they don't seem to imply his result, as far as I can see... deBruijn showed that 1xa bricks will tile an mxn only when m or n is a multiple of a for example, you can't tile a 6x6 box with 1x4 bricks his proof is by a coloring argument that uses "a" colors in a checkerboard-like pattern ron graham showed that a fault-free tiling of a pxq rectangle with axb tiles exists (where we assume pq>ab and (a,b)=1) if and only if each of a and b divides p or q; each of p and q can be expressed as a linear combination of a and b into at least two ways; for {a,b} = {1,2}, (p,q) is not equal to (6,6), ie there is no fault-free tiling of a 6x6 by 1x2's (argument due to Golomb and Jewett) Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm