Since I don't know all the proper math lingo for this question, I'll just state the problem as it arose:
My wife was quilting and had the front of the quilt done, but needed to put the backing on. Square-footage wise, she had enough backing material to cover the back. The backing material she had was in decent size scraps, but all different shapes. Since the front had congruent squares stitched together, she wanted the back to have some sort of pattern too (basically she didnt just want all the scraps sewn together and trimmed), so some or all of the scraps the same size.
Her question to me was, what is the fewest number of stitches she'll have to sew, using scraps of either some or all the same size.
Does this problem have a general solution?