Enhanced Sets of Polyforms
If we take a set of polyforms and add n copies of one of the pieces we create and enhanced set. These pages investigate what figures can be made with these sets.
As an example of what is meant we look at a simple example - the tetrominoes. Here we have one unbalanced piece and so the only way in which a rectangle could be formed is by adding an odd number of copies of that piece. The diagram below shows solutions for n = 1, 3, 5 and 7. Also shown is a 4x4 square formed by four of the added pieces. This shows that rectangles can be made for all odd values of n. Such squares can also be added to form any rectangle of the form (8a+4) x 2b or 8a x b.
Such a complete analysis is not feasible in most cases and in these pages we shall restict the analysis in various ways. The links below look at various other sets of polyforms enhanced in this manner.