instance, the 16-omino in the form of a 4 × 4 square and the 18-omino in the form of a 3 × 6 rectangle are both equable. For polyominoes with fewer than 15 squares, the perimeter always exceeds the area. Tiling with polyominoes In recreational mathematics, challenges are often posed for tiling a prescribed region, or the entire plane, with polyominoes, and related problems are investigated in mathematics and computer science. Tiling regions with sets of polyominoes Puzzles commonly ask for tiling a given region with a given set of polyominoes, such as the 12 pentominoes. Golomb's and Gardner's books have many examples. A typical puzzle is to tile a 6×10 rectangle with the twelve pentominoes; the 2339 solutions to this were found in 1960. Where multiple copies of the polyominoes in the set are allowed, Golomb defines a hierarchy of different regions that a set may be able to tile, such as rectangles, strips, and the whole plane, and shows that whether polyominoes from a given set can tile the plane is undecidable, by mapping sets of Wang tiles to sets of polyominoes. Because the general problem of tiling regions of the plane with sets of polyominoes is NP-complete, tiling with more than a few pieces rapidly becomes intractable and so the aid of a computer is required. The traditional approach to tiling finite regions of the plane uses a technique in computer science called backtracking. In Jigsaw Sudokus a square grid is tiled with polynomino-shaped regions . Tiling regions with copies of a single polyomino Another class of problems asks whether copies of a given polyomino can tile a rectangle, and if so, what rectangles they can tile. These problems have been extensively studied for particular polyominoes, and tables of results for individual polyominoes are available. Klarner and Göbel showed that for any polyomino there is a finite set of prime rectangles it tiles, such that all other rectangles it tiles can be tiled by those prime rectangles. Kamenetsky and Cooke showed how various disjoint (called "holey") polyominoes can tile rectangles. Beyond rectangles, Golomb gave his hierarchy for single polyominoes: a polyomino may tile a rectangle, a half strip, a bent strip, an enlarged copy of itself, a quadrant, a strip, a half plane, the whole plane, certain combinations, or none of these. There are certain implications among these, both obvious (for example, if a polyomino tiles the