We present two methods for designing amino acid sequences of proteins that will fold to have good hydrophobic cores. Given the coordinates of the desired target protein or polymer structure, the methods generate sequences of hydrophobic (H) and polar (P) monomers that are intended to fold to these structures. One method designs hydrophobic inside, polar outside; the other minimizes an energy function in a sequence evolution process. The sequences generated by these methods agree at the level of 60-80% of the sequence positions in 20 proteins in the Protein Data Bank. A major challenge in protein design is to create sequences that can fold uniquely, i.e. to a single conformation rather than to many. While an earlier lattice-based sequence evolution method was shown not to design unique folders, our method generates unique folders in lattice model tests. These methods may also be useful in designing other types of foldable polymer not based on amino acids.