Statement

Giorgio has recently started to build mosaics out of mosaics. A "mosaic of mosaics" is a mosaic that, instead of using small pieces of stone or glass, uses actual mosaics as "tiles". For simplicity, Giorgio will only use black-and-white square mosaics as tiles for his mosaic. In other words, each tile is a A × A binary matrix. Giorgio has N of such tiles available, and he doesn't need to use all of them. He just needs to arrange some of those pieces in some way as to form a B × B matrix of tiles (that is: a matrix of matrices). Two tiles can be adjacent in the final mosaic only if the colors of the edges match (pixel by pixel). Remember: tiles cannot be rotated nor reflected! Help Giorgio find an arrangement of mosaics that correctly forms a mosaic of mosaics.