I'm assuming drilling into the sides of the tiles is not possible?
Because if you can, drilling two holes, in the diameter of your magnets, on each side of the tiles (at the exact same locations for each side, and each tile), and then push/glue in the magnets flush with the sides of the tiles. Each side should have one with the N pole and the other with the S pole showing. And (this is crucial!) all sides and all tiles need to have them positioned exactly the same.