A set (1) of tiles (5) adapted to cover a surface (10) perpendicular to a thickness direction (V) of the tiles (5), each of the tiles comprising at least one upper layer (24), and an underlying rigid core layer (22), the core layer and the upper layer being superimposed in the thickness direction, and the core layer defining a lower surface (S) opposite the upper layer. The tiles comprise at least one first tile (15) having a first edge extending in a longitudinal direction (L), the core layer of the first tile (15) defining a connecting groove (28) in the first edge. The tiles comprise at least one second tile (20) having a second edge extending in the longitudinal direction, the core layer of the second tile defining a connecting tongue (34) protruding from the second edge, the connecting tongue being adapted to be snap-fit into the connecting groove in a connecting direction (C) perpendicular to the longitudinal direction (L) and to the thickness direction in a locked configuration of the first tile and the second tile. The lower surface defines an additional groove (30) parallel to the first edge.