Abstract: A building block for a wall enables the blocks to be mounted in offset and flush modes. The block has an extension portion on the bottom, making the bottom longer than the top. The rearward lug protrudes from the bottom at the extension portion. The forward lug protrudes from the bottom forward of the rearward lug. In the offset mode, the upper row of blocks rests on the lower row with the forward lug of the upper row engaging the rearward end of the lower row of blocks. In the flush mode, the forward lug is removed and the blocks positioned with the forward end substantially flush. The rearward lugs of the upper row will then engage the rearward ends of the lower row. Holes extend through the blocks for receiving pins for interlocking them together. Some of the holes are elongated. The pins have enlarged heads which locate in the elongated holes, but will not fit in the cylindrical holes.