How many unique tiles are there when a tile has four corners, each of which can have 0-6 dots in it, and 0-6 dots in those dots, and a further 0-6 dots in those. The tile cannot be rotated, every corner is unique.
+2666 There are 4 corners to put them in.
There are 7 dots in 3 rounds, so there is \(4 \times 7 \times 7 \times 7 = \color{brown}\boxed{1,372}\)
