There is a set of tiles which are all different and coloured just on the edges. Each edge on a tile is a different colour. For example: Altogether $10$ different colours are used for the edges, and there is an equal number of edges of each colour used throughout the set. The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?