It depends how much tolerance they have for gaps between tiles. Worst case they will need one type of tile for each ring of tiles around the nose cone. Not sure how many that is but it must be many dozen. On top of that a range of specialist tiles will be needed for the nose cone tip, flap tips and flap edge joins. Two or three types will be needed to cover the raceways and a similar number to protect the flap joints. Then there’s the standard tile itself and half tiles and any special tiles for leg covers (if required).
Probably between 50 and 100 types of tile will be needed most of which would be on the nose cone.
Here is one potential layout for the nose cone tiles (obviously the real thing will involve many more layers.