643 solves here to get all 4 (not counting the ring and the scarab thingy, perhaps I am missing one, it has been a long time) rares, last one was the mount.
It is actually worth using another toon to get a 'rarer' item, as Archeology works like this. There is a difference between rares as I mentioned above. If you have not yet solved the ring or the scarab thing, you have a higher chance of finding a rarer rare. The game rolls first between common vs rare, with rare being probably a 20% chance, but then it rolls again, ring/srabab vs. Other rares. The other rares have again probably a 20% chance. If you are lucky enough, the game then just rolls 1-4 and one of the rarer rares is 'won'. Now, each time you get a new solve it is actually a 4% chance of getting the mount-pet-staff-sword. This sounds small, but 4 % isnt actually correct, as almost everyone has 2 rares after 12-15 solves, these are almost guaranteed. And on those guarantees you have a 20% chance of getting a real rare. Its not a 4% chance on those 12-15 solves, it is 20% on 2 solves. If you hit a superduper rare one, you have another 20% chance at your next rare solve, which is guaranteed to 'drop' within 5-6 solves.
This changes on the moment you have solves the ring and the scarab thing, then the chance drops to 1%. It works the same way (with different percentages) with all the other super rares, like the Dwarf Staff, Fossil Shield, Troll Sword and Nightelf Trinket. You either get it really early in your digging, or it takes a hell of a grind.
Ofcourse it requires you to level another chars archeology, which also takes a lot of time.