The rate of Zin'rohk appears to be 1%, which means you will need to perform a lot of solves (probably) in order to get the sword. I've done about 80 solves so far and have not yet received the sword. Statistically it takes 138 solves to even have a 75% chance of attaining it. It's important to know that the sword will never show up until after you have 450 skill in Archeology, and so I would hold on to your troll fragments until you reach that skill.
Thank you for the info, let me see if i got this right , i will lvl my archeology to 450lvl and then use Troll fragment to solve and hope for the sword, right ? Anyone who has already got the 2 handed sword, was it really difficult ?