I notice that the stones are counted in a cycle of 16, where the first and the last stones are repeated. So, I can divide 99 by 16 and look at the remainder to find out which stone is counted as 99. I know that 16 times 6 is 96, so 99 is 3 more than 96. That means the stone counted as 99 is the same as the stone counted as 3 in the first cycle. The stone counted as 3 in the first cycle is the third stone from the left, which was originally counted as 3. So, the original stone that is counted as 99 is 3. 
Nine stones are arranged in a straight line. They are counted from  left to right as $1,2,3, \ldots, 9$, and then from right to left, so that the stone previously counted as 8 is counted as 10. The pattern is continued to the left until the stone previously counted as 1 is counted as 17. The pattern then reverses so that the stone originally counted as 2 is counted as 18, 3 as 19, and so on. The counting continues in this manner. Which of the original stones is counted as 99? Express your answer as a single digit which corresponds to the first digit assigned to that stone.