2. There are ten cards, each with one of the ten digits $0-9$. They are arranged in a row to display the number 9072543681. If swapping the positions of two adjacent cards is considered one operation, then the minimum number of operations required to change the original number into one that is divisible by 99 is $\qquad$.
2.2

Analysis: A necessary and sufficient condition for a positive integer to be a multiple of 11 is that the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11 (counting from left to right). Since the number 9072543681 has a digit sum that is clearly divisible by 9, and the sum of its digits is 45, the sum of the digits in the odd positions is $9+7+5+3+8=32$, and the sum of the digits in the even positions is $0+2+4+6+1=13$. The difference must be a multiple of 11, which can only be $28+17$ or $39+6$. It is evident that a single operation cannot increase the sum of the odd-position digits by 7 or decrease it by 4, and thus cannot reach 17 and 6. Therefore, a single operation is insufficient. However, swapping the digits 3 and 6, and swapping the digits 8 and 1 in two operations can change 9072543681 to 9072546318, at which point the sum of the digits in the odd positions is 28, and the sum of the digits in the even positions is 17. Hence, this number is a multiple of 11, and at least two operations are required.