An 8 digit number is divisible by 99. If the digits are shuffled, then the number is always divisible by __________.

The correct answer is 9.

Step 1: Understand the test for divisibility by 99
A number is divisible by 99 if and only if it is divisible by both 9 and 11, because 9 and 11 are coprime factors of 99.

Step 2: Recall the rule for divisibility by 9
A number is divisible by 9 if and only if the sum of all its digits is divisible by 9.

Step 3: Analyze what happens when the digits are shuffled
Since the original 8-digit number is divisible by 99, it must be divisible by 9. Therefore, the sum of its digits must be a multiple of 9.
When the digits of the number are rearranged or shuffled, the set of digits remains exactly the same. Consequently, the sum of the digits remains unchanged and is still divisible by 9.
Thus, any permutation of the digits will produce a number whose sum of digits is divisible by 9, meaning the newly formed number is guaranteed to be divisible by 9.

Step 4: Check divisibility by other options
Shuffling the digits can change the alternating sum of digits (affecting divisibility by 11) or the last digit (affecting divisibility by 2, 5, or 6). Therefore, divisibility by 6, 5, or 11 is not guaranteed for all shuffled arrangements, but divisibility by 9 is always guaranteed.

Hence, if the digits are shuffled, the number is always divisible by 9.