9. (10 points) If the digits of a natural number can be divided into two groups such that the sum of the digits in each group is equal, then the number is called a "balanced number". For example, 25254 is a "balanced number" because $5+2+2=4+5$. If two consecutive natural numbers are both "balanced numbers", then this pair of "balanced numbers" is called a "twin balanced number". What is the sum of the smallest pair of "twin balanced numbers"? $\qquad$
【Solution】Solution: (1) The "balanced numbers" among two-digit numbers are $11, 22, 33, 44, 55, 66, 77, 88, 99$, none of which meet the requirements.
(2) Among two-digit and three-digit numbers, $99, 100$ do not meet the requirements either.
(3) In three-digit numbers, if the sum of the digits of two adjacent numbers is always even, it indicates that there must be a carry, and the three-digit number must carry only once (the sum of the digits plus 1 and then subtract 9), i.e., these two numbers are $A B 9$ and $A(B+1) 0$, so we have:
$$
A+B=9 \text { and } A=B+1
$$

Solving these, we get: $A=5, B=4$
Therefore, these two numbers are 549 and 550.
$$
549+550=1099
$$

Thus, the sum of the smallest pair of "twin balanced numbers" is 1099.