11. (12 points) If the sum of the digits of a natural number is the same as the sum of the digits of its triple, but different from the sum of the digits of its double, we call such a number a "wonderful number". Therefore, the smallest "wonderful number" is $\qquad$
11. (12 points) If the sum of the digits of a natural number is the same as the sum of the digits of its triple, but different from the sum of the digits of its double, we call such a number a “wonderful number”. Therefore, the smallest “wonderful number” is $\qquad$ . $\qquad$
【Solution】Solution: According to the problem, let this number be $x$.
Based on the rule of casting out nines, the sum of the digits of the sum = the sum of the digits of the addends - the number of carries $\times 9$.
If $x$ is a single-digit number, then it can only be $9, 9+9=18$, which does not meet the requirement that the sum of the digits of $x+x$ is different from the sum of the digits of $x$; if $x$ is a two-digit number, and the sum of these two digits is 18, then it can only be 99, and $99+99=198$ does not meet the requirement that the sum of the digits of $x+x$ is different from the sum of the digits of $x$;

If $x$ is a two-digit number, and the sum of these two digits is 9, then the sum of the digits of its double has one carry, and the final sum of the digits is still 9; if $x$ is a three-digit number, and the sum of the digits is 9, then we can let this three-digit number's double have no carry, the smallest is 144, which meets the requirement;

Therefore, the answer is: 144