6. (10 points) There are several consecutive natural numbers. By selecting any 4 different numbers from them and adding them up, 385 different sums can be obtained. Then these natural numbers have $\qquad$.

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6. (10 points) There are several consecutive natural numbers. By selecting any 4 different numbers from them and adding them up, 385 different sums can be obtained. Then these natural numbers have $\qquad$ numbers.
【Analysis】Assume the smallest number among these consecutive natural numbers is $a$, and the largest number is $a+n+3$. Then, the smallest sum of any 4 numbers must be $a+a+1+a+2+a+3=4a+6$, and the largest sum is $a+n+a+n+1+a+n+2+a+n+3=4a+6+4n$. Since all sums between the minimum and maximum can be obtained from the consecutive natural numbers, we get the equation $4n=385-1$, solving for $n$ gives $n=96$. Thus, the smallest natural number is $a$, and the largest natural number is $a+99$, making a total of 100 numbers, leading to the solution.

【Solution】Solution: Let the smallest number among these consecutive natural numbers be $a$, and the largest number be $a+n+3$. Then, the smallest sum of any 4 numbers must be $a+a+1+a+2+a+3=4a+6$, and the largest sum is $a+n+a+n+1+a+n+2+a+n+3=4a+6+4n$. According to the problem, we have
$$
4n=385-1,
$$

solving for $n$ gives $n=96$.
Thus, the smallest natural number is $a$, and the largest natural number is $a+99$, making a total of 100 numbers.
Answer: There are 100 natural numbers.
Therefore, the answer is: 100.