14. (15 points) Let the sum of one hundred natural numbers $x, x+1, x+2, \cdots, x+99$ be $a$. If the sum of the digits of $a$ equals 50, what is the smallest value of $x$?
【Analysis】First, use the sum formula of an arithmetic sequence to get the sum of one hundred natural numbers, then discuss the cases where the addition of $100 x+4950$ does not carry over; and where the addition of $100 x+4950$ carries over $t$ times to find the solution.

【Solution】Solution: The total sum $a=100 x+9900 \div 2=100 x+4950$,
If the addition of $100 x+4950$ does not carry over, then the digit sum $=x$'s digit sum $+4+9+5=50, x$'s digit sum $=32$, $x$ must be at least a 5-digit number: 99950;

If the addition of $100 x+4950$ carries over $t$ times, then the digit sum $=x$'s digit sum $+4+9+5-9 t=50, x$'s digit sum $-9 t=32$, carrying over once then $x$'s digit sum $=41$, the smallest is 199949; carrying over twice then $x$'s digit sum $=50$, the smallest is 699899; more carries, $x$ must also exceed 5 digits.

Therefore, the smallest $x$ is 99950.