15. The sum of all three-digit palindromic numbers is

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【Answer】49500
【Analysis】Key points: Addition and Multiplication Principle, Place Value Principle
In three-digit palindromic numbers, as long as the hundreds and units digits are equal, the tens digit can be any number from 0 to 9. Therefore, the sum of palindromic numbers with a hundreds digit of 1 is $101 \times 10+10 \times(0+1+2+\cdots+9)$, similarly, the sum of palindromic numbers with a hundreds digit of $a$ is $a \times 101 \times 10+10 \times(0+1+2+\cdots+9)$, thus, the sum of all three-digit palindromic numbers is $101 \times 10 \times(1+2+\cdots+9)+9 \times 10 \times(0+1+2+\cdots+9)=49500$