# Adding 0 makes no change, Really ?

Given that in the 8-digit number $$\overline{\mathrm{ABCDEFGH}}$$,

(i) $$\overline{\mathrm{ABCD}}=\overline{\mathrm{EFGH}}$$
(ii) The numbers $$\overline{\mathrm{ABCDEFGH}}$$ and $$\overline{\mathrm{ABCD0EFGH}}$$ are both divisible by $$11$$.
Let the sum of all possible values of $$\overline{\mathrm{ABCDEFGH}}$$ be $$N$$.

Find the digit sum of $$N$$.

Details and assumptions:-

• $$\overline{\mathrm{ABC}}$$ means the number in decimal representation with digits $$A,B,C$$ i.e. $$\overline{\mathrm{ABC}} = \mathrm{100A+10B+C}$$
• The letters $$A$$ to $$H$$ do not necessarily stand for distinct digits.
• In the second number, the digit $$0$$ is added in the middle of the 8-digit number, which makes it a 9-digit number.
• Digit sum is sum of all digits in decimal representation, digit sum of $$12023$$ is $$1+2+0+2+3=8$$
• 00123 is not a 5-digit number.
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