Hi-five

Determine the number of 5-digit positive integers A B C D E \overline{ABCDE} ( A A , B , C , D B,C,D and E E not necessarily distinct) such that the sum of the 3-digit number A B C \overline{ABC} and the 2-digit number D E \overline{DE} is divisible by 11.


The answer is 8181.

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