Hatred of Eleven III

Number Theory Level pending

We define an "Eleven Hater" as a number that is not a multiple of eleven, but becomes a multiple of \(11\) when any one digit is removed.

For clarity, consider a 3 digit number \( \overline {abc} \). if \( \overline {abc} \) is an "Eleven Hater", then \( \overline {ab}, \overline{ac},\) and \(\overline{bc} \) should all be multiples of \(11\). Note that the order of the digits are not to be altered.

Find the sum of all "Eleven Haters" from 1 to 1,000,000.

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