THE MYSTIC ELEVEN

Can you find the largest possible number containing any nine of the ten digits (calling nought a digit) that can be divided by `11` without a remainder? Can you also find the smallest possible number produced in the same way that is divisible by `11`? Here is an example, where the digit `5` has been omitted: `896743012`. This number contains nine of the digits and is divisible by `11`, but it is neither the largest nor the smallest number that will work.


Topics:
Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rule by 11
Sources:
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