The Mystic Eleven

Unreviewed import — a classic from the public domain; its solution has not been machine-checked yet.

math

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.

Solution

Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.

Solution

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