Problem: The Mystic Eleven

Can you find the largest possible number containing any nine of the ten digits (calling naught 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.

Solutions: 1

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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