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Enigmas & puzzles

The rule of eleven

By Ian Stewart   March 2009

“Did you know,” said Innumeratus, “that the number 618,235,079 contains all of the digits from 0 to 9, except the number 4, and is exactly divisible by 11?”

Mathophila did a quick sum in her head. “You’re right, it’s 11×56,203,189. I wonder if you can find a number that uses all ten digits which is divisible by 11?”

A moment later: “Yes, you can.”

“You can’t have tried all the possible arrangements in that short a time!”

“No, don’t be silly. I used an old trick. Take your number, for instance. Add up every other digit, starting from the…

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