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Problem of the Week 1240

Nondivisibility by 11

The number 545 has the curious property that upon replacing the digit in any single position by an arbitrary digit (from 0 to 9; it can be a leading 0 or just the same digit), the result is not divisible by 11.

Is there a positive integer with this property having an even number of digits?

Source: Sid Hollander, who found the ambiguity.

[View the solution]

27 July 2017