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Problem of the Week 1116

The Digits of 44444444

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The sum of the digits of 44444444 is A (in base 10). The sum of the digits of A is B. What is the sum of the digits in B?

I know that we could ask our favorite CAS, but there is a relatively short pencil proof.

Source: Mathematical Morsels by Ross Honsberger, 1978.

© Copyright 2009 Dave Ehren and Shilad Sen. Reproduced with permission.

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26 March 2009