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Powerful digit sum

Problem 56

Published on Friday, 7th November 2003, 06:00 pm; Solved by 39544; Difficulty rating: 5%

A googol (10100) is a massive number: one followed by one-hundred zeros; 100100 is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.

Considering natural numbers of the form, ab, where a, b < 100, what is the maximum digital sum?