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PUZZLET 108

A Sequence of Summed Cubes


Take a certain 3-digit integer and sum the cubes of its digits to form a new integer. Do this again to get back to the original integer. What is the starting integer? Find all possible solutions.

Example:  217  gives 23+13+73 = 352. 352 gives 33+53+23 = 217.

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Last Updated: January 13th, 2010.