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PUZZLET 098

Derived UniDigit Numbers

Take a 6-digit integer, abcdef, all of whose digits are different. Then apply the process a*b^c + d*e^f to generate a four-digit unidigital integer (that is, one whose digits are all the same).

For example, this works with 237954 because 2 x 37 + 9 x 54 = 9999. Are there any other six-digit integers which can be processed in this way to yield four-digit unidigitals?

           
unidigitals


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Last Updated: January 13th, 2010.