Pandigital and Pretty Powerful IV (Posted on 2009-06-06)

Determine all possible triplet(s) of positive integers (X, Y, Z) such that the decimal representation of X^{Y}*(X+1)^{Z} has no leading zeroes and contains each of the digits from 0 to 9 exactly once.

Many triplets are possible in terms of the given conditions.

For a comprehensive list of all these triplets together with the methods for deriving them, refer to the solution submitted by Daniel in this location, and the solution submitted by Charlie in this location.

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