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I provide the algorithm that solves the challenge proposed by Wm. G. Hooverand Carol G. Hoover in their recent paper "Time-Reversible Random NumberGenerators", arXiv:1305.0961, with an explanation on how to derive itanalytically.

The solution to the challenge in "Time-Reversible Random Number Generators" by Wm. G. Hoover and Carol G. Hoover