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The question of the title is a famous puzzle in the field of recreationalmathematics, and can be addressed by several approaches. A compilation ofsolutions, some of them very ingenious, can be found in [1]. In thiscontribution we present an alternative solution based on the second law ofthermodynamics. The method can be extended to derive a more general resultinvolving the exponential function.

Which is greater: $\boldsymbol{e^\pi}$ or $\boldsymbol{\pi^{e}}$? An unorthodox solution to a classic puzzle