  Mpemba effect refers to the counterintuitive phenomenon of a hotter system
equilibrating faster than a colder system when both are quenched to the same
low temperature. For a Brownian particle trapped in a piece-wise linear single
well potential that is devoid of any other metastable minima we show the
existence of Mpemba effect for a wide range of parameters through an exact
solution. This result challenges the prevalent explanation of the Mpemba effect
that requires the energy landscape to be rugged with multiple minima. We also
demonstrate the existence of inverse and strong Mpemba effects.
