Welcome to Science class. 4 possible explanations for the Mpemba effect
1) Evaporation -- As the initially warmer water cools to the initial temperature of the initially cooler water, it may lose significant amounts of water to evaporation. The reduced mass will make it easier for the water to cool and freeze. Then the initially warmer water can freeze before the initially cooler water, but will make less ice. Theoretical calculations have shown that evaporation can explain the Mpemba effect if you assume that the water loses heat solely through evaporation [11]. This explanation is solid, intuitive, and evaporation is undoubtedly important in most situations. However, it is not the only mechanism. Evaporation cannot explain experiments that were done in closed containers, where no mass was lost to evaporation [12]. And many scientists have claimed that evaporation alone is insufficient to explain their results [5,9,12].
2) Dissolved Gasses -- Hot water can hold less dissolved gas than cold water, and large amounts of gas escape upon boiling. So the initially warmer water may have less dissolved gas than the initially cooler water. It has been speculated that this changes the properties of the water in some way, perhaps making it easier to develop convection currents (and thus making it easier to cool), or decreasing the amount of heat required to freeze a unit mass of water, or changing the boiling point. There are some experiments that favor this explanation [10,14], but no supporting theoretical calculations.
3) Convection -- As the water cools it will eventually develop convection currents and a non-uniform temperature distribution. At most temperatures, density decreases with increasing temperature, and so the surface of the water will be warmer than the bottom -- this has been called a "hot top." Now if the water loses heat primarily through the surface, then water with a "hot top" will lose heat faster than we would expect based on its average temperature. When the initially warmer water has cooled to an average temperature the same as the initial temperature of the initially cooler water, it will have a "hot top", and thus its rate of cooling will be faster than the rate of cooling of the initially cooler water at the same average temperature. Got all that? You might want to read this paragraph again, paying careful distinction to the difference between initial temperature, average temperature, and temperature. While experiments have seen the "hot top", and related convection currents, it is unknown whether convection can by itself explain the Mpemba effect.
4) Surroundings -- A final difference between the cooling of the two containers relates not to the water itself, but to the surrounding environment. The initially warmer water may change the environment around it in some complex fashion, and thus affect the cooling process. For example, if the container is sitting on a layer of frost which conducts heat poorly, the hot water may melt that layer of frost, and thus establish a better cooling system in the long run. Obviously explanations like this are not very general, since most experiments are not done with containers sitting on layers of frost.
