An honestly unfinished answer
Hot Water Sometimes Freezes First, and Nobody Is Sure Why
Put hot water and cold water in the freezer and the hot one occasionally reaches ice first. It has been reported for two thousand years, and there is still no agreed explanation.
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Step 1 of 5
A schoolboy making ice cream refused to drop it.
In 1963 Erasto Mpemba, a Tanzanian student, put his hot ice-cream mix in the freezer rather than wait for it to cool, and it froze before his classmates' cooled mixes. His teacher told him he was mistaken. He kept asking, eventually asked a visiting physicist, and the two of them published it in 1969.
Aristotle described the same thing, and so did Francis Bacon and Descartes. Mpemba's contribution was refusing to let it be dismissed again.
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Step 2 of 5
The reason it is startling is that cooling is supposed to be a one-way trip.
This is the whole puzzle in four pictures. To reach 0°C, hot water has to pass through every temperature the cold water starts at. At that moment it looks identical — same liquid, same container, same freezer. If it then wins, something must be different about it that a thermometer does not show.
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Step 3 of 5
There is no shortage of explanations. That is the problem.
Evaporation removes some of the hot water, leaving less to freeze. Convection currents set up by heating may cool it faster. Dissolved gases driven off by boiling change how it behaves. Frost under the container melts, improving contact with the shelf. Each is real; none accounts for every reported case.
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Step 4 of 5
Careful experiments keep disagreeing with each other.
A 2016 study ran the comparison with tight controls and found no reliable effect at all, concluding it depends almost entirely on where you put the thermometer. Other groups, using different vessels and definitions of frozen, still see it. When the result changes with the apparatus, the honest reading is that the question has not been asked precisely enough yet.
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Step 5 of 5
An unresolved answer is still an answer.
It would be easy to end this page with a tidy mechanism, and plenty of sources do. But the useful thing here is watching what an unfinished piece of science actually looks like. An effect too stubborn to dismiss, several partial explanations, and experiments that do not yet agree. Most of science looks like this before it looks tidy.
The short version
Hot water sometimes freezes before cold, several real mechanisms could contribute, no one of them explains every case, and careful experiments still disagree — the question is genuinely open.
Try it yourself
Run it yourself with two identical cups, one hot and one cool, and write down exactly what you mean by frozen before you start. Deciding that in advance is most of the difficulty.