There's an important confusion you need to clear up in this question: the calories used to describe the energy content of food are actually KILOcalories, that is, one food calorie is enough to raise 1 cc of water by 1000 degrees C, not by 1 degree. So to lose 9 lb of weight on the proposed plan, you'd need to drink 1,000 litres of ice water, which would be very uncomfortable and possibly dangerous.
[Editor: To put it another way, your scheme might work, but you are off by a factor of 1000. Hence, in the perfect case, drinking one litre of ice water would lower your weight by .009 pounds, or 0.14 ounces, which is about 4 grams--almost insignificant compared to the 2.2lb of water. That would be the answer if there was no other source of heat but calories in body fat. In reality, many of those calories would come from the ambient environment, not from burning fat, so you'd probably actually lose about a gram of weight by drinking a litre of ice water. A paper clip weighs about one gram.]
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