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There are infinitely many sets.

Consider the sets: {16}, {16, 16}, {16, 16, 16}, {16, 16, ... , 16} etc.

It is easy to see that the mean, i each case, will be 16.

Then, leaving aside the first set, add one to any number and subtract 1 from any number bigger than 1. The mean of this new set will also be 16. And you can keep going.

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Q: What set of positive numbers have the mean of 16?
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