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It is easy to prove that such a set of numbers cannot exist.

If the median is -1 and the mean is different from the median, then there must be at least one number that is less than or equal to -1. Then, if the range is 6, the largest number can only be 5.

If the largest number is 5 and the mean is 5, then all the numbers must be 5. That is not possible because there is at least one that is -1 or smaller.

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