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There are infinitely many possible answer.

Pick any 4 numbers, a, b, c and d. And then let the fifth number, e = 300 - (a + b + c+ d)

Then a, b, c, d and e have an average of 300. Since the choice of a, b c and d was arbitrary, there are infinitely many possible answer.

For example, today's date is 22 November 2012 and the local time now is 1123

So let the first four number be 22 , 11 , 12 and 1123

Then the fifth is 300 - (22 + 11 + 12 + 1123) = -868

The average of the 5 numbers is 1/5*(22 + 11 +12 + 1123 -868) = 1/5*300 = 60

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Q: What five numbers have an average of 60?
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