Posted by **Rock** on Thursday, April 15, 2010 at 3:55am.

Suppose a1, a2, . . . , an is a list of n numbers with the following properties:

The sum of those n numbers is 500.

The sum of the smallest three of those numbers is 48.

The sum of the largest two of those numbers is 35.

(Note: There might be some repetitions among the numbers ak in that list.)

(a) What are the possible values of n ? Explain your reasoning.

(b) Can each of those values of n occur if we require all the numbers ak to be integers?

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