Add a fifth number to the set {3,7,9,10} so that the mean is equal to the median of the set.

Show whether or not it is possible to create a set of numbers where the same problem yields more solutions than the above.

(In reply to solution by Charlie)

Nice extension.  You seem to have restricted to positive integers. 

Note the high and low "possible add-ons" are guaranteed to be integers.

Ady pretty much shows how to guarantee the middle number will be an integer:  The original numbers sum to  multiple of 4.  Also you'd need two above and two below the mean.

Posted by Jer on 2014-02-21 01:03:35