You may wish to explore Equal Averages before tackling this problem.
Can you find sets of five positive whole numbers that satisfy the following properties?
Mode < Median < Mean
Mode < Mean < Median
Mean < Mode < Median
Mean < Median < Mode
Median < Mode < Mean
Median < Mean < Mode
Not all of them can be done! Can you explain why?
Would it help if you could use six numbers instead of just five?