Problem
Find a set A of five numbers that satisifies mean(A) = 10 and median(A) = 9.
Progress
The only method I can think of here is brute force, which hasn't yielded any results for me yet. I could probably write a small script that does it, but I have a feeling there's a more elegant way of doing it.
Any tips and/or solution appreciated!
Best Answer
easiest approach - let median be one of the numbers, then you have $a,b,9,x,y$ where $a \le b < 9 < x \le y$. Note that the average constraint means that $$ a + b + x + y = 41 $$ and now pick any 4 subject to above constraints...