If the toppest height is 9, what are the possible arrangement? Answers: pile 1 : 5, 4; pile 2 : 5, 4; pile 3 : 3, 3, 3. Wait. We still have an extra 5 m tall barrel at hand. Which pile should we put it on? Nowhere without breaking the premise that none of the piles is taller than 9. In fact, even 10 is impossible.
The other way to look at this problem is to calculate the every height for the three piles = (15 + 8 + 9)/3 =10.6. So the tallest pile has to be at least 11 m tall.