You have 15 pool balls arranged in a triangle.
What is the greatest number of balls you will ever have to swap in order to ensure that they are all in the correct position at the start of the game?
An allowable position is either the one in the diagram above, the same position mirrored left-to-right, or either of these arrangements with the red and yellow balls switched.
The solving of the question itself is tedious. It needs those people that are patient to solve the puzzle.
In order to increase the number of balls' movement, the shifting out of the ball should be counted as one step and then followed by another ball to fill up the position and that should be considered as another step. After that, shifting the ball that is outside to fill up the triangle to be the other step.
The solution is not so easy, but tedious.