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.*

Usually questions tend to ask what is the smallest number of balls to swap. However, this question asks what is the greatest number of balls to swap.

As the phrase, greatest number, is mentioned in the question, it demands people to move also the unnecessary move. The prominent one should be the black. One must move the black ball since it could increase the number of unnecessary moves.