The goal is to move the pieces so as to gather them all in the same square - in the minimal number of moves. Chess pieces can move as normal. Additionally, whenever the king and one or more knights are placed in the same square, the player may choose to move the king and one of the knights together from that point on, as a single knight, up to the final gathering point. Moving the knight together with the king counts as a single move.
Given the following setup, what is the minimum number of moves to gather all the pieces together? Provide the path as well as the answer.
Source: USACO training pages - I cannot figure out why my answer appears to be wrong and the site provides no reason for its answer. This is one of 20 cases.