There are 15 marbles with different colors. Their weight are all different, but the only way to rank them is by using a three-tray scale. The scale accepts exactly 3 marbles, one in each tray, and only indicates which of the three weighs the most, the least and consequently the one in between.
What is the least number of weighings necessary to rank the 15 marbles from lightest to heaviest ?
P.S. I have a strategy that ranks the 15 marbles, but I do not have a proof that no strategy can ensure it with fewer weighings.