Bulgarian Solitaire

Choose a number n, then drag the 15 boxes into columns.
Note that one column can hold multiple boxes.
Click "Play" to simulate the Bulgarian Solitaire process:
here one box is taken from each non-empty column to form a new column.

Will this process always converge?

Container

Columns

Find out more about Bulgarian Solitaire on Wikipedia. I learned of this game from Akash Kumar, who very kindly walked me through the argument found in Peter Winkler's beautiful puzzle book, available here. The game was introduced by Martin Gardner.