Problem of the Week

Every week Billboard magazine publishes a list of the Top 20 pop songs in the United States.  If the order is never the same in any two consecutive weeks, and no song ever regains any lost popularity (i.e. no song rises in ranking once it starts to drop in ranking) how many consecutive weeks could the same twenty songs remain on the Top 20 list?  

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ã2004 Alberto L. Delgado