Priority sampling is an efficient method of selecting a representative set of samples from a large, non-repeating stream of weighted data (such as, for example, the TCP/IP packets that pass through a router over the course of a year). At the Joint Meetings in San Francisco (Jan 13-16, 2010), Knuth posed a combinatorial problem inspired by (if not directly related to) priority sampling. I'll describe this problem, and a nice solution that I found. At present it's unclear to me whether the result is actually applicable to priority sampling, but I'll explain the connection if I can figure it out in time!