It’s common for the Putnam exam to include problems that involve the number of the current year in some way. (There weren’t any such problems on the past exam, but in 2011 there were two, A1 and B4.) Usually these problems don’t rely on any specific property of the number, but they simply use the number as a stand-in for “n”, so as to make the problem a little bit more concrete; for example, for either of the 2011 problems, you could replace the number 2011 with any other number without changing the nature of the problem.

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