Consider the set (2, 5, 9, 13). Which of these numbers can be tossed out, and for what reason?

We might choose:

• 2 because it’s the only even number.
• 9 because it’s the only non-prime.
• 13 because it doesn’t fit in the sequence A_n – A_n-1 = 1 + (A_n-1 – A_n-2).

“Hence one could toss out either 2, 9 or 13,” observes Marquette University mathematician George R. Sell. “Therefore one should toss out 5 because it is the only number that cannot be tossed out.”

(George R. Sell, “A Paradox,” Pi Mu Epsilon Journal 2:6 [Spring 1957], 278.)