Abstract: This article answers some questions generated by students in a developmental mathematics course at Bronx Community College. They noticed that (12)(21) = 252, (112)(211) = 23632, and (221)(122) = 26962. That is, the product is sometimes "symmetric" in the digits when a number is multiplied by the number obtained by writing its digits backward. On the other hand, the backward product (13)(31) = 403 is not symmetric. This paper gives a simple yet interesting condition on the digits of a given number which determines whether or not its backward product is symmetric.
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