For $n$ a natural number, consider the sequence of $n$ rational numbers $n/1, n/2, n/3, \dots, n/n$. Round each to the nearest integer to obtain sequence of $n$ integers. How many are odd?

In this talk we will see how knowledge of sums of squares and a result of Gauss will help to lead us to a somewhat surprising result. Time permitting, we will discuss similar results.