2012/13 AHSMC Part 1 Problem 12

Let the smallest and the largest numbers Weifeng writes down be $n^2$ and $m^2$ respectively. Since they are the ends of a block of $28$ consecutive numbers, $(m + n)(m - n) = m^2 - n^2 = 27$. We may have $m + n = 27$ and $m - n = 1$, whereby $m = 14$ and $n = 13$. We may have $m + n = 9$ and $m - n = 3$, whereby $m = 6$ and $n = 3$. Thus the smallest number Weifeng writes down may be $3^2 = 9$ or $13^2 = 169$. The answer is (E).