The digit sum of the year 2007 is 2 + 0 + 0 + 7 = 9, which is a square number. How many years during the twenty-first century have a square digital sum?  Choose the correct choice: A) 13 B) 14 C) 15 D) 16 E) 17
The twenty-first century runs from the year 2001 to 2100 inclusive, so with the   exception of the year 2100, for which the digital sum is three anyway, the first two   digits of all the other years are fixed as 20. Hence for the sum of all the digits to be   square the sum of the last two digits number be two less than a perfect square.   As the maximum sum of the last two digits is 18, the greatest sum will be 20.   Therefore we can obtain digital sums of 4, 9, or 16, with the last two digits adding to   2, 7, or 14 respectively.   4: 2002, 2011, 2020   9: 2007, 2016, 2025, 2034, 2043, 2052, 2061, 2070   16: 2059, 2068, 2077, 2086, 2095   That is, there are sixteen years during the twenty-first century for which the digital   sum is square.   ANSWER:16
<result>D</result>
The digit sum of the year 2007 is 2 + 0 + 0 + 7 = 9, which is a square number. How many years during the twenty-first century have a square digital sum?