The number 70 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? Select.
A) 17  B) 16  C) 15  D) 14  E) 13
I think brute force with some common sense should be used to solve this problem.   Write down all perfect squares less than 70: 1, 4, 9, 16, 25, 36, 49, 64.   Now, 70 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 70 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).   We can find that 60 equals to 9+25+36=3^2+5^2+6^2=70 --&gt; 3+5+6=14.   Answer: 14.
<result>D</result>
The number 70 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?