The number 61 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?  Choose the correct choice from the following answers
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 61: 1, 4, 9, 16, 25, 36, 49.   Now, 61 should be the sum of 3 of those 7 numbers. Also to simplify a little bit trial and error, we can notice that as 61 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 61 equals to 9+16+36=3^2+4^2+6^2=61 --&gt; 3+4+6=13.   Answer: 13.
<result>E</result>
The number 61 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?