The number 49 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 options:
A) 11 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 49: 1, 4, 9, 16, 25, 36, 49..   Now, 49 should be the sum of 3 of those 7 numbers. Also to simplify a little bit trial and error, we can notice that as 49 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 49 equals to 4+9+36=2^2+3^2+6^2=49 --&gt; 2+3+6=11.   11nswer: 11.
<result>A</result>
The number 49 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?