The number 46 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? Answers
A) 17
B) 16
C) 15
D) 10
E) 13
I think brute force with some common sense should be used to solve this problem.   Write down all perfect squares less than 46: 1, 4, 9, 16, 25, 36.   Now, 46 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 46 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 46 equals to 1+9+36=1^2+3^2+6^2=46 --&gt; 1+3+6=10.   Answer: 10.
<result>D</result>
The number 46 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?