Math Questions  - 
 
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+LuVbeingYoungster My first guess was just glancing at it...  I've analyzed the problem and found not only the solution 36, but also the general mathematical model for this equation which is 4n².  In other words I can now quickly solve it for any number...

Breaking it down we can determine the algorithm by hand.
1*1 + 1*1 + 1*1 +1*1 = 4
2*2 + 2*2 + 2*2 + 2*2 = 16
3*3 + 3*3 + 3*3 + 3*3 = 36

We can thus simplify the algorithm and condense it into a mathematical model for n. 

Looking at line 3, there are 4 terms each term uses n².
3² + 3² + 3² + 3²

We could represent this quantity using factorization...
4 * 3²

Now we can write a general solution to model n
f(n)= 4 n²

Proof by example
n(1) =  4(1)² = 4*1 = 4
n(2) =  4(2)² = 4*4 = 16
n(3) =  4(3)² = 4*9 = 36
n(4) =  4(4)² = 4*16 = 64
n(5) =  4(5)² = 4*25 = 100
 
+LuVbeingYoungster I think you'll like my new solution, it is not only correct but it takes it a step further and devises a general mathematical model which is 100% accurate.  Let's see any one else arrive at that :)
 
can you solve the series as:
1 , 7, 17,31,49,71,?

What should be the next number
 
+sanjeet choudhary That's an easy one
If we look at how much is being added each time we see the pattern 6 10 14 18 22.  So each time you are adding for more to the previous summation.


Thus 22 + 4 = 26
71+26 = 97

For fun I'll try to find that equations general solution...
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It's 18!

11*11 = 121 - add the digits = 4
22*22 = 484 - add the digits = 16
33*33 = 1089 - add the digits =18!
 
11 x 11= 121 =1+2+1 =4
22 x 22 =484= 4+8+4 = 16
33 x33 = 1089 
1+0+8+9 = 18
 
(1plus1 =2 ) x (1plus1=2)= 4
(2 plus 2= 4) x (2 plus 2=4)= 16
(3 plus 3= 6) x (3 plus 3=6)= 36
 
18 (since 11x11 = 121 [sum of digits =4] 22x22 = 484 [sum of digits = 16] 33x33 = 1089 [sum of digits = 18])
 
How you are saying it is 81? i cant understand how it will come as 81.... i hope 36 is correct upto 3*3.....

If it is given as 33*33 = 18 then 44*44=?? it would be calculated as philip hadkins suggested.... So AFA my knowledge 36 and 81 correct :). Hope i am correct
 
11x11=121, Digital index of 121 = 4
22x22=484, Digital index of 484 = 16
33x33=1089, Digital index of 1089 = 18
Hence, answer = 18
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