Think logically not mathematically [part-27]

Since the digits of a number have to be from 0-9, the sum of the digits have to be between 0 and 18. The perfect squares between 0 and 18 are 0,1,4,9, and 16.

Due to the constraints of our two digit number being between 11 and 99, we can ignore 0 and 1 as sums of digits, since the largest value we can get for a two digit number would be 10.

For 4, there is 40, 22, 31, and 13

If the sum of the digits add up to 9, the number is a multiple of 9, so we have 11 multiples of 9 up to 99, but the sum of the digits of 99 add up to 18, which isn't a perfect square, and 9 is less than 11, so we have 9 total.

For 16, theres 88, 97, and 79,

Since we have covered every possible sum of digits to produce a perfect square, now we just have to count them.

4+3+9= $\boxed{16}$

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#include <iostream>
int main()
{ int n, k=0;
for(int i=1;i<10;i++)
{
   for(int j=0;j<10;j++)
   {  n=i+j;
      if (n==4)
          { std::cout<<10*i+j<<"\n";
             k++; }
      else if (n==9)
                  { std::cout<<10*i+j<<"\n";
                    k++; }
      else if (n==16)
                   { std::cout<<10*i+j<<"\n";
                     k++; }
     }
}
std::cout<<"Total number of such numbers = "<<k;
return 0;
}

13

18

22

27

31

36

40

45

54

63

72

79

81

88

90

97

Total number of such numbers = 16

MIN : 1+1=2 MAX = 9+9 = 18

Square numbers between 2 & 18 :4,9,16

4 = 4+0, 3+1, 2+2 9 = 9+0, 8+1, 7+2, 6+3, 5+4 16= 9+7, 8+8,

40 13 31 22 / 90 81 18 27 72 36 63 45 54 / 97 79 88 ==> 16 Numbers

I got that right...but i think answer should also be different. For example→ $32=3+2=5$ ....Can also be written as $(\sqrt{5})^{2}$ ...The question does not mention any particular no.

The possible square numbers are 4,9,16. Because sum of and to digits is always less than or equal to 18,since maximum possible sum is 9+9=18. So, now the possible numbers are 13,22,31,40 as a sum of 4,and 18,27,36,45,54,63,72,81,90 as a sum of 9 and 79,97 as a sum of 16. So the total possible numbers are 15.