Find amount of numbers that are between 1 and 100 inclusive, when converted to binary have a digit sum of less than 5?

Question

Two natural numbers have a sum of less than 100 and are greater than one.

John knows the product of the numbers and Jacob knows the sum of numbers.

The following conversation takes place between them:
John: ‘I am not aware of those numbers.’
Jacob: ‘I knew you wouldn’t be. I am not aware myself.’
John: ‘Now I know them!’
Jacob: ‘Now I know them, too!’

What are the two numbers?

Answer 1

There are 87 decimal numbers from 1 to 100 (including 1 and 100)
That have their binary version's digits add upto 4 or as given in the question less than 5.

Comments

Here is the c code I used.
#include <stdio.h>
#include<math.h>
int main ()
{
    int a,b,c,d,count;
    count=0;
    for (a=1;a<101;a++)
    {
        b=a;
        d=0;
        while (b>0)
        {
            c=b%2;
            b=b/2;
            d=d+c;
        }
       if (d<5)
        {
            count=count+1;
        }
    }
    
   printf("There are %d many decimal numbers which have thier binary version's digits add upto or lesser than 5",count);
    
}

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i have yet to study the listing but KUDOS