Finding the largest palindrome of the product of two three digit numbers problem

Question

So on Project Euler the Problem 4 states the following:

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 99.

Find the largest palindrome made from the product of two 3-digit numbers.

I have tried the following:

    #include <stdio.h>
    #include <stdlib.h>

    int check(int result)
    {
        char b[7];
        sprintf(b, "%d", result);
        if (b[0] == b[5] && b[1] == b[4] && b[2] == b[3])
        {
            return 1;
        }
        else 
        {
            return 0;
        }
    }

    int main () {
        int i;
        int g;
        int final;
        for (i = 999; i > 99; i--)
        {
            for (g = 999; g > 99; g--)
            {
                if (check(g*i) == 1)
                {
                    final = g*i;
                    goto here;
                }
            }
        }
        here:
        printf("%d", final);
}

But, this does not work. Instead of the right answer, I get 580085, which I guess is a palindrome at least, but still not the right answer.

Let me explain my program starting from int main:

1. int i and int g are my multipliers. They are those two three digit numbers.
2. int final is the number that will store the largest palindrome.
3. I start two for loops going to down to get every number possibility.
4. I get out of the loop using a goto when the first palindrome is reached(probably should not but, it doesn't effect a small program like this too much).
5. The first palindrome should be the biggest one possible since I am counting down from the top.

Let me now explain my check:

1. First off since these are two three digit numbers multiplying together to determine the size a char would need to be to hold that value I went to a calculator and multiplied 999 * 999 and it ended up being 6 then I need to add one because I found out from one the questions I posted earlier that sprintf puts a \0 character at the end.
2. Ok, now that I have a char and all, I copied result (which i*g in int main) and put it in char b[7].
3. Then I just checked b to see if it equalled it self with by hard coding each slot I needed to check for.
4. Then I returned accordingly, 1 for true, and 2 for false.

This seems perfectly logical to me but, it does not work for some weird reason. Any hints?

Answer 1

This assumption is wrong:

The first palindrome should be the biggest one possible since I am counting down from the top.

You will check 999*100 = 99900 before 998*101 = 100798, so clearly you can´t count on that.