The 7-Eleven problem (idea)

In general, finding four numbers like this is can be expressed by the equation, a+b+c+d=a*b*c*d/1000000, where a, b, c, d are all positive integers.

Unfortunately, I don't know how to solve that, so like all good Computer Scientists, I use the brute force method:

#include <stdio.h>
#include <limits.h>

int main()
{
    unsigned a, b, c, d;
    
    for(a=4; a<=UINT_MAX; a++)
        for(b=3; b<=a; b++)
            for(c=2; c<=b; c++)
                for(d=1; d<=c; d++)
                    if((a+b+c+d)*1000000 == a*b*c*d)
                        printf("%4.2f: %4.2f, %4.2f, %4.2f, %4.2f\n",
                               (a+b+c+d)/100.0,
                               a/100.0, b/100.0, c/100.0, d/100.0);
    return 0;
}

Some numbers of note: 6.44, the smallest number that works, 6.75, the first number with two solutions, 7.20, the first number with three solutions, 7.56, the first with four, 8.10, the first with five, ... phew, I could go on all night! (also, 10.89 - that's just a cool number, there)