four_integers_sum_63.c

/*

    four_integers_sum_63.c

    Task:

    If a, b, c, d are positive integers, with a sum of 63,
    what is the maximum value of ab + bc + cd ?

    Answer: maximum sum is 991
    for a=1, b=30, c=31, d=1
    or
    for a=1, b=31, c=30, d=1


    You can find all my C programs at Dragan Milicev's pastebin:

    https://pastebin.com/u/dmilicev

    https://www.facebook.com/dmilicev

*/

#include <stdio.h>

int main(void)
{
    int a, b, c, d, sum, max_sum=0, changed_max_sum=0;

    // maximum value for one integer is 60 when rest three integers are equal to 1.
    for(a=1; a<=60; a++)
        for(b=1; b<=60; b++)
            for(c=1; c<=60; c++)
                for(d=1; d<=60; d++)
                {
                    if ( a+b+c+d == 63 )
                    {
                        sum = a*b + b*c + c*d;

                        if (max_sum < sum)
                        {
                            max_sum = sum;
                            changed_max_sum = 1;
                        }

                        if ( changed_max_sum )
                        {
                            printf("\n Max sum is %3d  for  a = %d , b = %d , c = %d , d = %d \n", max_sum, a, b, c, d );
                            changed_max_sum = 0;
                        }
                    }
                }

    return 0;

} // main()