Task: 4-rings or 4-squares puzzle
C: #include <stdio.h>

#define TRUE 1
#define FALSE 0

int a,b,c,d,e,f,g;
int lo,hi,unique,show;
int solutions;

void
bf()
{
    for (f = lo;f <= hi; f++)
        if ((!unique) ||
           ((f != a) && (f != c) && (f != d) && (f != g) && (f != e)))
            {
            b = e + f - c;
            if ((b >= lo) && (b <= hi) &&
                   ((!unique) || ((b != a) && (b != c) &&
                   (b != d) && (b != g) && (b != e) && (b != f))))
                {
                solutions++;
                if (show)
                    printf("%d %d %d %d %d %d %d\n",a,b,c,d,e,f,g);
                }
            }
}


void
ge()
{
    for (e = lo;e <= hi; e++)
        if ((!unique) || ((e != a) && (e != c) && (e != d)))
            {
            g = d + e;
            if ((g >= lo) && (g <= hi) &&
                   ((!unique) || ((g != a) && (g != c) &&
                   (g != d) && (g != e))))
                bf();
            }
}

void
acd()
{
    for (c = lo;c <= hi; c++)
        for (d = lo;d <= hi; d++)
            if ((!unique) || (c != d))
                {
                a = c + d;
                if ((a >= lo) && (a <= hi) &&
                   ((!unique) || ((c != 0) && (d != 0))))
                    ge();
                }
}


void
foursquares(int plo,int phi, int punique,int pshow)
{
    lo = plo;
    hi = phi;
    unique = punique;
    show = pshow;
    solutions = 0;

    printf("\n");

    acd();

    if (unique)
        printf("\n%d unique solutions in %d to %d\n",solutions,lo,hi);
    else
        printf("\n%d non-unique solutions in %d to %d\n",solutions,lo,hi);
}

main()
{
    foursquares(1,7,TRUE,TRUE);
    foursquares(3,9,TRUE,TRUE);
    foursquares(0,9,FALSE,FALSE);
}

Java: import java.util.Arrays;

public class FourSquares {
    public static void main(String[] args) {
        fourSquare(1, 7, true, true);
        fourSquare(3, 9, true, true);
        fourSquare(0, 9, false, false);
    }

    private static void fourSquare(int low, int high, boolean unique, boolean print) {
        int count = 0;

        if (print) {
            System.out.println("a b c d e f g");
        }
        for (int a = low; a <= high; ++a) {
            for (int b = low; b <= high; ++b) {
                if (notValid(unique, a, b)) continue;

                int fp = a + b;
                for (int c = low; c <= high; ++c) {
                    if (notValid(unique, c, a, b)) continue;
                    for (int d = low; d <= high; ++d) {
                        if (notValid(unique, d, a, b, c)) continue;
                        if (fp != b + c + d) continue;

                        for (int e = low; e <= high; ++e) {
                            if (notValid(unique, e, a, b, c, d)) continue;
                            for (int f = low; f <= high; ++f) {
                                if (notValid(unique, f, a, b, c, d, e)) continue;
                                if (fp != d + e + f) continue;

                                for (int g = low; g <= high; ++g) {
                                    if (notValid(unique, g, a, b, c, d, e, f)) continue;
                                    if (fp != f + g) continue;

                                    ++count;
                                    if (print) {
                                        System.out.printf("%d %d %d %d %d %d %d%n", a, b, c, d, e, f, g);
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        if (unique) {
            System.out.printf("There are %d unique solutions in [%d, %d]%n", count, low, high);
        } else {
            System.out.printf("There are %d non-unique solutions in [%d, %d]%n", count, low, high);
        }
    }

    private static boolean notValid(boolean unique, int needle, int... haystack) {
        return unique && Arrays.stream(haystack).anyMatch(p -> p == needle);
    }
}