Task: 4-rings or 4-squares puzzle
Go: package main

import "fmt"

func main(){
	n, c := getCombs(1,7,true)
	fmt.Printf("%d unique solutions in 1 to 7\n",n)
	fmt.Println(c)
	n, c = getCombs(3,9,true)
	fmt.Printf("%d unique solutions in 3 to 9\n",n)
	fmt.Println(c)
	n, _ = getCombs(0,9,false)
	fmt.Printf("%d non-unique solutions in 0 to 9\n",n)
}

func getCombs(low,high int,unique bool) (num int,validCombs [][]int){
	for a := low; a <= high; a++ {
		for b := low; b <= high; b++ {
			for c := low; c <= high; c++ {
				for d := low; d <= high; d++ {
					for e := low; e <= high; e++ {
						for f := low; f <= high; f++ {
							for g := low; g <= high; g++ {
								if validComb(a,b,c,d,e,f,g) {
									if !unique || isUnique(a,b,c,d,e,f,g) {
										num++
										validCombs = append(validCombs,[]int{a,b,c,d,e,f,g})
									}
								}
							}
						}
					}
				}
			}
		}
	}
	return
}
func isUnique(a,b,c,d,e,f,g int) (res bool) {
	data := make(map[int]int)
	data[a]++
	data[b]++
	data[c]++
	data[d]++
	data[e]++
	data[f]++
	data[g]++
	return len(data) == 7
}
func validComb(a,b,c,d,e,f,g int) bool{
	square1 := a + b
	square2 := b + c + d
	square3 := d + e + f
	square4 := f + g
	return square1 == square2 && square2 == square3 && square3 == square4
}

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);
    }
}