4-rings or 4-squares puzzle

You are encouraged to solve this task according to the task description, using any language you may know.
Task

Replace       a, b, c, d, e, f,   and
  g        with the decimal
digits   LOW   ───►   HIGH

such that the sum of the letters inside of each of the four large squares add up to
the same sum.

            ╔══════════════╗      ╔══════════════╗
            ║              ║      ║              ║
            ║      a       ║      ║      e       ║
            ║              ║      ║              ║
            ║          ┌───╫──────╫───┐      ┌───╫─────────┐
            ║          │   ║      ║   │      │   ║         │
            ║          │ b ║      ║ d │      │ f ║         │
            ║          │   ║      ║   │      │   ║         │
            ║          │   ║      ║   │      │   ║         │
            ╚══════════╪═══╝      ╚═══╪══════╪═══╝         │
                       │       c      │      │      g      │
                       │              │      │             │
                       │              │      │             │
                       └──────────────┘      └─────────────┘

Show all output here.



   Show all solutions for each letter being unique with
        LOW=1     HIGH=7

   Show all solutions for each letter being unique with
        LOW=3     HIGH=9

   Show only the   number   of solutions when each letter can be non-unique
        LOW=0     HIGH=9



Related task

 Solve the no connection puzzle


#lang racket
 
(define solution? (match-lambda [(list a b c d e f g) (= (+ a b) (+ b c d) (+ d e f) (+ f g))]))
 
(define (fold-4-rings-or-4-squares-puzzle lo hi kons k0)
  (for*/fold ((k k0))
            ((combination (in-combinations (range lo (add1 hi)) 7))
             (permutation (in-permutations combination))
             #:when (solution? permutation))
            (kons permutation k)))
 
(fold-4-rings-or-4-squares-puzzle 1 7 cons null)
(fold-4-rings-or-4-squares-puzzle 3 9 cons null)
(fold-4-rings-or-4-squares-puzzle 0 9 (λ (ignored-solution count) (add1 count)) 0)