import random
def constrained_sum_sample_pos(n, total):
    """Return a randomly chosen list of n positive integers summing to total.
    Each such list is equally likely to occur."""

    dividers = sorted(random.sample(xrange(1, total), n - 1))
    return [a - b for a, b in zip(dividers + [total], [0] + dividers)]

success = False
while True:
    solutions = 0
    correct = False
    while not correct:
        random_values = constrained_sum_sample_pos(4, 40)
        if len(list(set(random_values))) == 4:
            correct = True
            # if 1 in random_values:
              #  correct = True
    print "Testing: ", random_values

    for weight in range (1, 41):
        success = False
        for y in range (0, 4):
            A = random_values[y]
            B = random_values[(y + 1) % 3]
            C = random_values[(y + 2) % 3]
            D = random_values[(y + 3) % 3]
            if A == weight:
                print "{0} == [{1}]".format(str(A), str(weight))
                success = True
            elif A + weight == B:
                print "{0} + [{1}] == {2}".format(str(A), str(weight), str(B))
                success = True
            elif A + weight == C:
                print "{0} + [{1}] == {2}".format(str(A), str(weight), str(B))
                success = True
            elif A + weight == D:
                print "{0} + [{1}] == {2}".format(str(A), str(weight), str(B))
                success = True
            elif A + B == weight:
                print "{0} + {1} == [{2}]".format(str(A), str(B), str(weight))
                success = True
            elif A + B + C == weight:
                print "{0} + {1} + {2} == [{3}]".format(str(A), str(B), str(C), str(weight))
                success = True
            elif A + B + weight == C:
                print "{0} + {1} + [{2}] == {3}".format(str(A), str(B), str(weight), str(C))
                success = True
            elif A + B == weight + C:
                print "{0} + {1} == [{2}] + {3}".format(str(A), str(B), str(weight), str(C))
                success = True
            elif A + B == weight + D:
                print "{0} + {1} == [{2}] + {3}".format(str(A), str(B), str(weight), str(D))
                success = True
            elif A + B + C == D + weight:
                print "{0} + {1} + {2} == {3} + [{4}]".format(str(A), str(B), str(C), str(D), str(weight))
                success = True
            elif A + B + C + weight == D:
                print "{0} + {1} + {2} + [{3}] == {4}".format(str(A), str(B), str(C), str(D), str(weight))
                success = True
            if success is True:
                solutions += 1
                break
        if success is False:
            break
    if solutions > 15:
        raw_input("")

if success == True:
    print "Found: ", random_values