http://www.reddit.com/r/math/comments/r6qbl/cant_figure_out_if_this_puzzle_is_solvable_or_not/

gistfile1.py

def checkdist(a,b,c,d,e,f,g):
    array = sorted([abs(0-a),abs(1-b),abs(2-c),abs(3-d),abs(4-e),abs(5-f),abs(6-g)])
    i = 0
    goodanswer = 1
    while (i + 1 < len(array)):
        if (array[i] == array[i + 1]):
            goodanswer = 0
        i += 1
    if (goodanswer == 1):
        print a,b,c,d,e,f,g,array,"GOOD"
    else:
        print a,b,c,d,e,f,g,array,"BAD"

for a in range(7):
    for b in range(7):
        if (a != b):
            for c in range(7):
                if (a != c and b != c):
                    for d in range(7):
                        if (a != d and b != d and c != d):
                            for e in range(7):
                                if (a != e and b != e and c != e and d != e):
                                    for f in range(7):
                                        if (a != f and b != f and c != f and d != f and e != f):
                                            for g in range(7):
                                                if (a != g and b != g and c != g and d != g and e != g and f != g):
                                                    checkdist(a,b,c,d,e,f,g)