Inspired by this reddit comment thread: http://www.reddit.com/r/programming/comments/cehbe/awesome_lego_robot_monster_chessand_shit_gets/c0s0afu

distinct-colourings-2x2-square.py

class Colouring(object):
    def __init__(self, colouring):
        self.colouring = colouring

    def __eq__(self, other):
        # Two colourings are "equal" (read: "equivalent") if one is a 
        # rotational-shift of the other. (I'm sure there are smarter 
        # ways to do this (this may not even be *right*), but I was in 
        # a hurry, and it seems to work.)
        current = self.colouring
        for i in range(0, len(current)):
            # There's *definitely* cleverer ways of rotating an array
            # in-place, I'm sure. But I was lazy.
            temp = current[1:]
            temp.append(current[0])
            current = temp
            if (current == other.colouring): return True
        return False

    def __ne__(self, other):
        return not self.__eq__(other)

    def __repr__(self):
        return "<%s>" % (self.colouring.__repr__()[1:-1])

class NoDupeList(object):
    # Can't use a set, because objects that are "equal" have to hash to 
    # the same value; and I couldn't think of clever way to do that, quickly.

    def __init__(self, iterable):
        self.list = []
        for x in iterable:
            add = True
            for y in self.list:
                if (x == y): add = False
            if add: self.list.append(x)

    def __repr__(self):
        return self.list.__repr__()

    def __len__(self):
        return self.list.__len__()

    def __iter__(self):
        return self.list.__iter__()

# Some previous lame attempts at "testing"
#print Colouring(["a", "b", "a", "b"]) == Colouring(["a", "b", "a", "b"])
#print Colouring(["a", "b", "a", "b"]) == Colouring(["a", "b", "a", "c"])
#print Colouring(["a", "b", "a", "b"]) == Colouring(["b", "a", "b", "a"])

#print Colouring(["a", "b"]) == Colouring(["b", "a"])
#print NoDupeList([Colouring(["a", "b"]), Colouring(["a", "b"])])
#print NoDupeList([Colouring(["a", "b"]), Colouring(["b", "a"])])

colours = ["a", "b"]
distinct_colourings = NoDupeList([Colouring([w, x, y, z]) for w in colours for x in colours for y in colours for z in colours])

print "\nUsing %s elements: %s" % (len(colours), colours)
print "Creates %s distinct colourings:" % (len(distinct_colourings))
for x in distinct_colourings: print x

colours = ["a", "b", "c"]
distinct_colourings = NoDupeList([Colouring([w, x, y, z]) for w in colours for x in colours for y in colours for z in colours])

print "\nUsing %s elements: %s" % (len(colours), colours)
print "Creates %s distinct colourings:" % (len(distinct_colourings))
for x in distinct_colourings: print x

colours = ["a", "b", "c", "d"]
distinct_colourings = NoDupeList([Colouring([w, x, y, z]) for w in colours for x in colours for y in colours for z in colours])

print "\nUsing %s elements: %s" % (len(colours), colours)
print "Creates %s distinct colourings:" % (len(distinct_colourings))
for x in distinct_colourings: print x

output.txt

Using 2 elements: ['a', 'b']
Creates 6 distinct colourings:
<'a', 'a', 'a', 'a'>
<'a', 'a', 'a', 'b'>
<'a', 'a', 'b', 'b'>
<'a', 'b', 'a', 'b'>
<'a', 'b', 'b', 'b'>
<'b', 'b', 'b', 'b'>

Using 3 elements: ['a', 'b', 'c']
Creates 24 distinct colourings:
<'a', 'a', 'a', 'a'>
<'a', 'a', 'a', 'b'>
<'a', 'a', 'a', 'c'>
<'a', 'a', 'b', 'b'>
<'a', 'a', 'b', 'c'>
<'a', 'a', 'c', 'b'>
<'a', 'a', 'c', 'c'>
<'a', 'b', 'a', 'b'>
<'a', 'b', 'a', 'c'>
<'a', 'b', 'b', 'b'>
<'a', 'b', 'b', 'c'>
<'a', 'b', 'c', 'b'>
<'a', 'b', 'c', 'c'>
<'a', 'c', 'a', 'c'>
<'a', 'c', 'b', 'b'>
<'a', 'c', 'b', 'c'>
<'a', 'c', 'c', 'b'>
<'a', 'c', 'c', 'c'>
<'b', 'b', 'b', 'b'>
<'b', 'b', 'b', 'c'>
<'b', 'b', 'c', 'c'>
<'b', 'c', 'b', 'c'>
<'b', 'c', 'c', 'c'>
<'c', 'c', 'c', 'c'>

Using 4 elements: ['a', 'b', 'c', 'd']
Creates 70 distinct colourings:
<'a', 'a', 'a', 'a'>
<'a', 'a', 'a', 'b'>
<'a', 'a', 'a', 'c'>
<'a', 'a', 'a', 'd'>
<'a', 'a', 'b', 'b'>
<'a', 'a', 'b', 'c'>
<'a', 'a', 'b', 'd'>
<'a', 'a', 'c', 'b'>
<'a', 'a', 'c', 'c'>
<'a', 'a', 'c', 'd'>
<'a', 'a', 'd', 'b'>
<'a', 'a', 'd', 'c'>
<'a', 'a', 'd', 'd'>
<'a', 'b', 'a', 'b'>
<'a', 'b', 'a', 'c'>
<'a', 'b', 'a', 'd'>
<'a', 'b', 'b', 'b'>
<'a', 'b', 'b', 'c'>
<'a', 'b', 'b', 'd'>
<'a', 'b', 'c', 'b'>
<'a', 'b', 'c', 'c'>
<'a', 'b', 'c', 'd'>
<'a', 'b', 'd', 'b'>
<'a', 'b', 'd', 'c'>
<'a', 'b', 'd', 'd'>
<'a', 'c', 'a', 'c'>
<'a', 'c', 'a', 'd'>
<'a', 'c', 'b', 'b'>
<'a', 'c', 'b', 'c'>
<'a', 'c', 'b', 'd'>
<'a', 'c', 'c', 'b'>
<'a', 'c', 'c', 'c'>
<'a', 'c', 'c', 'd'>
<'a', 'c', 'd', 'b'>
<'a', 'c', 'd', 'c'>
<'a', 'c', 'd', 'd'>
<'a', 'd', 'a', 'd'>
<'a', 'd', 'b', 'b'>
<'a', 'd', 'b', 'c'>
<'a', 'd', 'b', 'd'>
<'a', 'd', 'c', 'b'>
<'a', 'd', 'c', 'c'>
<'a', 'd', 'c', 'd'>
<'a', 'd', 'd', 'b'>
<'a', 'd', 'd', 'c'>
<'a', 'd', 'd', 'd'>
<'b', 'b', 'b', 'b'>
<'b', 'b', 'b', 'c'>
<'b', 'b', 'b', 'd'>
<'b', 'b', 'c', 'c'>
<'b', 'b', 'c', 'd'>
<'b', 'b', 'd', 'c'>
<'b', 'b', 'd', 'd'>
<'b', 'c', 'b', 'c'>
<'b', 'c', 'b', 'd'>
<'b', 'c', 'c', 'c'>
<'b', 'c', 'c', 'd'>
<'b', 'c', 'd', 'c'>
<'b', 'c', 'd', 'd'>
<'b', 'd', 'b', 'd'>
<'b', 'd', 'c', 'c'>
<'b', 'd', 'c', 'd'>
<'b', 'd', 'd', 'c'>
<'b', 'd', 'd', 'd'>
<'c', 'c', 'c', 'c'>
<'c', 'c', 'c', 'd'>
<'c', 'c', 'd', 'd'>
<'c', 'd', 'c', 'd'>
<'c', 'd', 'd', 'd'>
<'d', 'd', 'd', 'd'>