GenerateCards.py

import itertools as itt
from collections import deque

# Each element of a sequence can have these values
possible_elements = [0, 1, 2, 3, 4, 5, 6, 7]
element_count = len(possible_elements)

# A sequence contains this many elements
sequence_length = 4

# An iterator for every possible tuple of length "sequence_length"
# with elements selected from "possible_elements"
card_iterator = itt.product(possible_elements, repeat=sequence_length)

# valid cards
card_set = set()

# test each card
for card in card_iterator:

    # create a set containing all the orientations of a card
    # Basically, rotate the sequence and add it to the set.  Do this
    # until each element has a turn appearing at the start of the sequence
    orientation = deque(card)
    orientations = set()
    for i in range(0, sequence_length):
        orientation.rotate(1)
        orientations.add(tuple(orientation))

    # If the number of orientation in the set at this point is not
    # equal to "sequence_length" there are duplicate orientations that can
    # be confused.  These cards are not processed.
    if len(orientations) == sequence_length:

        # Test if any of the orientations are in the valid card set.  This
        # can be done by finding the intersection of valid cards and all
        # the orientations of a single card.  If the intersection is a null
        # the original card can be added to the valid card set.
        setint = orientations.intersection(card_set)
        if len(setint) == 0:
            card_set.add(tuple(orientation))

# print results
for card in card_set:
    print(card)

message = ''.join(['number of cards = ', str(len(card_set))])
print(message)