find_slots.py

from itertools import permutations


def diff(a, b):
    return abs(a - b) - 1


def all_different(indices):
    first, second, third, fourth, fifth = indices
    size = len({diff(first, second), diff(first, third), diff(first, fourth), diff(first, fifth),
     diff(second, third), diff(second, fourth), diff(second, fifth),
     diff(third, fourth), diff(third, fifth),
     diff(fourth, fifth)})
    if size == 10:
        return True
    return False


def find_if_suitable(l):
    first = l.index('u')
    second = l.index('a')
    third = l.index('b')
    fourth = l.index('c')
    fifth = l.index('e')
    indices = [first, second, third, fourth, fifth]
    return all_different(indices)


cols = ['u', 'a', 'b', 'c', 'e', 0, 0, 0, 0, 0, 0, 0]

#print(len(cols))
#find_indices(cols)

import sys

seen = set()

for vec in permutations(cols):
    if find_if_suitable(vec):
        s = str(vec)
        s = s.replace('a','u')
        s = s.replace('b','u')
        s = s.replace('c','u')
        s = s.replace('e','u')
        if s not in seen:
            seen.add(s)
            print(s)


"""
(python_virtualenv) root@jcbose:~# python find_solutions.py
('u', 'u', 0, 0, 'u', 0, 0, 0, 0, 'u', 0, 'u')
('u', 0, 'u', 0, 0, 0, 0, 'u', 'u', 0, 0, 'u')
('u', 0, 'u', 0, 0, 0, 0, 'u', 0, 0, 'u', 'u')
('u', 0, 0, 'u', 'u', 0, 0, 0, 0, 'u', 0, 'u')
(python_virtualenv) root@jcbose:~#

"""