PRINCESS='2'
TIGER='1'
EMPTY='0'

def generate_variants(n):
    for i in range(2**(n-1)):
        s = bin(i)[2:].zfill(n-1)
        for p in range(n):
            yield ' ' + s[:p] + PRINCESS + s[p:]

v = []

def k(n):
    if n==1: return v.find(PRINCESS) % 2 == 1
    elif n==2: return v[2] == EMPTY
    elif n==3: return k(5) or not k(7)
    elif n==4: return not k(1)
    elif n==5: return k(2) or k(4)
    elif n==6: return not k(3)
    elif n==7: return v[7] != PRINCESS
    elif n==8: return v[8] == TIGER and v[9] == EMPTY
    elif n==9: return v[9] == TIGER and not k(6)

for v in generate_variants(9):

    good = v[8] != EMPTY

    for i in range(1,10):
        good = good and (
                (v[i] == PRINCESS and k(i))
                or (v[i] == TIGER and not k(i))
                or (v[i] == EMPTY)
            )

    if good:
        print(v)

D:\>python 1.py
 210000011
 210010011
 210100011
 210110011
 211000011
 211010011
 211100011
 211110011