Calculate the answer to this puzzle: https://i.stack.imgur.com/4MMS7.jpg

puzzle.py

# Build a list of all possible combinations
a = []
for i in range(0, 10):
    for j in range(0, 10):
        for k in range(0, 10):
            a.append('{}{}{}'.format(i, j, k))

# For each of the possible answers, check the five constraints
for v in a:
    pass_1 = \
        (v[0] == '6' and '8' not in v and '2' not in v) or \
        (v[1] == '8' and '6' not in v and '2' not in v) or \
        (v[2] == '2' and '6' not in v and '8' not in v)
    pass_2 = \
        ((v[1] == '6' or v[2] == '6') and '1' not in v and '4' not in v) or \
        ((v[0] == '1' or v[2] == '1') and '6' not in v and '4' not in v) or \
        ((v[0] == '4' or v[1] == '4') and '6' not in v and '1' not in v)
    pass_3 = \
        ((v[1] == '2' or v[2] == '2') and (v[0] == '0' or v[2] == '0') and '6' not in v) or \
        ((v[0] == '0' or v[2] == '0') and (v[0] == '6' or v[1] == '6') and '2' not in v) or \
        ((v[1] == '2' or v[2] == '2') and (v[0] == '6' or v[1] == '6') and '0' not in v)
    pass_4 = '7' not in v and '3' not in v and '8' not in v
    pass_5 = \
        ((v[1] == '3' or v[2] == '3') and '8' not in v and '0' not in v) or \
        ((v[0] == '8' or v[2] == '8') and '3' not in v and '0' not in v) or \
        ((v[0] == '0' or v[1] == '0') and '3' not in v and '8' not in v)
    if pass_1 and pass_2 and pass_3 and pass_4 and pass_5:
        print(v)