code_breaker.py

#####
# The sum of the middle two digits is a Square Number.
# The sum of the middle four digits is a Cube number
# The net difference between the first and tenth digit is 2
# The net difference between the second and ninth digit is 3
# The net difference between the third and eighth digit is 4
# The sum of the first five digits is a Prime number
# The sum of the last five digits is a Triangular number
# The sum of the digits in odd positions (first, third, fifth, seventh and ninth digits) is an Odd number
# The digit 4 is in first 5 positions
#####

def check1(code):
    return code[4] + code[5] in {1, 4, 9, 16}

def check2(code):
    return code[3] + code[4] + code[5] + code[6] in {1, 8, 27}

def check3(code):
    return abs(code[0] - code[9]) == 2

def check4(code):
    return abs(code[1] - code[8]) == 3

def check5(code):
    return abs(code[2] - code[7]) == 4

def check6(code):
    return (code[0] + code[1] + code[2] + code[3] + code[4]) in {5, 7, 11, 13, 17, 19, 23, 29, 31}

def check7(code):
    return (code[5] + code[6] + code[7] + code[8] + code[9]) in {6, 10, 15, 21, 28}

def check8(code):
    return (code[0] + code[2] + code[4] + code[6] + code[8]) % 2 != 0

def check9(code):
    return 4 in {code[0], code[1], code[2], code[3], code[4]}

def permute(code):
    if len(code) == 2:
        return [code, code[1] + code[0]]
    codes = []
    new_code = code
    while True:
        codes += map(lambda p: new_code[0] + p, permute(new_code[1:]))
        new_code = new_code[1:] + new_code[0]
        if new_code == code:
            break
    return codes

def check(code):
    return (check1(code) and
            check2(code) and
            check3(code) and
            check4(code) and
            check5(code) and
            check6(code) and
            check7(code) and
            check8(code) and
            check9(code))

if __name__ == '__main__':
    i = 0
    for code in permute('0123456789'):
        if i % 100000 == 0:
            print code
        i += 1
        if check(map(int, code)):
            print 'code found: %s' % code
            exit(0)
    print 'no code found'