DATES = ['May 15',    'May 16',    'May 19',
        'June 17',   'June 18',
        'July 14',   'July 16',
      'August 14', 'August 15', 'August 17']

def Month(date): return date.split()[0]

def Day(date):   return date.split()[1]

Month('May 15')

Day('May 15')

def tell(part, possible_dates=DATES):
    "Cheryl tells a part of her birthdate to someone; return a new list of possible dates that match the part."
    return [date for date in possible_dates if part in date]

def know(possible_dates):
    "A person knows the birthdate if they have exactly one possible date."
    return len(possible_dates) == 1

tell('May')

tell('15')

know(tell('15'))

def cheryls_birthday(possible_dates=DATES):
    "Return a list of the possible dates for which statements 3 to 5 are true."
    return filter(statements3to5, possible_dates)

def statements3to5(date): return statement3(date) and statement4(date) and statement5(date)

## TO DO: define statement3, statement4, statement5

def statement3(date):
    "Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too."
    possible_dates = tell(Month(date))
    return (not know(possible_dates) 
            and all(not know(tell(Day(d)))
                    for d in possible_dates))

statement3('May 15')

filter(statement3, DATES)

def statement4(date):
    "Bernard: At first I don't know when Cheryl's birthday is, but I know now."
    at_first = tell(Day(date))
    return (not know(at_first)
            and know(filter(statement3, at_first)))

filter(statement4, filter(statement3, DATES))

def statement5(date):
    "Albert: Then I also know when Cheryl's birthday is."
    return know(filter(statement4, tell(Month(date))))

cheryls_birthday()

know(cheryls_birthday())