FizzBuzzWithoutNumbers

ZERO = None

def succ(prior):
  return [prior]

def pred(x):
  for val in x:
    return val
  raise Exception("Nope")

ONE = succ(ZERO)
TWO = succ(ONE)
THREE = succ(TWO)
FOUR = succ(THREE)
FIVE = succ(FOUR)
SIX = succ(FIVE)
SEVEN = succ(SIX)
EIGHT = succ(SEVEN)
NINE = succ(EIGHT)
TEN = succ(NINE)

def add(a, b):
    x = a
    y = b
    while x is not None:
        x = pred(x)
        y = [y]
    return y

def multiply(a,b):
    x = a
    y = None
    while x is not None:
      x = pred(x)
      y = add(y, b)
    return y

def roman_digits_pattern(lo, hi, hihi):
    return [
        '',
        lo,
        "".join([lo, lo]),
        "".join([lo, lo, lo]),
        "".join([lo, hi]),
        hi,
        "".join([hi, lo]),
        "".join([hi, lo, lo]),
        "".join([hi, lo, lo, lo]),
        "".join([lo, hihi])
    ]

def build_roman_table():
    tens = roman_digits_pattern('I', 'V', 'X')
    hundreds = roman_digits_pattern('X', 'L', 'C')
    thousands = roman_digits_pattern('C', 'D', 'M')
    table = []
    for a in thousands:
        for b in hundreds:
            for c in tens:
                table.append("".join([a,b,c]))
    return table

ROMAN_DIGITS = build_roman_table()

def print_number(x):
    z = x
    for digit in ROMAN_DIGITS:
        if z is None:
            print(digit)
            return
        z = pred(z)

def fizz_buzz(limit):
    div_by_five = FOUR
    div_by_three = TWO
    at = ONE
    x = limit
    while x is not None:
        x = pred(x)
        result = []
        show_number = True
        if div_by_three is None:
            show_number = False
            div_by_three = THREE
            result.append("Fizz")
        if div_by_five is None:
            show_number = False
            div_by_five = FIVE
            result.append("Buzz")
        if show_number:
            print_number(at)
        else:
            print("".join(result))
        div_by_three = pred(div_by_three)
        div_by_five = pred(div_by_five)
        at = succ(at)

ONE_HUNDRED = multiply(TEN, TEN)
fizz_buzz(ONE_HUNDRED)