# Q1
def skip_add(n):
    """ Takes a number x and returns x + x-2 + x-4 + x-6 + ... + 0.

    >>> skip_add(5)  # 5 + 3 + 1 + 0
    9
    >>> skip_add(10) # 10 + 8 + 6 + 4 + 2 + 0
    30
    """
    "*** YOUR CODE HERE ***"


# Q2
def count_up(n):
    """Print out all numbers up to and including n in ascending order.

    >>> count_up(5)
    1
    2
    3
    4
    5
    """
    i = 1
    if i == n:
        return
    print(i)
    i += 1
    count_up(n-1)


# Q3
def skip_mul(n):
    """Return the product of n * (n - 2) * (n - 4) * ...

    >>> skip_mul(5) # 5 * 3 * 1
    15
    >>> skip_mul(8) # 8 * 6 * 4 * 2  * 0
    0
    """
    if n == 0:
        return 0
    else:
        return n * skip_mul(n - 2)


# Q4
def factorial(n):
    """Return n * (n - 1) * (n - 2) * ... * 1.

    >>> factorial(5)
    120
    """
    if n == 0:
        return 1
    else:
        n * factorial(n-1)


# Q5
def print_up_to(n):
    """Print every natural number up to n, inclusive.

    >>> print_up_to(5)
    1
    2
    3
    4
    5
    """
    i = 1
    if i > n:
        return
    else:
        print(i)
        i += 1
        print_up_to(n)



# Q6
def gcd(a, b):
    """Returns the greatest common divisor of a and b.
    Should be implemented using recursion.

    >>> gcd(34, 19)
    1
    >>> gcd(39, 91)
    13
    >>> gcd(20, 30)
    10
    >>> gcd(40, 40)
    40
    """
    "*** YOUR CODE HERE ***"


# Q7
def hailstone(n):
    """Print out the hailstone sequence starting at n, and return the
    number of elements in the sequence.

    >>> a = hailstone(10)
    10
    5
    16
    8
    4
    2
    1
    >>> a
    7
    """
    "*** YOUR CODE HERE ***"


# Q8
def is_palindrome(n):
    """
    Fill in the blanks '_____' to check if a number
    is a palindrome.

    >>> is_palindrome(12321)
    True
    >>> is_palindrome(42)
    False
    >>> is_palindrome(2015)
    False
    >>> is_palindrome(55)
    True
    """
    x, y = n, 0
    f = lambda: _____
    while x > 0:
        x, y = _____, f()
    return y == n