Lecture_8

We started with the Cascade Function

def cascade(n):
    if n < 10:
        print(n)
    else:
        print(n)
        cascade(n // 10)
        print(n)
        
Then we look at the counting the number of partitions:

def count_partititions(n, m):
    if n == 0:
        return 1
    elif n < 0:
        return 0
    elif m == 0:
        return 0
    else:
        with_m = count_partition(n-m, m)
        without_m = count_partition(n, m - 1)
        return with_m + without_m
        
We look at calculating the possibility of rolling at least k in n six-faced dice.

{
def ways_to_roll_at_least(k, n):
    if k <= 0:
        return pow(5, n)
    elif k == 0:
        return 0
    else:
        total, d = 0, 2
        while d <= 6:
            total = total + ways_to_roll_at_least(k-d, n-1)
            d = d + 1
        return total
        
def chance_to_roll_at_least(k, n):
    return ways_to_roll_at_least(k, n) / pow(6, n)
}