def prob5():
    def helper1(n, m, a):
        list = [ ]
        list.append(a)# saves the last number = 9
        for n in range(1, n): # checks every number for n up to 9
            num = [ 0 ] * m
            for i in range(m):
                if i == 0:
                    num[i] = list[n-1][1]
                elif i == m - 1:
                    num[i] = list[n-1][i-1]
                else:
                    num[i] = list[n-1][i-1] + list[n-1][i+1]
            list.append(num)
        return sum(map(sum, list)) # i keep the numbers mapped rather than using of using dictionary which i helps
                                   # i use that to memmoize

    def helper2(n, start, end):
        m = end - start + 1
        if start == 0:
            a = [ 0 ] + [ 1 ] * (m - 1)
        else:
            a = [ 1 ] * m
        return helper1(n, end - start + 1, a) # plus one so i can use range and still get the correct numbers

    N = 40
    return helper2(N, 0, 9) - helper2(N, 0, 8) - helper2(N, 1, 9) + helper2(N, 1, 8) # returns the count of numbers
    """
    here i got a bit confused for it always returned 1931330459886 so i battled a bit more and got it after some
    some googeling :) that you need to find where the number has 0 and 9 than subtrackt the numbers which have
    0 but not 9 , neither 0 ore 9 and than add the numbers that include 9 but not 0