tanks!.py

MAX = 114
MIN = 22

def falling_factorial(n, k):
    """
    computes (n) * (n-1) * ... * (n-(k-1))
    """ 
    running_product = n
    for p in range(n-1, n-k, -1):
        running_product *= p
    return running_product


def P_max_le_ub_min_ge_lb(N, n, lb, ub):
    return falling_factorial(ub - lb + 1, n) / falling_factorial(N, n)


def P_max_eq_ub_min_eq_lb(N, n, lb, ub):
    if ub > N:
        return 0
    return (P_max_le_ub_min_ge_lb(N, n, lb, ub) - 
           P_max_le_ub_min_ge_lb(N, n, lb, ub - 1) -  
           P_max_le_ub_min_ge_lb(N, n, lb + 1, ub) + 
           P_max_le_ub_min_ge_lb(N, n, lb+1, ub-1))


running_max = 0
arg_running_max = (None, None)

for N in range(114, 200):
    for n in range(2, N+1):
        p = P_max_eq_ub_min_eq_lb(N, n, MIN, MAX)
        if p > running_max:
            running_max = p
            arg_running_max = (N, n)
            print(p, arg_running_max)

    print(N)



# Our estimate of the number of tanks seen is 9
# Using the UMVUE formula

tanks = MAX*(1 + 1/arg_running_max[1]) + 1