15.py

# Note:  This program will take ~5 days to run to compleation.  Look at using (2n)!/(n!)^2 based equation instead of brute force method

import time

n = 20
starttime = time.time()
counter = 1
numbers = [0] * n
while True:
    if numbers[0] == n:  #Is the leftmost digit the highest it can be?  If so, we're done
        break
    numbers[n - 1] += 1  #Since we're not done, we can at least add 1
    counter += 1  # Increment the counter
    if numbers[n - 1] > n:  # If right number is maxed out, then time for carrying
        for i in range(1, n):  # Iterate over the list from left to right, skipping the leftmost digit
            if numbers[i] >= n:  # is the number maxed out?
                numbers[i - 1] += 1  # increment the number before it
                for x in range(i, n):
                    numbers[x] = numbers[
                        i - 1]  # Set all the numbers after it to the value of the number we incremented
                break
print(n, '*', n, 'cube:', counter, ' Time:', time.time() - starttime, 'seconds')