igorvanloo

def sum_digits_mod(x):
    facts = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
    totalsum = 0
    while x != 0:
        totalsum += facts[x % 10]
        x = x // 10
    return totalsum

def compute():
    overalltotal = 0

igorvanloo

def compute():
    checker = ['1', '2', '3', '4', '5', '6', '7', '8', '9']
    concatenated_product_list = []
    for z in range(2,10):
        for x in range(1,10**math.floor(9/z)):
            temp_str = ""
            for y in range(1,z+1):
                product = x*y
                temp_str += str(product)
                if sorted(temp_str) == checker:

igorvanloo

Triangle_number = [ "the triangle numbers from the txt file" ]

def sumofname(x):
    namesum = 0
    for i in range(len(words[x])):
        namesum += ord(words[x][i])-64
    return namesum

def compute():
    count = 0

igorvanloo

def is_pentagonal(x):
    #Take the inverse function to test whether or not a number is pentagonal
    if (1+(24*x+1)**0.5) % 6 == 0:
        return True
    return False

def compute():
    k = 1
    while True:
        for j in range(1,k): # this ensures that a > b therefore a-b is minimised 

igorvanloo

def is_pentagonal(x):
    #Take the inverse function to test whether or not a number is pentagonal
    if (1+(24*x+1)**0.5) % 6 == 0:
        return True
    return False

def is_hexagonal(x):
    #Take the inverse function to test whether or not a number is hexagonal
    if (1+(8*x+1)**0.5) % 4 == 0:
        return True

igorvanloo

def all_numbers(alist):
    nums = set()
    for x in alist:
        for y in x:
            nums.add(y)
    return list(nums)
    
def method1():
    possible_numbers = (all_numbers(keys))
    possible_passcode = list(itertools.permutations(possible_numbers))

igorvanloo

def goldbachs(number):
    for x in range(1, int(math.sqrt(number))+1):
        temp_var = number - 2*(x**2)
        if is_prime(temp_var) == True:
            return True
    return False

def compute():
    count = 33
    while True:

igorvanloo

def list_primality_modified(n):
	result = [0] * (n + 1) #Initialize an array of length n+1
	for i in range(2,int((n)) + 1): #We want to go all the way to the length instead of sqrt(n) 
					#to include all prime factors
		if result[i] == 0: #If this value has not been marked yet, continue
			for j in range(2 * i, len(result), i):
				result[j] += 1 #Add all the prime factors
	return result
#We will obtain a list where array[x] represents the number of prime factors of x,
#if array[x] = 0 then x is a prime

igorvanloo

def compute():
    primes = sorted(list(set(list_primes(10000)) - set((list_primes(1000)))))
    
    supercandidates = []
    while len(primes) != 0:
        curr = primes.pop()
        candidates = [curr]
        for y in primes:
            if sorted(str(curr)) == sorted(str(y)):
                candidates.append(y)

igorvanloo

def compute():
    x = 100
    while True:
        count = 1
        for i in range(2, 7):
            if sorted(str(x)) != sorted(str(i*x)):
                break
            count += 1
        if count == 6:
            return x