igorvanloo

#x % 10 will be the first digit, then we x // 10 to remove it and repeat

def sum_digits(x):
    totalsum = 0
    while x != 0:
        totalsum += x % 10
        x = x // 10
    return totalsum

igorvanloo

def Divisors(x): 
    divisors = []
    for i in range(1, int(math.sqrt(x)) + 1):
        if x % i == 0:
            divisors.append(i)
            divisors.append(int(x/i))
    divisors.remove(x) #Remove this line if you want to include x as a divisor of x
    return (divisors)

igorvanloo

def continued_fraction(x):
    m0 = 0
    d0 = 1
    a0 = math.floor(math.sqrt(x)) #These are the starting values
    temp_list = [a0]
    while True:
        mn = int(d0*a0 - m0) 
        dn = int((x - mn**2)/d0)
        an = int(math.floor((math.sqrt(x) + mn) / dn)) #new values
        temp_list.append(an)

igorvanloo

def Partition(goal, alist):
    ways = [0] + [1] * (goal)
    for options in alist:
        for i in range(len(ways) - options):
            ways[i + options] += ways[i]
    return ways[-1] #-1 here if you don't want to include 4 + 0 as a partition of 4 for example

igorvanloo

def ppt(limit):
    triples = []
    for m in range(2,int(math.sqrt(limit))+1):
        for n in range(1,m):
            if (m+n) % 2 == 1 and math.gcd(m,n) == 1:
                a = m**2 + n**2
                b = m**2 - n**2
                c = 2*m*n
             
                p = max(a,b,c)

igorvanloo

def Divisors(x):
    divisors = []
    for i in range(1,int(math.sqrt(x))+1):
        if x % i == 0:
            divisors.append(i)
            if i != int(x/i):
                divisors.append(int(x/i))
    divisors.remove(x)
    return sum(set(divisors))

igorvanloo

# These are the fifth power digit sum numbers except the last one is missing
#[4150, 4151, 54748, 92727, 93084] 

def sum_digits_mod(x):
    totalsum = 0
    while x != 0:
        totalsum += (x % 10)**5
        x = x // 10
    return totalsum
    

igorvanloo

def compute():
    totalways = 1
    for a in range(0,3):
        for b in range(0,(2-a)*2 + 1):
            for c in range(0,math.ceil((2-a-b*0.5)*10)+1):
                for d in range(0,math.ceil((2-a-b*0.5-c*0.2)*20)+1):
                    for e in range(0,math.ceil((2-a-b*0.5-c*0.2-d*0.1)*40)+1):
                        for f in range(0,math.ceil((2-a-b*0.5-c*0.2-d*0.1-e*0.05)*100)+1):
                            for g in range(0,math.ceil((2-a-b*0.5-c*0.2-d*0.1-e*0.05-f*0.02)*200)+1):
                                if a*100 + b*50 + c*20 + d*10 + e*5 + f*2 + g*1 == 200:

igorvanloo

def compute():
    testlist = ['1', '2', '3', '4', '5', '6', '7', '8', '9']
    values = set()
    for x in range(9,99):
        for y in range(99,999):
            answer = x*y
            if answer < 10000:
                testingvalue = sorted(str(x) + str(y) + str(answer))
                if testingvalue == testlist:
                    values.add(answer)

igorvanloo

def compute():
    values = []
    numer = 1
    denom = 1
    for x in range(10,100):
        for y in range(x+1, 100):
            if x%10 != 0 and y%10 != 0:
                value1 = str(x)
                value2 = str(y)
                for a in value1: