import time
start = time.time()
 
length = 0 ; x = 1 ; y = 2 ; n = z = 3
#y = previous term
#x is the term before that
#z = current term
#use n to count terms
while length < 1000:
    #create new term
    #reassign old values
    #set length
    z = x+y
    x, y = y, z
    length = len(str(z))
    n += 1
print n
 
print time.time()-start

import time, math
start = time.time()
 
def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)
 
target = 1000000
answer = []
digits = range(10)
nDigits = len(digits)
#the sorted permutation list will have 10! = 3628800 permutations
#solve a digit at a time
#narrowing the target and crossing off digits
while len(digits) != 1:
    x = factorial(nDigits-1)
    y = int(math.ceil(target/float(x)))
    answer.append(digits[y-1])
    digits.remove(digits[y-1])
    target -= x*(y-1)
    nDigits -= 1
#avoid being off by one digit
answer.append(digits[0])
 
print ''.join(map(str, answer))
 
print time.time()-start

import time
start = time.time() 
 
def sumDivisors(n, total=1):
    #look for divisors with modulus
    sqr = int((n**0.5)+1)
    for i in range(2, sqr):
        if n % i == 0:
            total += i + n / i
    if (n**0.5)+1 == sqr:
        total -= sqr
    return total
 
total = 0
abundants = set()
for n in range(1, 28123):
    #use sumDivisors to populate abundants set
    if sumDivisors(n) > n:
        abundants.add(n)
    #look in abundants for n - abundant
    #if it's not present then n is not the sum of two abundants
    if not any((n-a in abundants) for a in abundants):
        total += n
print total
 
print time.time()-start

import time, string
start = time.time() 
 
names = open("names.txt").read().replace('"', '').split(',')
names.sort()
 
letterScores={'a':1, 'b':2, 'c':3, 'd':4, 'e':5, 'f':6, 
'g':7, 'h':8, 'i':9, 'j':10, 'k':11, 'l':12, 'm':13, 'n':14, 
'o':15, 'p':16, 'q':17, 'r':18, 's':19, 't':20, 'u':21, 
'v':22, 'w':23, 'x':24, 'y':25, 'z':26}
 
#loop through names, nest to loop chars
#use char and letterScores to tally up the total
total = 0
for index, name in enumerate(names):
    nameScore = 0
    for letter in range(len(name)):
        nameScore += letterScores[string.lower(name[letter])]
    total += nameScore * (index+1)
print total    
 
print time.time()-start

import time
start = time.time() 
 
def sumDivisors(n, total=1):
    #look for divisors with modulus
    for i in range(2, int(n**0.5)+1):
        if n % i == 0:
            total += i + n / i
    return total
 
total = 0
for i in range(2, 10000):
    #test for amicables
    if sumDivisors(i) > i and sumDivisors(sumDivisors(i)) == i:
        #tally up both numbers
        total += sumDivisors(i)+i
 
print total
 
print time.time()-start

import time
start = time.time()
 
#find the number
n = 1
for i in range(1, 100):
    n = n * i
 
#convert to string
#convert chars to ints and add them to total
nStr = str(n)
answer = 0
for i in range(len(nStr)):
    answer += int(nStr[i])
 
print answer
 
print time.time()-start

import time, datetime
start = time.time()
 
#loop years and nest for months
#get datetime object for first day
#test for sundays
total = 0
for year in range(1901, 2001):
    for month in range(1, 13):
        day = datetime.date(year, month, 1)
        if day.weekday() == 6:
            total += 1    
print total 
 
print time.time()-start

import time
start = time.time()
 
triangle = [
    [75,],
    [95, 64,],
    [17, 47, 82,],
    [18, 35, 87, 10,],
    [20,  4, 82, 47, 65,],
    [19,  1, 23, 75,  3, 34,],
    [88,  2, 77, 73,  7, 63, 67,],
    [99, 65,  4, 28,  6, 16, 70, 92,],
    [41, 41, 26, 56, 83, 40, 80, 70, 33,],
    [41, 48, 72, 33, 47, 32, 37, 16, 94, 29,],
    [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14,],
    [70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57,],
    [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48,],
    [63, 66,  4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31,],
    [ 4, 62, 98, 27, 23,  9, 70, 98, 73, 93, 38, 53, 60,  4, 23,],
    ]
 
#work up from the bottom row
for row in range(len(triangle)-1, 0, -1):
    for col in range(row):
        #assign the number in the row above each adjacent pair
        #to the greatest value of that pair
        triangle[row-1][col] += max(triangle[row][col], triangle[row][col+1])
 
print triangle[0][0]
 
print time.time()-start

import time
start = time.time()
 
def num2txt(n):
    if n == 1000:
        return len('onethousand')
 
    words = {1:'one',2:'two',3:'three',4:'four',5:'five',6:'six',7:'seven',
    8:'eight',9:'nine',10:'ten',11:'eleven',12:'twelve',13:'thirteen',
    14:'fourteen',15:'fifteen',16:'sixteen',17:'seventeen',
    18:'eighteen',19:'nineteen',20:'twenty',30:'thirty',40:'forty',
    50:'fifty',60:'sixty',70:'seventy',80:'eighty',90:'ninety',
    100:'hundred',1000:'thousand'}
 
    total = 0
    hundreds = n / 100 #digit from hundreds column
    tens = n % 100 / 10 #digit from tens column
    ones = n % 10 #digit from ones column
 
    if hundreds > 0: #3 digit number
        total += len(words[hundreds]) #digit as text (eg: one)
        total += len(words[100]) #hundred
        if tens > 1: #two digit number > 19
            total += len(words[tens*10])+3 #+3 accounts for "and"
            if ones > 0:
                total += len(words[ones])
        elif tens == 1: #teen or ten/eleven/twelve
            total += len(words[ones+10])+3
        elif ones > 0: #and digit (eg: "andone")
            total += len(words[ones])+3
    elif tens > 0: #2 digit number
        if tens == 1: #teen or ten/eleven/twelve
            total += len(words[ones+10])
        else:
            if tens > 1: #two digit number > 19
                total += len(words[tens*10])
                if ones > 0:
                    total += len(words[ones])
    else: #single digit number
        total += len(words[ones])
 
    return total
 
print sum(map(num2txt, range(1, 1001)))
 
print time.time()-start

import time
start = time.time()
 
#set value as string
numStr = str(2**1000)
#loop by char, convert to int and add to total
total = 0
for i in range(len(numStr)):
    total += int(numStr[i])
print total
 
print time.time()-start