problems.py

#!/user/bin/env python2

def problem_01():
    # If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
    # Find the sum of all the multiples of 3 or 5 below 1000.
    sum = 0
    for i in range(1, 1000):
        if i % 3 == 0 or i % 5 == 0:
            sum = sum + i
    return sum

def problem_02():
    # Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
    # 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
    # By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
    sum = 0
    prev = 1
    curr = 1
    while curr <= 4000000:
        if curr % 2 == 0:
            sum = sum + curr
        next = prev + curr
        prev = curr
        curr = next
    print sum

def problem_03():
    # The prime factors of 13195 are 5, 7, 13 and 29.
    # What is the largest prime factor of the number 600851475143 ?
    result = factorize(600851475143)
    print result[-1]

def factorize(num):
    factors = []
    divisor = 2
    while num != 1:
        if num % divisor == 0:
            num = num / divisor
            factors.append(divisor)
        else:
            divisor = divisor + 1
    return factors

def is_palindrome(num):
    num = str(num)
    if num[::-1] == num:
        return True
    else:
        return False

def problem_04():
    # A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
    # Find the largest palindrome made from the product of two 3-digit numbers.
    current = 0
    for multi1 in range(100,1000):
        for multi2 in range(100,1000):
            product = multi1 * multi2
            if is_palindrome(product):
                if current < product:
                    current = product
    print current

print problem_04()