用Python解答 ProjectEuler問題(1)

有個很有意思的網站 ProjectEuler.net ，提出了200多道數學問題，要求讀者用計算機求解，不限制所用的計算機語言。

（2008年11月）試着用Python做了幾道，挺有意思的。

• Add all the natural numbers below one thousand that are multiples of 3 or 5.
• Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed four million.
• Find the largest prime factor of a composite number.
• Find the largest palindrome made from the product of two 3-digit numbers.
• What is the smallest number divisible by each of the numbers 1 to 20?

E001

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.

求1000以下，所有是3或5倍數的數之和。

def problem1():
    a, b, c = 3, 5, 999
    f = lambda x,lmt=c: x*(lmt/x)*(lmt/x+1)/2
    return f(a)+f(b)-f(a*b)

if __name__=='__main__':
    print str(problem1())
      

關鍵是 1000以内能被3整除的數之和是 3(1+2+3+...+333)