写在前面：

毅然决然决定开这个坑！！好吧，本文主要为个人做笔记用，也可以方便大家交流，但是做题时为了节省时间，代码写得有些乱，思路有时也比较粗暴，方法和变量命名请不要吐槽。。我看过讨论版上有很多精彩的方法，但是这里只做一个自己的笔记用而已！！

题目翻译摘自Project Euler 中文翻译站，特此感谢，虽然我做题的时候都是看英文的。。

另外，题目里面有些数学上的东西，比如说平方那些，我就懒得修改了。。看得懂就行。 

再另外，虽然我一般的习惯是不分P来写博客，也就是说一个主题就开一篇，比如我以前写的所有的笔记性质的博客，全是一篇超长的，但是有人跟我说这样看起来挺累的，所以我也就决定分一下P，正好博客搬家，水一下数量给搜索引擎看。。。而且，被我搞到现在每一道题的解答的格式有点复杂，所以也是为了保险起见，我还是分一下P吧，不然哪一天WP抽风了，一打开修改后全部格式全乱了就神作了。。。老师教导我们，鸡蛋不要放在一个篮子里！！

前言部分就这么多吧~每10题1P，前面30到40题都是超级简单的。。。
顺带提一下，如果有谁发现里面有错，麻烦告知一声，我总感觉不可能没搞错。。

Problem 1:Multiples of 3 and 5

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.

Code：Mathematica

法一：
m = 1000;
Total@Union@Flatten@Append[Range[3, m - 1, 3], Range[5, m - 1, 5]]
法二：
Total[#] & /@ {Range[3, m - 1, 3], Range[5, m - 1, 5], -Range[15, m - 1, 15]} // Total

Problem 2:Even Fibonacci numbers

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.

Code：Mathematica

Total@Select[
  Table[Fibonacci[i + 1], {i, 1, 
    NestWhile[# + 1 &, 1, Fibonacci[#] < 4000000 &]}], EvenQ]

Problem 3:Largest prime factor

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

Code：Mathematica

Sort[FactorInteger[600851475143], First &] // Last // First

Problem 4:Largest palindrome product

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.

Code：Mathematica

palindromicQ[n_] := (Characters[ToString[n]] // Reverse) === Characters[ToString[n]];
list=Table[i*j, {i, 100, 999}, {j, 110, 999, 11}] // Flatten
Select[list, palindromicQ[#] &] // Sort // Last

Problem 5:Smallest multiple

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Code：Mathematica

Times @@ Power @@@ 
  Function[p, (Select[
        Flatten[FactorInteger /@ Range[2, 20], 1], #[[1]] == p &]~
       SortBy~Last) // Last] /@ Select[Table[i, {i, 2, 20}], PrimeQ]

Problem 6:Sum square difference

The sum of the squares of the first ten natural numbers is,

\(1^2 + 2^2 + … + 10^2 = 385\)

The square of the sum of the first ten natural numbers is,

\((1 + 2 + … + 10)^2 = 55^2 = 3025\)

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025-385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Code：Mathematica

法一：
m = 100;
Sum[i, {i, 1, m}]^2 - Sum[i^2, {i, 1, m}]
法二：
m = 100;
1/4 m^2 (1 + m)^2 - 1/6 m (m + 1) (2 m + 1)

Problem 7:10001st prime

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10 001st prime number?

Code：Mathematica

Prime[10001]

Problem 8:Largest product in a series

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Code：Mathematica

str="题目字符串"
num = ToExpression@Characters@str;
Table[Times @@ Table[num[[i]], {i, j, j + 4}], {j, 1, 996}] // Sort // Last

Problem 9:Special Pythagorean triplet

A Pythagorean triplet is a set of three natural numbers, \(a < b < c\), for which,

\(a^2 + b^2 = c^2\)

For example, \(3^2 + 4^2 = 9 + 16 = 25 = 5^2\).

There exists exactly one Pythagorean triplet for which a + b + c = 1000.

Find the product abc.

Code：Python

#法一
for a in range(1,500):
    for b in range(max(500-a,a),500):
        c = 1000-a-b;
        if a*a+b*b==c*c:
            print a*b*c
#法二
#略
#法三
for a in range(1,292):
    b = 1000*(500-a)/(1000-a);
    if b == int(b):
        print a*b*(1000-a-b)

Code：Mathematica

(*一行解决大法*)
Solve[a^2 + b^2 == c^2 && a + b + c == 1000 && 0 < a < b < c, {a, b, c}, Integers]

Problem 10:Summation of primes

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

Code：Python

#法一
def PrimeQ(n):
    if n <= 1:
        return False
    for i in xrange(2,int(n**0.5+1)):
        if n%i == 0:
            return False;
    return True;

sum = 2;
for i in range(3,2000000,2):
    if PrimeQ(i):
        sum += i;
print sum
#法二
num = 2000000

total = (num-1) * num / 2-1 
primes = [1]*num

m = int(sqrt(num)) + 1

for i in xrange(2, m):
    if primes[i] == 1:
        for j in xrange(i*2, num, i):
            if primes[j] == 1:
                primes[j] = 0
                total -= j
print total

Code：Mathematica

法一：
Total@Select[Range[2000000], PrimeQ]
#法二
#略

【完】

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