Project Euler 1~10

dcy posted @ 2009年5月30日 22:49 in Project Euler , 4218 阅读

Problem 1

05 October 2001

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.

Answer:

233168

代码：

#!/usr/bin/env python
print sum(a for a in range(1000) if a%3==0 or a%5==0)

Problem 2

19 October 2001

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, ...

Find the sum of all the even-valued terms in the sequence which do not exceed four million.

Answer:	4613732

代码：

#!/usr/bin/env python

def firstThink():
list=[1,2]
for i in range(2,4000001):
r=list[i-1]+list[i-2]
if r<4000000:
list.append(r)
else:
break
print sum(i for i in list if i %2==0)

def secondThink():
a=1
b=1
c=a+b
sum=0
while c<=4000000:
sum=sum+c
a=b+c
b=c+a
c=a+b
print sum

def thirdThink():
'E(n)=4*E(n-1)+E(n-2)'
a=2
b=8
sum=2
while b<=4000000:
h=4*b+a
a=b
b=h
sum=sum+a
print sum

firstThink()
secondThink()
thirdThink()

Problem 3

02 November 2001

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

What is the largest prime factor of the number 600851475143 ?

Answer:

6857

代码：

#!/usr/bin env python
import math
def primer(n):
m=int(math.sqrt(n))
for i in range(2,m):
if n%i ==0:
return 0
return 1

b=600851475143
a=int(math.sqrt(b))
maximum=0
while(a):
if b%a==0 and primer(a)==1:
maximum=a
break
a=a-1

print maximum

Problem 4

16 November 2001

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.

Answer:

906609

一句话代码：

#!/usr/bin/env python
print max(m*n for m in range(100,1000) for n in range(m,1000) if str(m*n)==str(m*n)[::-1])

代码：

#!/usr/bin/env python

def ispalmindron2(num):
num=str(num)
return num==num[::-1]

def func(length):
print max(m*n for m in range(10**(length-1),10**length) for n in range(m,10**length) if ispalmindron2(m*n))

import time
start=time.time()
if __name__=='__main__':
func(3)
print time.time()-start

Problem 5

30 November 2001

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

Answer:	232792560

代码：

#!/usr/bin/env python
def func(num):
result=1
list=range(1,num+1)
for i in range(1,num):
for j in range(i+1,num):
if list[j]%list[i]==0:
list[j]/=list[i]
result=result*list[i]
print result

func(20)

Problem 6

14 December 2001

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

1² + 2² + ... + 10² = 385

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

(1 + 2 + ... + 10)² = 55² = 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.

Answer:

25164150

#!/usr/bin/env python
print sum(range(101))**2-sum(i*i for i in range(101))

Problem 7

28 December 2001

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

What is the 10001^st prime number?

Answer:	104743

#!/usr/bin/env python
import math
def isprime(num):
for i in range(2,int(math.sqrt(num)+1)):
if num%i==0:
return False
return True

def func1(num):
flag=1
flagnum=3
while flag<num:
if isprime(flagnum):
flag=flag+1
## print '%d---%d' %(flag,flagnum)
flagnum=flagnum+2
print '*'*20
print flagnum-2

if __name__=='__main__':
func1(10001)

Problem 8

11 January 2002

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

Answer:	40824

代码：

#!/usr/bin/env python
str='73167176531330624919225119674426574742355349194934\
96983520312774506326239578318016984801869478851843\
85861560789112949495459501737958331952853208805511\
12540698747158523863050715693290963295227443043557\
66896648950445244523161731856403098711121722383113\
62229893423380308135336276614282806444486645238749\
30358907296290491560440772390713810515859307960866\
70172427121883998797908792274921901699720888093776\
65727333001053367881220235421809751254540594752243\
52584907711670556013604839586446706324415722155397\
53697817977846174064955149290862569321978468622482\
83972241375657056057490261407972968652414535100474\
82166370484403199890008895243450658541227588666881\
16427171479924442928230863465674813919123162824586\
17866458359124566529476545682848912883142607690042\
24219022671055626321111109370544217506941658960408\
07198403850962455444362981230987879927244284909188\
84580156166097919133875499200524063689912560717606\
05886116467109405077541002256983155200055935729725\
71636269561882670428252483600823257530420752963450'

def func1():
max=0
for i in range(996):
t=1
for x in str[i:i+5]:
t*=int(x)
if t>max:
max=t
print max

func1()