What is Project Euler?
Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.
The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.
这些解基本上都是用Python暴力解出来的,没有经过优化,只求答案不起速度,但是为了知道运算在什么位置了还加了一些额外的附加代码的,哇咔咔。
问题5:
What is the smallest number divisible by each of the numbers 1 to 20?
求1,2,..,19,20的最小公倍数。
i = 2520
while ( True ) :
flag = True
for j in range ( 11 , 21 ) :
if i % j <> 0 :
flag = False
#else:
# print i,j
if flag :
print i
break
i = i + 2520
if i % 1000000 == 0 :
print "now is" , i
问题6:
Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
求1至100和的平方与1至100的平方和之差。
a = 0
b = 0
for i in range ( 1 , 101 ) :
a = a + i * i
b = b + i
print b * b - a
问题7:
Find the 10001st prime.
求第10001个素数(质数)。
from itertools import count
def ispre ( n ) :
flag = True
for x in range ( 2 , n - 1 ) :
if n % x == 0 :
flag = False
break
return flag
t = 0
for i in count ( 2 ) :
if ispre ( i ) :
t += 1
if t > 10000 :
print i
break
问题8:
Discover the largest product of five consecutive digits in the 1000-digit number.
在给定的1000个数中,求出连续5个数的最大乘积。
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nums = '73167176531330624919225119674426574742355349194934\
96983520312774506326239578318016984801869478851843\
85861560789112949495459501737958331952853208805511\
12540698747158523863050715693290963295227443043557\
66896648950445244523161731856403098711121722383113\
62229893423380308135336276614282806444486645238749\
30358907296290491560440772390713810515859307960866\
70172427121883998797908792274921901699720888093776\
65727333001053367881220235421809751254540594752243\
52584907711670556013604839586446706324415722155397\
53697817977846174064955149290862569321978468622482\
83972241375657056057490261407972968652414535100474\
82166370484403199890008895243450658541227588666881\
16427171479924442928230863465674813919123162824586\
17866458359124566529476545682848912883142607690042\
24219022671055626321111109370544217506941658960408\
07198403850962455444362981230987879927244284909188\
84580156166097919133875499200524063689912560717606\
05886116467109405077541002256983155200055935729725\
71636269561882670428252483600823257530420752963450'
m = 0
for i in range ( 0 , 996 ) :
n = 1
for x in nums [ i : i + 5 ] :
n *= int ( x )
if n > m :
m = n
print m
问题9:
Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.
求满足a+b+c = 1000的勾股数的积。(注:勾股数指满足a^2+b^2=c^2的自然数a,b,c)
flag = False
for x in range ( 1 , 1000 ) :
for y in range ( 1 , 1000 ) :
z = 1000 - x - y
if x * x + y * y == z * z and x < y :
print x * y * z
flag = True
if flag :
break
问题10:
Calculate the sum of all the primes below two million.
求2,000,000以内所有素数的和。
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from math import sqrt
def ispre ( n ) :
flag = True
for x in range ( 2 , int ( sqrt ( n ) + 1 ) ) :
if n % x == 0 :
flag = False
break
return flag
t = 0
n = 1
for i in range ( 2 , 2000000 ) :
if ispre ( i ) :
t += i
if i > 20000 * n :
n = n + 1
print i
print t
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