Problem 5-8

Posted on 2015-03-18 15:14  gklee  阅读(153)  评论(0)    收藏  举报

5、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?

 1 def gcd(x,y):
 2     if x < y:
 3         x,y = y,x
 4     if y == 0:
 5         return x
 6     else:
 7         return gcd(y,x%y)
 8 
 9 def lcm(x,y):
10     return (x * y) / gcd(x, y)
11 
12 result = reduce(lcm,range(1,20))
13 
14 print result

6、 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.

1 a = sum([x*x for x in range(1,101)])
2 b = sum(range(1,101)) ** 2
3 result = b - a
4 print result

 7、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?

 1 import math
 2 
 3 def isprime(x):
 4     for i in range(2,int(math.sqrt(x))+1):
 5         if x % i == 0:
 6             return False
 7     return True
 8 
 9 def func():
10     n = 1
11     num = 2
12     while n <= 10001:
13         if isprime(num):
14             n += 1   
15         num += 1
16     return num - 1
17 print func()

 8、

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

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

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

 1 f = open('008','r')
 2 alllines = f.readlines()
 3 f.close()
 4 
 5 product = 0
 6 ilist = []
 7 s = ''
 8 
 9 for eachline in alllines:
10     line = eachline.strip()
11     s += line
12 i = 0
13 while i < 988:
14     for j in range(13):
15         ilist.append(int(s[i+j]))
16     pre = reduce(lambda x,y:x*y,ilist)
17     if pre > product:
18         product = pre
19     ilist = []
20     i += 1
21 print product