Project Euler Problems 4-6 by Easter Joy Trocio

Project Euler Problems 4-6

 

 

 

   CODER:

 

Easter Joy Trocio

Data Scientist

 

Language Used:

 

 

Problem Sets:

 

Largest palindrome product

Problem 4

Published on Friday, 16th November 2001, 06:00 pm; Solved by 274960; Difficulty rating: 5%

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.

Smallest multiple

Problem 5

Published on Friday, 30th November 2001, 06:00 pm; Solved by 286811; Difficulty rating: 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?

Sum square difference

Problem 6

Published on Friday, 14th December 2001, 06:00 pm; Solved by 288687; Difficulty rating: 5%

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.

CODES:

Problem 4

 



def ReverseNumber(n, partial=0):

if n == 0:

return partial

print ReverseNumber(n / 10),partial

return ReverseNumber(n / 10, partial * 10 + n % 10)



A=range(700,999)

B=range(700,999)

A.reverse()

B.reverse()

 

for i in A:

for j in B:

a=i*j

if a == ReverseNumber(a):

print a

break

Problem 5

 

# Python code to find the factors of a number

# define a function



def primes(n):



primfac = []




d = 2

while d*d <= n:




while (n % d) == 0:




primfac.append(d)  

n //= d


d += 1




if n > 1:


 

primfac.append(n)

return primfac

 



def factor(n):



fact=[]

p=n/2+1



for i in range(2,p):

  if n%i==0:




fact.append(i)  




return fact




F=[]

for i in range(2,11):




F.append(primes(i))

 

 

 
 

Problem 6

sum(i**2 for i in range(101))-sum(range(101))**2

 

 

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