Project Euler in Python Series 1

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.

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.

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 ?

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.

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?

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.

Problem 8 Largest product in a series

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

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

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, 32 + 42 = 9 + 16 = 25 = 52.

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

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.