Project Euler solutions

Project Euler

1

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.

999 integers
[ [ 3 % ] [ 5 % ] bi [ zero? ] either? ] filter
sum

[ 233168 ]

2

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.

( 1 1 [ dup 4000000 < ] [ dupd next-fib* ] while drop )
[ even? ] filter
sum

[4613732]

3

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

What is the largest prime factor of the number 600851475143 ?

600851475143 divisors last

[6857]

4

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.

[906609]

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?

[232792560]

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.

100 integers
[ sum-of-squares ] [ square-of-sum ] bi
- abs

[25164150]

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?

10001 nth-prime

[104743]