# Euler problems/1 to 10

### From HaskellWiki

(→[http://projecteuler.net/index.php?section=problems&id=1 Problem 1]: bug fix) |
(→[http://projecteuler.net/index.php?section=problems&id=5 Problem 5]: faster solution) |
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<haskell> | <haskell> | ||

problem_5 = head [ x | x <- [2520,5040..], all (\y -> x `mod` y == 0) [1..20]] | problem_5 = head [ x | x <- [2520,5040..], all (\y -> x `mod` y == 0) [1..20]] | ||

+ | </haskell> | ||

+ | An alternative solution that takes advantage of the Prelude to avoid generate and test: | ||

+ | <haskell> | ||

+ | problem_5' = foldr1 lcm [1..20] | ||

</haskell> | </haskell> | ||

## Revision as of 16:33, 27 March 2007

## Contents |

## 1 Problem 1

Add all the natural numbers below 1000 that are multiples of 3 or 5.

Solution:

problem_1 = sum [ x | x <- [1..999], (x `mod` 3 == 0) || (x `mod` 5 == 0)]

## 2 Problem 2

Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed one million.

Solution:

problem_2 = sum [ x | x <- takeWhile (<= 1000000) fibs, x `mod` 2 == 0] where fibs = 1 : 1 : zipWith (+) fibs (tail fibs)

## 3 Problem 3

Find the largest prime factor of 317584931803.

Solution:

problem_3 = maximum [ x | x <- [1..round $ sqrt (fromInteger c)], c `mod` x == 0] where c = 317584931803

## 4 Problem 4

Find the largest palindrome made from the product of two 3-digit numbers.

Solution:

problem_4 = foldr max 0 [ x | y <- [100..999], z <- [100..999], let x = y * z, let s = show x, s == reverse s]

## 5 Problem 5

What is the smallest number divisible by each of the numbers 1 to 20?

Solution:

problem_5 = head [ x | x <- [2520,5040..], all (\y -> x `mod` y == 0) [1..20]]

An alternative solution that takes advantage of the Prelude to avoid generate and test:

problem_5' = foldr1 lcm [1..20]

## 6 Problem 6

What is the difference between the sum of the squares and the square of the sums?

Solution:

problem_6 = sum [ x^2 | x <- [1..100]] - (sum [1..100])^2

## 7 Problem 7

Find the 10001st prime.

Solution:

problem_7 = head $ drop 10000 primes where primes = 2:3:..

## 8 Problem 8

Discover the largest product of five consecutive digits in the 1000-digit number.

Solution:

problem_8 = undefined

## 9 Problem 9

There is only one Pythagorean triplet, {*a*, *b*, *c*}, for which *a* + *b* + *c* = 1000. Find the product *abc*.

Solution:

problem_9 = head [a*b*c | a <- [1..500], b <- [a..500], let c = 1000-a-b, a^2 + b^2 == c^2]

## 10 Problem 10

Calculate the sum of all the primes below one million.

Solution:

problem_10 = sum (takeWhile (< 1000000) primes)