# Euler problems/11 to 20

### From HaskellWiki

(→[http://projecteuler.net/index.php?section=problems&id=16 Problem 16]: fix problem description) |
(→[http://projecteuler.net/index.php?section=problems&id=12 Problem 12]: add a solution) |
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Line 12: | Line 12: | ||

Solution: | Solution: | ||

<haskell> | <haskell> | ||

− | problem_12 = | + | problem_12 = head $ filter ((> 500) . nDivisors) triangleNumbers |

+ | where triangleNumbers = scanl1 (+) [1..] | ||

+ | nDivisors n = product $ map ((+1) . length) (group (primeFactors n)) | ||

+ | primes = 2 : filter ((== 1) . length . primeFactors) [3,5..] | ||

+ | primeFactors n = factor n primes | ||

+ | where factor n (p:ps) | p*p > n = [n] | ||

+ | | n `mod` p == 0 = p : factor (n `div` p) (p:ps) | ||

+ | | otherwise = factor n ps | ||

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

## Revision as of 01:33, 28 March 2007

## Contents |

## 1 Problem 11

What is the greatest product of four numbers on the same straight line in the 20 by 20 grid?

Solution:

problem_11 = undefined

## 2 Problem 12

What is the first triangle number to have over five-hundred divisors?

Solution:

problem_12 = head $ filter ((> 500) . nDivisors) triangleNumbers where triangleNumbers = scanl1 (+) [1..] nDivisors n = product $ map ((+1) . length) (group (primeFactors n)) primes = 2 : filter ((== 1) . length . primeFactors) [3,5..] primeFactors n = factor n primes where factor n (p:ps) | p*p > n = [n] | n `mod` p == 0 = p : factor (n `div` p) (p:ps) | otherwise = factor n ps

## 3 Problem 13

Find the first ten digits of the sum of one-hundred 50-digit numbers.

Solution:

problem_13 = undefined

## 4 Problem 14

Find the longest sequence using a starting number under one million.

Solution:

problem_14 = undefined

## 5 Problem 15

Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?

Solution:

problem_15 = undefined

## 6 Problem 16

What is the sum of the digits of the number 2^{1000}?

Solution:

problem_16 = undefined

## 7 Problem 17

How many letters would be needed to write all the numbers in words from 1 to 1000?

Solution:

problem_17 = undefined

## 8 Problem 18

Find the maximum sum travelling from the top of the triangle to the base.

Solution:

problem_18 = undefined

## 9 Problem 19

How many Sundays fell on the first of the month during the twentieth century?

Solution:

problem_19 = undefined

## 10 Problem 20

Find the sum of digits in 100!

Solution:

problem_20 = undefined