# Euler problems/11 to 20

## 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 21000?

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 = let fac n = product [1..n] in
foldr ((+) . Data.Char.digitToInt) 0 \$ show \$ fac 100```