# Difference between revisions of "Euler problems/11 to 20"

(→[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: |
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<haskell> |
<haskell> |
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− | problem_12 = undefined |
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+ | problem_12 = head $ filter ((> 500) . nDivisors) triangleNumbers |
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+ | where triangleNumbers = scanl1 (+) [1..] |
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+ | nDivisors n = product $ map ((+1) . length) (group (primeFactors n)) |
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+ | primes = 2 : filter ((== 1) . length . primeFactors) [3,5..] |
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+ | primeFactors n = factor n primes |
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+ | where factor n (p:ps) | p*p > n = [n] |
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+ | | n `mod` p == 0 = p : factor (n `div` p) (p:ps) |
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+ | | otherwise = factor n ps |
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</haskell> |
</haskell> |
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## Revision as of 01:33, 28 March 2007

## Contents

## 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
```

## 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
```

## Problem 13

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

Solution:

```
problem_13 = undefined
```

## Problem 14

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

Solution:

```
problem_14 = undefined
```

## 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
```

## Problem 16

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

Solution:

```
problem_16 = undefined
```

## Problem 17

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

Solution:

```
problem_17 = undefined
```

## Problem 18

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

Solution:

```
problem_18 = undefined
```

## Problem 19

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

Solution:

```
problem_19 = undefined
```

## Problem 20

Find the sum of digits in 100!

Solution:

```
problem_20 = undefined
```