# Difference between revisions of "Euler problems/121 to 130"

(Removing category tags. See Talk:Euler_problems) |
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Solution: |
Solution: |
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<haskell> |
<haskell> |
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− | problem_124 = undefined |
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+ | import List |
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+ | primes :: [Integer] |
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+ | primes = 2 : filter ((==1) . length . primeFactors) [3,5..] |
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+ | |||

+ | primeFactors :: Integer -> [Integer] |
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+ | primeFactors n = factor n primes |
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+ | where |
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+ | factor _ [] = [] |
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+ | factor m (p:ps) | p*p > m = [m] |
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+ | | m `mod` p == 0 = p : factor (m `div` p) (p:ps) |
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+ | | otherwise = factor m ps |
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+ | problem_124=snd$(!!9999)$sort[(product$nub$primeFactors x,x)|x<-[1..100000]] |
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+ | |||

</haskell> |
</haskell> |
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## Revision as of 08:02, 10 December 2007

## Contents

## Problem 121

Investigate the game of chance involving coloured discs.

Solution:

```
problem_121 = undefined
```

## Problem 122

Finding the most efficient exponentiation method.

Solution using a depth first search, pretty fast :

```
import Data.List
import Data.Array.Diff
import Control.Monad
depthAddChain 12 branch mins = mins
depthAddChain d branch mins = foldl' step mins $ nub $ filter (> head branch)
$ liftM2 (+) branch branch
where
step da e | e > 200 = da
| otherwise =
case compare (da ! e) d of
GT -> depthAddChain (d+1) (e:branch) $ da // [(e,d)]
EQ -> depthAddChain (d+1) (e:branch) da
LT -> da
baseBranch = [2,1]
baseMins :: DiffUArray Int Int
baseMins = listArray (1,200) $ 0:1: repeat maxBound
problem_122 = sum . elems $ depthAddChain 2 baseBranch baseMins
```

## Problem 123

Determining the remainder when (pn − 1)n + (pn + 1)n is divided by pn2.

Solution:

```
problem_123 = undefined
```

## Problem 124

Determining the kth element of the sorted radical function.

Solution:

```
import List
primes :: [Integer]
primes = 2 : filter ((==1) . length . primeFactors) [3,5..]
primeFactors :: Integer -> [Integer]
primeFactors n = factor n primes
where
factor _ [] = []
factor m (p:ps) | p*p > m = [m]
| m `mod` p == 0 = p : factor (m `div` p) (p:ps)
| otherwise = factor m ps
problem_124=snd$(!!9999)$sort[(product$nub$primeFactors x,x)|x<-[1..100000]]
```

## Problem 125

Finding square sums that are palindromic.

Solution:

```
problem_125 = undefined
```

## Problem 126

Exploring the number of cubes required to cover every visible face on a cuboid.

Solution:

```
problem_126 = undefined
```

## Problem 127

Investigating the number of abc-hits below a given limit.

Solution:

```
problem_127 = undefined
```

## Problem 128

Which tiles in the hexagonal arrangement have prime differences with neighbours?

Solution:

```
problem_128 = undefined
```

## Problem 129

Investigating minimal repunits that divide by n.

Solution:

```
problem_129 = undefined
```

## Problem 130

Finding composite values, n, for which n−1 is divisible by the length of the smallest repunits that divide it.

Solution:

```
problem_130 = undefined
```