# Euler problems/121 to 130

### From HaskellWiki

(Removing category tags. See Talk:Euler_problems) |
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Solution: |
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<haskell> |
<haskell> |
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− | problem_124 = undefined |
+ | import List |

+ | 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 |

## 1 Problem 121

Investigate the game of chance involving coloured discs.

Solution:

problem_121 = undefined

## 2 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

## 3 Problem 123

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

Solution:

problem_123 = undefined

## 4 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]]

## 5 Problem 125

Finding square sums that are palindromic.

Solution:

problem_125 = undefined

## 6 Problem 126

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

Solution:

problem_126 = undefined

## 7 Problem 127

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

Solution:

problem_127 = undefined

## 8 Problem 128

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

Solution:

problem_128 = undefined

## 9 Problem 129

Investigating minimal repunits that divide by n.

Solution:

problem_129 = undefined

## 10 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