Euler problems/121 to 130

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