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| − | == [http://projecteuler.net/index.php?section=problems&id=21 Problem 21] ==
| + | Do them on your own! |
| − | Evaluate the sum of all amicable pairs under 10000.
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | problem_21 =
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| − | sum [n |
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| − | n <- [2..9999],
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| − | let m = eulerTotient n,
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| − | m > 1,
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| − | m < 10000,
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| − | n == eulerTotient m
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| − | ]
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| − | </haskell>
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| − | | |
| − | == [http://projecteuler.net/index.php?section=problems&id=22 Problem 22] ==
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| − | What is the total of all the name scores in the file of first names?
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | import Data.List
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| − | import Data.Char
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| − | problem_22 = do
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| − | input <- readFile "names.txt"
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| − | let names = sort $ read$"["++ input++"]"
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| − | let scores = zipWith score names [1..]
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| − | print $ show $ sum $ scores
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| − | where
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| − | score w i = (i *) $ sum $ map (\c -> ord c - ord 'A' + 1) w
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| − | </haskell>
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| − | | |
| − | == [http://projecteuler.net/index.php?section=problems&id=23 Problem 23] ==
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| − | Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | import Data.Array
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| − | n = 28124
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| − | abundant n = eulerTotient n - n > n
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| − | abunds_array = listArray (1,n) $ map abundant [1..n]
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| − | abunds = filter (abunds_array !) [1..n]
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| − | | |
| − | rests x = map (x-) $ takeWhile (<= x `div` 2) abunds
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| − | isSum = any (abunds_array !) . rests
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| − | | |
| − | problem_23 = putStrLn $ show $ foldl1 (+) $ filter (not . isSum) [1..n]
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| − | </haskell>
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| − | | |
| − | == [http://projecteuler.net/index.php?section=problems&id=24 Problem 24] ==
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| − | What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | import Data.List
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| − |
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| − | fac 0 = 1
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| − | fac n = n * fac (n - 1)
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| − | perms [] _= []
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| − | perms xs n=
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| − | x:( perms ( delete x $ xs ) (mod n m))
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| − | where
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| − | m=fac$(length(xs) -1)
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| − | y=div n m
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| − | x = xs!!y
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| − |
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| − | problem_24 = perms "0123456789" 999999
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| − | </haskell>
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| − | | |
| − | == [http://projecteuler.net/index.php?section=problems&id=25 Problem 25] ==
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| − | What is the first term in the Fibonacci sequence to contain 1000 digits?
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | import Data.List
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| − | fib x
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| − | |x==0=0
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| − | |x==1=1
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| − | |x==2=1
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| − | |odd x=(fib (d+1))^2+(fib d)^2
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| − | |otherwise=(fib (d+1))^2-(fib (d-1))^2
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| − | where
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| − | d=div x 2
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| − | | |
| − | phi=(1+sqrt 5)/2
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| − | dig x=floor( (fromInteger x-1) * log 10 /log phi)
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| − | problem_25 =
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| − | head[a|a<-[dig num..],(>=limit)$fib a]
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| − | where
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| − | num=1000
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| − | limit=10^(num-1)
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| − | </haskell>
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| − | | |
| − | == [http://projecteuler.net/index.php?section=problems&id=26 Problem 26] ==
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| − | Find the value of d < 1000 for which 1/d contains the longest recurring cycle.
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | next n d = (n `mod` d):next (10*n`mod`d) d
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| − | | |
| − | idigs n = tail $ take (1+n) $ next 1 n
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| − | | |
| − | pos x = map fst . filter ((==x) . snd) . zip [1..]
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| − | | |
| − | periods n = let d = idigs n in pos (head d) (tail d)
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| − | | |
| − | problem_26 =
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| − | snd$maximum [(m,a)|
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| − | a<-[800..1000] ,
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| − | let k=periods a,
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| − | not$null k,
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| − | let m=head k
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| − | ]
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| − | </haskell>
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| − | | |
| − | == [http://projecteuler.net/index.php?section=problems&id=27 Problem 27] ==
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| − | Find a quadratic formula that produces the maximum number of primes for consecutive values of n.
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | eulerCoefficients n
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| − | = [((len, a*b), (a, b))
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| − | | b <- takeWhile (<n) primes, a <- [-b+1..n-1],
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| − | let len = length $ takeWhile (isPrime . (\x -> x^2 + a*x + b)) [0..],
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| − | if b == 2 then even a else odd a, len > 39]
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| − |
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| − | problem_27 = snd . fst . maximum . eulerCoefficients $ 1000
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| − | </haskell>
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| − | | |
| − | == [http://projecteuler.net/index.php?section=problems&id=28 Problem 28] ==
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| − | What is the sum of both diagonals in a 1001 by 1001 spiral?
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | problem_28 = sum (map (\n -> 4*(n-2)^2+10*(n-1)) [3,5..1001]) + 1
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| − | </haskell>
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| − | | |
| − | == [http://projecteuler.net/index.php?section=problems&id=29 Problem 29] ==
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| − | How many distinct terms are in the sequence generated by a<sup>b</sup> for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | import Control.Monad
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| − | problem_29 = length . group . sort $ liftM2 (^) [2..100] [2..100]
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| − | </haskell>
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| − | | |
| − | == [http://projecteuler.net/index.php?section=problems&id=30 Problem 30] ==
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| − | Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
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| − | | |
| − | Solution:
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| − | <haskell>
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| − | import Data.Array
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| − | import Data.Char
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| − |
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| − | p = listArray (0,9) $ map (^5) [0..9]
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| − |
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| − | upperLimit = 295277
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| − |
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| − | candidates =
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| − | [ n |
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| − | n <- [10..upperLimit],
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| − | (sum $ digits n) `mod` 10 == last(digits n),
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| − | powersum n == n
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| − | ]
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| − | where
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| − | digits n = map digitToInt $ show n
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| − | powersum n = sum $ map (p!) $ digits n
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| − |
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| − | problem_30 = sum candidates
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| − | </haskell>
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