Euler problems/21 to 30
(Added soplution for p28)
Revision as of 20:55, 23 June 2007
Evaluate the sum of all amicable pairs under 10000.
Solution: This is a little slow because of the naive method used to compute the divisors.
problem_21 = sum [m+n | m <- [2..9999], let n = divisorsSum ! m, amicable m n] where amicable m n = m < n && n < 10000 && divisorsSum ! n == m divisorsSum = array (1,9999) [(i, sum (divisors i)) | i <- [1..9999]] divisors n = [j | j <- [1..n `div` 2], n `mod` j == 0]
What is the total of all the name scores in the file of first names?
-- apply to a list of names problem_22 :: [String] -> Int problem_22 = sum . zipWith (*) [ 1 .. ] . map score where score = sum . map ( subtract 64 . ord )
Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
problem_23 = undefined
What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
perms  = [] perms xs = do x <- xs map ( x: ) ( perms . delete x $ xs ) problem_24 = ( perms "0123456789" ) !! 999999
What is the first term in the Fibonacci sequence to contain 1000 digits?
valid ( i, n ) = length ( show n ) == 1000 problem_25 = fst . head . filter valid . zip [ 1 .. ] $ fibs where fibs = 1 : 1 : 2 : zipWith (+) fibs ( tail fibs )
Find the value of d < 1000 for which 1/d contains the longest recurring cycle.
problem_26 = fst $ maximumBy (\a b -> snd a `compare` snd b) [(n,recurringCycle n) | n <- [1..999]] where recurringCycle d = remainders d 10  remainders d 0 rs = 0 remainders d r rs = let r' = r `mod` d in case findIndex (== r') rs of Just i -> i + 1 Nothing -> remainders d (10*r') (r':rs)
Find a quadratic formula that produces the maximum number of primes for consecutive values of n.
problem_27 = undefined
What is the sum of both diagonals in a 1001 by 1001 spiral?
corners :: Int -> (Int, Int, Int, Int) corners i = (n*n, 1+(n*(2*m)), 2+(n*(2*m-1)), 3+(n*(2*m-2))) where m = (i-1) `div` 2 n = 2*m+1 sumcorners :: Int -> Int sumcorners i = a+b+c+d where (a, b, c, d) = corners i sumdiags :: Int -> Int sumdiags i | even i = error "not a spiral" | i == 3 = s + 1 | otherwise = s + sumdiags (i-2) where s = sumcorners i problem_28 = sumdiags 1001
How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
problem_29 = length . group . sort $ [a^b | a <- [2..100], b <- [2..100]]
10 Problem 30
Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
problem_30 = undefined