194 lines
11 KiB
Haskell
194 lines
11 KiB
Haskell
-- (C) Copyright Collin Doering 2014
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--
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-- This program is free software: you can redistribute it and/or modify
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-- it under the terms of the GNU General Public License as published by
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-- the Free Software Foundation, either version 3 of the License, or
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-- (at your option) any later version.
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--
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-- This program is distributed in the hope that it will be useful,
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-- but WITHOUT ANY WARRANTY; without even the implied warranty of
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-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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-- GNU General Public License for more details.
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--
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-- You should have received a copy of the GNU General Public License
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-- along with this program. If not, see <http://www.gnu.org/licenses/>.
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-- File: ProjectEuler.hs
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-- Author: Collin J. Doering <rekahsoft@gmail.com>
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-- Date: May 18, 2014
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-----------------------------------------------------------------------------------------------
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-- Problem 4: Largest palindrome product --
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-----------------------------------------------------------------------------------------------
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isPalindrome :: (Eq a) => [a] -> Bool
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isPalindrome x
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| mod len 2 == 0 && take (div len 2) x == reverse (drop (div len 2) x) = True
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| otherwise = False
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where len = length x
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largestPalidromeOfSize :: Int -> Int
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largestPalidromeOfSize n = foldr max 0 . map (uncurry (*)) . filter (isPalindrome . show . uncurry (*)) $ [ (x,y) | x <- [s,s-1..t], y <- [s,s-1..t] ]
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where s = (10 ^ n) - 1
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t = s `quot` 2
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-----------------------------------------------------------------------------------------------
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-----------------------------------------------------------------------------------------------
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-- Problem 5: Smallest multiple --
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-----------------------------------------------------------------------------------------------
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-----------------------------------------------------------------------------------------------
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-----------------------------------------------------------------------------------------------
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-- Problem 7: 10001 prime --
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-----------------------------------------------------------------------------------------------
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isPrime :: Integral b => b -> Bool
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isPrime n = all (not . (== 0) . (n `mod`)) [2..quot n 2]
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nthPrime :: Integral a => Int -> a
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nthPrime n = [ x | x <- [2..], isPrime x] !! n
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-----------------------------------------------------------------------------------------------
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-----------------------------------------------------------------------------------------------
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-- Problem 8: Largest product in a series --
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-----------------------------------------------------------------------------------------------
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p8Series :: Integer
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p8Series = read . concat $
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[ "73167176531330624919225119674426574742355349194934"
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, "96983520312774506326239578318016984801869478851843"
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, "85861560789112949495459501737958331952853208805511"
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, "12540698747158523863050715693290963295227443043557"
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, "66896648950445244523161731856403098711121722383113"
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, "62229893423380308135336276614282806444486645238749"
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, "30358907296290491560440772390713810515859307960866"
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, "70172427121883998797908792274921901699720888093776"
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, "65727333001053367881220235421809751254540594752243"
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, "52584907711670556013604839586446706324415722155397"
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, "53697817977846174064955149290862569321978468622482"
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, "83972241375657056057490261407972968652414535100474"
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, "82166370484403199890008895243450658541227588666881"
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, "16427171479924442928230863465674813919123162824586"
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, "17866458359124566529476545682848912883142607690042"
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, "24219022671055626321111109370544217506941658960408"
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, "07198403850962455444362981230987879927244284909188"
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, "84580156166097919133875499200524063689912560717606"
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, "05886116467109405077541002256983155200055935729725"
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, "71636269561882670428252483600823257530420752963450" ]
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largestProduct :: Integer -> Integer
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largestProduct n = foldr max 0 . flip fiveProducts [] $ [ read [x] | x <- show n]
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fiveProducts :: Num a => [a] -> [a] -> [a]
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fiveProducts [] acc = acc
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fiveProducts (a:b:c:d:e:f:g:h:i:j:k:l:m:xs) acc = fiveProducts (b:c:d:e:f:g:h:i:j:k:l:m:xs) (a * b * c * d * e * f * g * h * i * j * k * l * m : acc)
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fiveProducts _ acc = acc
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-----------------------------------------------------------------------------------------------
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-----------------------------------------------------------------------------------------------
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-- Problem 13: Large Sum --
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-----------------------------------------------------------------------------------------------
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numsToSum = [ 37107287533902102798797998220837590246510135740250
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, 46376937677490009712648124896970078050417018260538
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, 74324986199524741059474233309513058123726617309629
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, 91942213363574161572522430563301811072406154908250
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, 23067588207539346171171980310421047513778063246676
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, 89261670696623633820136378418383684178734361726757
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, 28112879812849979408065481931592621691275889832738
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, 44274228917432520321923589422876796487670272189318
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, 47451445736001306439091167216856844588711603153276
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, 70386486105843025439939619828917593665686757934951
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, 62176457141856560629502157223196586755079324193331
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, 64906352462741904929101432445813822663347944758178
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, 92575867718337217661963751590579239728245598838407
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, 58203565325359399008402633568948830189458628227828
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, 80181199384826282014278194139940567587151170094390
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, 35398664372827112653829987240784473053190104293586
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, 86515506006295864861532075273371959191420517255829
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, 71693888707715466499115593487603532921714970056938
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, 54370070576826684624621495650076471787294438377604
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, 53282654108756828443191190634694037855217779295145
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, 36123272525000296071075082563815656710885258350721
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, 45876576172410976447339110607218265236877223636045
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, 17423706905851860660448207621209813287860733969412
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, 81142660418086830619328460811191061556940512689692
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, 51934325451728388641918047049293215058642563049483
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, 62467221648435076201727918039944693004732956340691
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, 15732444386908125794514089057706229429197107928209
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, 55037687525678773091862540744969844508330393682126
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, 18336384825330154686196124348767681297534375946515
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, 80386287592878490201521685554828717201219257766954
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, 78182833757993103614740356856449095527097864797581
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, 16726320100436897842553539920931837441497806860984
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, 48403098129077791799088218795327364475675590848030
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, 87086987551392711854517078544161852424320693150332
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, 59959406895756536782107074926966537676326235447210
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, 69793950679652694742597709739166693763042633987085
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, 41052684708299085211399427365734116182760315001271
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, 65378607361501080857009149939512557028198746004375
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, 35829035317434717326932123578154982629742552737307
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, 94953759765105305946966067683156574377167401875275
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, 88902802571733229619176668713819931811048770190271
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, 25267680276078003013678680992525463401061632866526
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, 36270218540497705585629946580636237993140746255962
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, 24074486908231174977792365466257246923322810917141
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, 91430288197103288597806669760892938638285025333403
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, 34413065578016127815921815005561868836468420090470
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, 23053081172816430487623791969842487255036638784583
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, 11487696932154902810424020138335124462181441773470
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, 63783299490636259666498587618221225225512486764533
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, 67720186971698544312419572409913959008952310058822
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, 95548255300263520781532296796249481641953868218774
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, 76085327132285723110424803456124867697064507995236
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, 37774242535411291684276865538926205024910326572967
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, 23701913275725675285653248258265463092207058596522
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, 29798860272258331913126375147341994889534765745501
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, 18495701454879288984856827726077713721403798879715
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, 38298203783031473527721580348144513491373226651381
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, 34829543829199918180278916522431027392251122869539
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, 40957953066405232632538044100059654939159879593635
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, 29746152185502371307642255121183693803580388584903
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, 41698116222072977186158236678424689157993532961922
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, 62467957194401269043877107275048102390895523597457
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, 23189706772547915061505504953922979530901129967519
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, 86188088225875314529584099251203829009407770775672
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, 11306739708304724483816533873502340845647058077308
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, 82959174767140363198008187129011875491310547126581
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, 97623331044818386269515456334926366572897563400500
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, 42846280183517070527831839425882145521227251250327
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, 55121603546981200581762165212827652751691296897789
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, 32238195734329339946437501907836945765883352399886
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, 75506164965184775180738168837861091527357929701337
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, 62177842752192623401942399639168044983993173312731
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, 32924185707147349566916674687634660915035914677504
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, 99518671430235219628894890102423325116913619626622
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, 73267460800591547471830798392868535206946944540724
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, 76841822524674417161514036427982273348055556214818
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, 97142617910342598647204516893989422179826088076852
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, 87783646182799346313767754307809363333018982642090
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, 10848802521674670883215120185883543223812876952786
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, 71329612474782464538636993009049310363619763878039
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, 62184073572399794223406235393808339651327408011116
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, 66627891981488087797941876876144230030984490851411
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, 60661826293682836764744779239180335110989069790714
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, 85786944089552990653640447425576083659976645795096
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, 66024396409905389607120198219976047599490197230297
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, 64913982680032973156037120041377903785566085089252
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, 16730939319872750275468906903707539413042652315011
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, 94809377245048795150954100921645863754710598436791
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, 78639167021187492431995700641917969777599028300699
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, 15368713711936614952811305876380278410754449733078
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, 40789923115535562561142322423255033685442488917353
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, 44889911501440648020369068063960672322193204149535
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, 41503128880339536053299340368006977710650566631954
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, 81234880673210146739058568557934581403627822703280
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, 82616570773948327592232845941706525094512325230608
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, 22918802058777319719839450180888072429661980811197
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, 77158542502016545090413245809786882778948721859617
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, 72107838435069186155435662884062257473692284509516
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, 20849603980134001723930671666823555245252804609722
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, 53503534226472524250874054075591789781264330331690 ]
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first10DigitsOfSum :: [Integer] -> Integer
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first10DigitsOfSum = read . take 10 . show . sum
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-----------------------------------------------------------------------------------------------
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