From 933351b64cebc5d10d61e66de91e534621ab0438 Mon Sep 17 00:00:00 2001 From: Jesse McDonald Date: Sun, 2 Aug 2015 21:50:06 -0500 Subject: [PATCH] Add solutions for problems 13-16. --- Problem13.hs | 105 +++++++++++++++++++++++++++++++++++++++++++++++++++ Problem14.hs | 28 ++++++++++++++ Problem15.hs | 12 ++++++ Problem16.hs | 2 + 4 files changed, 147 insertions(+) create mode 100644 Problem13.hs create mode 100644 Problem14.hs create mode 100644 Problem15.hs create mode 100644 Problem16.hs diff --git a/Problem13.hs b/Problem13.hs new file mode 100644 index 0000000..ca1ecf1 --- /dev/null +++ b/Problem13.hs @@ -0,0 +1,105 @@ +-- Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. + +numbers = [ 37107287533902102798797998220837590246510135740250 + , 46376937677490009712648124896970078050417018260538 + , 74324986199524741059474233309513058123726617309629 + , 91942213363574161572522430563301811072406154908250 + , 23067588207539346171171980310421047513778063246676 + , 89261670696623633820136378418383684178734361726757 + , 28112879812849979408065481931592621691275889832738 + , 44274228917432520321923589422876796487670272189318 + , 47451445736001306439091167216856844588711603153276 + , 70386486105843025439939619828917593665686757934951 + , 62176457141856560629502157223196586755079324193331 + , 64906352462741904929101432445813822663347944758178 + , 92575867718337217661963751590579239728245598838407 + , 58203565325359399008402633568948830189458628227828 + , 80181199384826282014278194139940567587151170094390 + , 35398664372827112653829987240784473053190104293586 + , 86515506006295864861532075273371959191420517255829 + , 71693888707715466499115593487603532921714970056938 + , 54370070576826684624621495650076471787294438377604 + , 53282654108756828443191190634694037855217779295145 + , 36123272525000296071075082563815656710885258350721 + , 45876576172410976447339110607218265236877223636045 + , 17423706905851860660448207621209813287860733969412 + , 81142660418086830619328460811191061556940512689692 + , 51934325451728388641918047049293215058642563049483 + , 62467221648435076201727918039944693004732956340691 + , 15732444386908125794514089057706229429197107928209 + , 55037687525678773091862540744969844508330393682126 + , 18336384825330154686196124348767681297534375946515 + , 80386287592878490201521685554828717201219257766954 + , 78182833757993103614740356856449095527097864797581 + , 16726320100436897842553539920931837441497806860984 + , 48403098129077791799088218795327364475675590848030 + , 87086987551392711854517078544161852424320693150332 + , 59959406895756536782107074926966537676326235447210 + , 69793950679652694742597709739166693763042633987085 + , 41052684708299085211399427365734116182760315001271 + , 65378607361501080857009149939512557028198746004375 + , 35829035317434717326932123578154982629742552737307 + , 94953759765105305946966067683156574377167401875275 + , 88902802571733229619176668713819931811048770190271 + , 25267680276078003013678680992525463401061632866526 + , 36270218540497705585629946580636237993140746255962 + , 24074486908231174977792365466257246923322810917141 + , 91430288197103288597806669760892938638285025333403 + , 34413065578016127815921815005561868836468420090470 + , 23053081172816430487623791969842487255036638784583 + , 11487696932154902810424020138335124462181441773470 + , 63783299490636259666498587618221225225512486764533 + , 67720186971698544312419572409913959008952310058822 + , 95548255300263520781532296796249481641953868218774 + , 76085327132285723110424803456124867697064507995236 + , 37774242535411291684276865538926205024910326572967 + , 23701913275725675285653248258265463092207058596522 + , 29798860272258331913126375147341994889534765745501 + , 18495701454879288984856827726077713721403798879715 + , 38298203783031473527721580348144513491373226651381 + , 34829543829199918180278916522431027392251122869539 + , 40957953066405232632538044100059654939159879593635 + , 29746152185502371307642255121183693803580388584903 + , 41698116222072977186158236678424689157993532961922 + , 62467957194401269043877107275048102390895523597457 + , 23189706772547915061505504953922979530901129967519 + , 86188088225875314529584099251203829009407770775672 + , 11306739708304724483816533873502340845647058077308 + , 82959174767140363198008187129011875491310547126581 + , 97623331044818386269515456334926366572897563400500 + , 42846280183517070527831839425882145521227251250327 + , 55121603546981200581762165212827652751691296897789 + , 32238195734329339946437501907836945765883352399886 + , 75506164965184775180738168837861091527357929701337 + , 62177842752192623401942399639168044983993173312731 + , 32924185707147349566916674687634660915035914677504 + , 99518671430235219628894890102423325116913619626622 + , 73267460800591547471830798392868535206946944540724 + , 76841822524674417161514036427982273348055556214818 + , 97142617910342598647204516893989422179826088076852 + , 87783646182799346313767754307809363333018982642090 + , 10848802521674670883215120185883543223812876952786 + , 71329612474782464538636993009049310363619763878039 + , 62184073572399794223406235393808339651327408011116 + , 66627891981488087797941876876144230030984490851411 + , 60661826293682836764744779239180335110989069790714 + , 85786944089552990653640447425576083659976645795096 + , 66024396409905389607120198219976047599490197230297 + , 64913982680032973156037120041377903785566085089252 + , 16730939319872750275468906903707539413042652315011 + , 94809377245048795150954100921645863754710598436791 + , 78639167021187492431995700641917969777599028300699 + , 15368713711936614952811305876380278410754449733078 + , 40789923115535562561142322423255033685442488917353 + , 44889911501440648020369068063960672322193204149535 + , 41503128880339536053299340368006977710650566631954 + , 81234880673210146739058568557934581403627822703280 + , 82616570773948327592232845941706525094512325230608 + , 22918802058777319719839450180888072429661980811197 + , 77158542502016545090413245809786882778948721859617 + , 72107838435069186155435662884062257473692284509516 + , 20849603980134001723930671666823555245252804609722 + , 53503534226472524250874054075591789781264330331690 + ] + +main = putStrLn $ take 10 $ show $ sum numbers diff --git a/Problem14.hs b/Problem14.hs new file mode 100644 index 0000000..f226cde --- /dev/null +++ b/Problem14.hs @@ -0,0 +1,28 @@ +-- The following iterative sequence is defined for the set of positive integers: +-- +-- n → n/2 (n is even) +-- n → 3n + 1 (n is odd) +-- +-- Using the rule above and starting with 13, we generate the following sequence: +-- +-- 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 +-- +-- It can be seen that this sequence (starting at 13 and finishing at 1) contains +-- 10 terms. Although it has not been proved yet (Collatz Problem), it is thought +-- that all starting numbers finish at 1. +-- +-- Which starting number, under one million, produces the longest chain? +-- +-- NOTE: Once the chain starts the terms are allowed to go above one million. +{-# LANGUAGE BangPatterns #-} +module Main (main) where +import Data.Function +import Data.List + +collatz n = if even n then n `div` 2 else 3*n + 1 + +collatzLength n = go n 1 + where go 1 !t = t + go n !t = go (collatz n) (t + 1) + +main = print $ fst $ maximumBy (compare `on` snd) $ map (\n -> (n, collatzLength n)) [1..999999] diff --git a/Problem15.hs b/Problem15.hs new file mode 100644 index 0000000..9070525 --- /dev/null +++ b/Problem15.hs @@ -0,0 +1,12 @@ +-- Starting in the top left corner of a 2×2 grid, and only being able to move +-- to the right and down, there are exactly 6 routes to the bottom right corner. +-- How many such routes are there through a 20×20 grid? +import Data.Array + +routesFrom = array ((0,0),(20,20)) $ + [ ((row,20), 1) | row <- [0..20] ] ++ + [ ((20,col), 1) | col <- [0..19] ] ++ + [ ((row, col), (routesFrom!(row+1,col)) + (routesFrom!(row,col+1))) + | row <- [0..19], col <- [0..19] ] + +main = print $ routesFrom ! (0,0) diff --git a/Problem16.hs b/Problem16.hs new file mode 100644 index 0000000..3b51d03 --- /dev/null +++ b/Problem16.hs @@ -0,0 +1,2 @@ +-- What is the sum of the digits of the number 2^1000? +main = print $ sum $ map (read . (:[])) $ show $ 2^1000