From 3d42c5a27b0fadbaba71529e8c982510afe1e121 Mon Sep 17 00:00:00 2001 From: MitchellHansen Date: Sat, 6 Feb 2016 21:26:44 -0800 Subject: [PATCH] A few more problems! --- problem_13.py | 108 ++++++++++++++++++++++++++++++++++++++++++++++++++ problem_14.py | 24 +++++++++++ problem_15.py | 7 ++++ problem_16.py | 14 +++++++ problem_17.py | 59 +++++++++++++++++++++++++++ problem_18.py | 0 6 files changed, 212 insertions(+) create mode 100644 problem_13.py create mode 100644 problem_14.py create mode 100644 problem_15.py create mode 100644 problem_16.py create mode 100644 problem_17.py create mode 100644 problem_18.py diff --git a/problem_13.py b/problem_13.py new file mode 100644 index 0000000..82870e5 --- /dev/null +++ b/problem_13.py @@ -0,0 +1,108 @@ +# add and find the first 10 digits of the following numbers +# oh boy is this real darn easy in python + +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 ] + +sum = 0 +for i in numbers: + sum += i +print(sum) diff --git a/problem_14.py b/problem_14.py new file mode 100644 index 0000000..65bc183 --- /dev/null +++ b/problem_14.py @@ -0,0 +1,24 @@ +#find the longest collatz sequence under one million +#if n is even n -> n/2 +#if n is odd n -> 3n + 1 + +longest_sequence = 0 +matching_number = 0 + +for i in range(1, 1000001): + sequence_count = 0 + number = i + while number != 1: + if number % 2 == 0: + number /= 2 + else: + number *= 3 + number += 1 + sequence_count += 1 + + if longest_sequence < sequence_count: + longest_sequence = sequence_count + matching_number = i + +print(longest_sequence) +print(matching_number) \ No newline at end of file diff --git a/problem_15.py b/problem_15.py new file mode 100644 index 0000000..e9d092b --- /dev/null +++ b/problem_15.py @@ -0,0 +1,7 @@ +import math + +#number of paths through a 20x20 grid +#thanks math 330! + +print(math.factorial(40) / (math.factorial(20) * math.factorial(20))) + diff --git a/problem_16.py b/problem_16.py new file mode 100644 index 0000000..de86545 --- /dev/null +++ b/problem_16.py @@ -0,0 +1,14 @@ +import math + +#print the sum of the digits of 2^1000 + +product = str('%f' % math.pow(2, 1000)) +sum = 0 + +for char in product: + if char == '.': # I can't really be bothered to do the conversion + break + sum += int(char) + +print(product) +print(sum) \ No newline at end of file diff --git a/problem_17.py b/problem_17.py new file mode 100644 index 0000000..f59f380 --- /dev/null +++ b/problem_17.py @@ -0,0 +1,59 @@ +#essentially an "english" number parser. +#count the letter counts of something like 399 "Three hundred and ninety nine" +#don't count spaces, hyphens + +# one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, +# thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen +ones_word_count_dict = {1: 3, 2: 3, 3: 5, 4: 4, 5: 4, 6: 3, 7: 5, 8: 5, 9: 4, 10: 3, 11: 6, 12:6, + 13: 8, 14: 8, 15: 7, 16: 7, 17: 9, 18: 8, 19: 8} + +# ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety +tens_word_count_dict = {1: 3, 2: 6, 3: 6, 4: 5, 5: 5, 6: 5, 7: 7, 8: 6, 9: 6} + +hundred_letter_count = 7 +and_letter_count = 3 + +def countLetters(number): + letter_count = 0 + + if number == 1000: + return 11 + + #count hundreds + hundreds = int(number / 100) + if hundreds > 0: + letter_count += hundred_letter_count + letter_count += ones_word_count_dict[hundreds] + + number -= hundreds * 100 + + # if the number is a "teen" + if number < 20 and number > 0: + if hundreds > 0: + letter_count += and_letter_count + letter_count += ones_word_count_dict[number] + return letter_count + + # if the number was an even 0 + elif number == 0: + return letter_count + + # there is a tens and later a ones value + else: + if hundreds > 0: + letter_count += and_letter_count + + tens = int(number / 10) + letter_count += tens_word_count_dict[tens] + + number -= tens * 10 + if number != 0: + letter_count += ones_word_count_dict[number] + return letter_count + + +sum_letters = 0 +for i in range(1, 1001): + sum_letters += countLetters(i) + +print(sum_letters) \ No newline at end of file diff --git a/problem_18.py b/problem_18.py new file mode 100644 index 0000000..e69de29