A few more problems!

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)

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)

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)))
+

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)

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)