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""" |
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Project Euler Problem 13: Large Sum |
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3
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=================================== |
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4
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5
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.. module:: solutions.problem13 |
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6
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:synopsis: My solution to problem #13. |
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8
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The source code for this problem can be |
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`found here <https://bitbucket.org/nekedome/project-euler/src/master/solutions/problem13.py>`_. |
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11
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Problem Statement |
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12
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################# |
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13
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14
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Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. |
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15
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16
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.. math:: |
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17
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18
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37107287533902102798797998220837590246510135740250 \\\\ |
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19
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46376937677490009712648124896970078050417018260538 \\\\ |
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20
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74324986199524741059474233309513058123726617309629 \\\\ |
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21
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91942213363574161572522430563301811072406154908250 \\\\ |
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22
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23067588207539346171171980310421047513778063246676 \\\\ |
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23
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89261670696623633820136378418383684178734361726757 \\\\ |
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24
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28112879812849979408065481931592621691275889832738 \\\\ |
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25
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44274228917432520321923589422876796487670272189318 \\\\ |
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26
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47451445736001306439091167216856844588711603153276 \\\\ |
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27
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70386486105843025439939619828917593665686757934951 \\\\ |
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28
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62176457141856560629502157223196586755079324193331 \\\\ |
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29
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64906352462741904929101432445813822663347944758178 \\\\ |
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30
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92575867718337217661963751590579239728245598838407 \\\\ |
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31
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58203565325359399008402633568948830189458628227828 \\\\ |
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32
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80181199384826282014278194139940567587151170094390 \\\\ |
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33
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35398664372827112653829987240784473053190104293586 \\\\ |
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34
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86515506006295864861532075273371959191420517255829 \\\\ |
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35
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71693888707715466499115593487603532921714970056938 \\\\ |
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36
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54370070576826684624621495650076471787294438377604 \\\\ |
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37
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53282654108756828443191190634694037855217779295145 \\\\ |
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38
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36123272525000296071075082563815656710885258350721 \\\\ |
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39
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45876576172410976447339110607218265236877223636045 \\\\ |
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40
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17423706905851860660448207621209813287860733969412 \\\\ |
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41
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81142660418086830619328460811191061556940512689692 \\\\ |
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42
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51934325451728388641918047049293215058642563049483 \\\\ |
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43
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62467221648435076201727918039944693004732956340691 \\\\ |
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44
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15732444386908125794514089057706229429197107928209 \\\\ |
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45
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55037687525678773091862540744969844508330393682126 \\\\ |
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46
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18336384825330154686196124348767681297534375946515 \\\\ |
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47
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80386287592878490201521685554828717201219257766954 \\\\ |
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48
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78182833757993103614740356856449095527097864797581 \\\\ |
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49
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16726320100436897842553539920931837441497806860984 \\\\ |
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50
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48403098129077791799088218795327364475675590848030 \\\\ |
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51
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87086987551392711854517078544161852424320693150332 \\\\ |
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52
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59959406895756536782107074926966537676326235447210 \\\\ |
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53
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69793950679652694742597709739166693763042633987085 \\\\ |
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54
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41052684708299085211399427365734116182760315001271 \\\\ |
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55
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65378607361501080857009149939512557028198746004375 \\\\ |
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56
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35829035317434717326932123578154982629742552737307 \\\\ |
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57
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94953759765105305946966067683156574377167401875275 \\\\ |
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58
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88902802571733229619176668713819931811048770190271 \\\\ |
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59
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25267680276078003013678680992525463401061632866526 \\\\ |
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60
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36270218540497705585629946580636237993140746255962 \\\\ |
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61
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24074486908231174977792365466257246923322810917141 \\\\ |
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62
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91430288197103288597806669760892938638285025333403 \\\\ |
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63
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34413065578016127815921815005561868836468420090470 \\\\ |
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64
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23053081172816430487623791969842487255036638784583 \\\\ |
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65
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11487696932154902810424020138335124462181441773470 \\\\ |
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66
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63783299490636259666498587618221225225512486764533 \\\\ |
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67
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67720186971698544312419572409913959008952310058822 \\\\ |
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68
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95548255300263520781532296796249481641953868218774 \\\\ |
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69
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76085327132285723110424803456124867697064507995236 \\\\ |
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70
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37774242535411291684276865538926205024910326572967 \\\\ |
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71
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23701913275725675285653248258265463092207058596522 \\\\ |
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72
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29798860272258331913126375147341994889534765745501 \\\\ |
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73
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18495701454879288984856827726077713721403798879715 \\\\ |
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74
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38298203783031473527721580348144513491373226651381 \\\\ |
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75
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34829543829199918180278916522431027392251122869539 \\\\ |
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76
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40957953066405232632538044100059654939159879593635 \\\\ |
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77
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29746152185502371307642255121183693803580388584903 \\\\ |
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78
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41698116222072977186158236678424689157993532961922 \\\\ |
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79
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62467957194401269043877107275048102390895523597457 \\\\ |
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80
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23189706772547915061505504953922979530901129967519 \\\\ |
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81
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86188088225875314529584099251203829009407770775672 \\\\ |
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82
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11306739708304724483816533873502340845647058077308 \\\\ |
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83
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82959174767140363198008187129011875491310547126581 \\\\ |
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84
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97623331044818386269515456334926366572897563400500 \\\\ |
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85
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42846280183517070527831839425882145521227251250327 \\\\ |
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86
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55121603546981200581762165212827652751691296897789 \\\\ |
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87
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32238195734329339946437501907836945765883352399886 \\\\ |
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88
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75506164965184775180738168837861091527357929701337 \\\\ |
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89
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62177842752192623401942399639168044983993173312731 \\\\ |
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90
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32924185707147349566916674687634660915035914677504 \\\\ |
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91
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99518671430235219628894890102423325116913619626622 \\\\ |
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92
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73267460800591547471830798392868535206946944540724 \\\\ |
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93
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76841822524674417161514036427982273348055556214818 \\\\ |
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94
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97142617910342598647204516893989422179826088076852 \\\\ |
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95
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87783646182799346313767754307809363333018982642090 \\\\ |
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96
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10848802521674670883215120185883543223812876952786 \\\\ |
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97
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71329612474782464538636993009049310363619763878039 \\\\ |
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98
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62184073572399794223406235393808339651327408011116 \\\\ |
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99
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66627891981488087797941876876144230030984490851411 \\\\ |
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100
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60661826293682836764744779239180335110989069790714 \\\\ |
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101
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85786944089552990653640447425576083659976645795096 \\\\ |
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102
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66024396409905389607120198219976047599490197230297 \\\\ |
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103
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64913982680032973156037120041377903785566085089252 \\\\ |
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104
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16730939319872750275468906903707539413042652315011 \\\\ |
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105
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94809377245048795150954100921645863754710598436791 \\\\ |
|
106
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78639167021187492431995700641917969777599028300699 \\\\ |
|
107
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15368713711936614952811305876380278410754449733078 \\\\ |
|
108
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40789923115535562561142322423255033685442488917353 \\\\ |
|
109
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44889911501440648020369068063960672322193204149535 \\\\ |
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110
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41503128880339536053299340368006977710650566631954 \\\\ |
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111
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81234880673210146739058568557934581403627822703280 \\\\ |
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112
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82616570773948327592232845941706525094512325230608 \\\\ |
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113
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22918802058777319719839450180888072429661980811197 \\\\ |
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114
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77158542502016545090413245809786882778948721859617 \\\\ |
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115
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72107838435069186155435662884062257473692284509516 \\\\ |
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116
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20849603980134001723930671666823555245252804609722 \\\\ |
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117
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53503534226472524250874054075591789781264330331690 |
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118
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119
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Solution Discussion |
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120
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################### |
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121
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122
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Simply use Python's arbitrary precision arithmetic to compute this large sum, then divide by the appropriate power of |
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123
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:math:`10` to leave the :math:`10` most significant digits. |
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124
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125
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Solution Implementation |
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126
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####################### |
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127
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128
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.. literalinclude:: ../../solutions/problem13.py |
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129
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:language: python |
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130
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:lines: 133- |
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""" |
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133
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from lib.digital import num_digits |
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134
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135
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136
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def solve(): |
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137
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""" Compute the answer to Project Euler's problem #13 """ |
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138
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139
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# Build a list of integers |
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140
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numbers = """ |
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141
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37107287533902102798797998220837590246510135740250 |
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142
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46376937677490009712648124896970078050417018260538 |
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143
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74324986199524741059474233309513058123726617309629 |
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144
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91942213363574161572522430563301811072406154908250 |
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145
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23067588207539346171171980310421047513778063246676 |
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146
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89261670696623633820136378418383684178734361726757 |
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147
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28112879812849979408065481931592621691275889832738 |
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148
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44274228917432520321923589422876796487670272189318 |
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149
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47451445736001306439091167216856844588711603153276 |
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150
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70386486105843025439939619828917593665686757934951 |
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151
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62176457141856560629502157223196586755079324193331 |
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152
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64906352462741904929101432445813822663347944758178 |
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153
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92575867718337217661963751590579239728245598838407 |
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154
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58203565325359399008402633568948830189458628227828 |
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155
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80181199384826282014278194139940567587151170094390 |
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156
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35398664372827112653829987240784473053190104293586 |
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157
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86515506006295864861532075273371959191420517255829 |
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158
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71693888707715466499115593487603532921714970056938 |
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159
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54370070576826684624621495650076471787294438377604 |
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160
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53282654108756828443191190634694037855217779295145 |
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161
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36123272525000296071075082563815656710885258350721 |
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162
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45876576172410976447339110607218265236877223636045 |
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163
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17423706905851860660448207621209813287860733969412 |
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164
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81142660418086830619328460811191061556940512689692 |
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165
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51934325451728388641918047049293215058642563049483 |
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166
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62467221648435076201727918039944693004732956340691 |
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167
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15732444386908125794514089057706229429197107928209 |
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168
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55037687525678773091862540744969844508330393682126 |
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169
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18336384825330154686196124348767681297534375946515 |
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170
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80386287592878490201521685554828717201219257766954 |
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171
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78182833757993103614740356856449095527097864797581 |
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172
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16726320100436897842553539920931837441497806860984 |
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173
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48403098129077791799088218795327364475675590848030 |
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174
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87086987551392711854517078544161852424320693150332 |
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175
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59959406895756536782107074926966537676326235447210 |
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176
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69793950679652694742597709739166693763042633987085 |
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177
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41052684708299085211399427365734116182760315001271 |
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178
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65378607361501080857009149939512557028198746004375 |
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179
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35829035317434717326932123578154982629742552737307 |
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180
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94953759765105305946966067683156574377167401875275 |
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181
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88902802571733229619176668713819931811048770190271 |
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182
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25267680276078003013678680992525463401061632866526 |
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183
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36270218540497705585629946580636237993140746255962 |
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184
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24074486908231174977792365466257246923322810917141 |
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185
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91430288197103288597806669760892938638285025333403 |
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186
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34413065578016127815921815005561868836468420090470 |
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187
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23053081172816430487623791969842487255036638784583 |
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188
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11487696932154902810424020138335124462181441773470 |
|
189
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63783299490636259666498587618221225225512486764533 |
|
190
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67720186971698544312419572409913959008952310058822 |
|
191
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95548255300263520781532296796249481641953868218774 |
|
192
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76085327132285723110424803456124867697064507995236 |
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193
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37774242535411291684276865538926205024910326572967 |
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194
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23701913275725675285653248258265463092207058596522 |
|
195
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29798860272258331913126375147341994889534765745501 |
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196
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18495701454879288984856827726077713721403798879715 |
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197
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38298203783031473527721580348144513491373226651381 |
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198
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34829543829199918180278916522431027392251122869539 |
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199
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40957953066405232632538044100059654939159879593635 |
|
200
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29746152185502371307642255121183693803580388584903 |
|
201
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41698116222072977186158236678424689157993532961922 |
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202
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62467957194401269043877107275048102390895523597457 |
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203
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23189706772547915061505504953922979530901129967519 |
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204
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86188088225875314529584099251203829009407770775672 |
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205
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11306739708304724483816533873502340845647058077308 |
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206
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82959174767140363198008187129011875491310547126581 |
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207
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97623331044818386269515456334926366572897563400500 |
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208
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42846280183517070527831839425882145521227251250327 |
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209
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55121603546981200581762165212827652751691296897789 |
|
210
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32238195734329339946437501907836945765883352399886 |
|
211
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75506164965184775180738168837861091527357929701337 |
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212
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62177842752192623401942399639168044983993173312731 |
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213
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32924185707147349566916674687634660915035914677504 |
|
214
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99518671430235219628894890102423325116913619626622 |
|
215
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73267460800591547471830798392868535206946944540724 |
|
216
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76841822524674417161514036427982273348055556214818 |
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217
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97142617910342598647204516893989422179826088076852 |
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218
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87783646182799346313767754307809363333018982642090 |
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219
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|
|
10848802521674670883215120185883543223812876952786 |
|
220
|
|
|
71329612474782464538636993009049310363619763878039 |
|
221
|
|
|
62184073572399794223406235393808339651327408011116 |
|
222
|
|
|
66627891981488087797941876876144230030984490851411 |
|
223
|
|
|
60661826293682836764744779239180335110989069790714 |
|
224
|
|
|
85786944089552990653640447425576083659976645795096 |
|
225
|
|
|
66024396409905389607120198219976047599490197230297 |
|
226
|
|
|
64913982680032973156037120041377903785566085089252 |
|
227
|
|
|
16730939319872750275468906903707539413042652315011 |
|
228
|
|
|
94809377245048795150954100921645863754710598436791 |
|
229
|
|
|
78639167021187492431995700641917969777599028300699 |
|
230
|
|
|
15368713711936614952811305876380278410754449733078 |
|
231
|
|
|
40789923115535562561142322423255033685442488917353 |
|
232
|
|
|
44889911501440648020369068063960672322193204149535 |
|
233
|
|
|
41503128880339536053299340368006977710650566631954 |
|
234
|
|
|
81234880673210146739058568557934581403627822703280 |
|
235
|
|
|
82616570773948327592232845941706525094512325230608 |
|
236
|
|
|
22918802058777319719839450180888072429661980811197 |
|
237
|
|
|
77158542502016545090413245809786882778948721859617 |
|
238
|
|
|
72107838435069186155435662884062257473692284509516 |
|
239
|
|
|
20849603980134001723930671666823555245252804609722 |
|
240
|
|
|
53503534226472524250874054075591789781264330331690 |
|
241
|
|
|
""" |
|
242
|
|
|
numbers = numbers.split("\n") |
|
243
|
|
|
numbers = [number.strip() for number in numbers] |
|
244
|
|
|
numbers = [int(number) for number in numbers if number != ""] |
|
245
|
|
|
|
|
246
|
|
|
# Sum the list of integers |
|
247
|
|
|
total = sum(numbers) |
|
248
|
|
|
|
|
249
|
|
|
# Compute the number of digits in the sum, and how many to truncate to give the top 10 digits |
|
250
|
|
|
target = 10 |
|
251
|
|
|
n_digits = num_digits(total) |
|
252
|
|
|
truncate_digits = n_digits - target |
|
253
|
|
|
|
|
254
|
|
|
# Compute the final answer (first 10 digits) |
|
255
|
|
|
answer = total // (10 ** truncate_digits) |
|
256
|
|
|
return answer |
|
257
|
|
|
|
|
258
|
|
|
|
|
259
|
|
|
expected_answer = 5537376230 |
|
|
|
|
|
|
260
|
|
|
|
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