project euler 11-20

problem011.py

plist=['08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08','49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00','81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65','52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91','22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80','24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50','32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70','67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21','24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72','21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95','78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92','16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57','86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58','19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40','04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66','88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69','04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36','20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16','20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54','01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48']

for i in range(20):plist[i]=[int(j) for j in plist[i].split(' ')]

mpro = 0
for i in range(20):
    for j in range(20):
        pro = 1
        for k in [plist[i][j+k] for k in range(4) if j+k<20]:pro*=k
        if mpro<pro:mpro=pro
        pro = 1
        for k in [plist[i+k][j] for k in range(4) if i+k<20]:pro*=k
        if mpro<pro:mpro=pro
        pro = 1
        for k in [plist[i+k][j+k] for k in range(4) if i+k<20 and j+k<20]:pro*=k
        if mpro<pro:mpro=pro
        pro = 1
        for k in [plist[i+k][j-k] for k in range(4) if i+k<20 and j-k>-1]:pro*=k
        if mpro<pro:mpro=pro

print mpro
        

problem012.py

a=[n*(n+1)/2 for n in range(1,15000)]
b = range(100)
b[1] = 0
for p in b:
    if not p:continue
    elif p > 10:break
    else:
        for multi in xrange(p+p, 100, p):b[multi] = 0

b = [x for x in b if x]
for j in a:
     x = j
     i = 0
     c = [1 for y in b]
     while True:
        if x%b[i]==0:
            x /= b[i]
            c[i] += 1
        else: i += 1
        if x==1: break
        if b[i] == 97: break
    pro=1
    for z in c:pro*=z
    if pro > 500:print pro
    if pro > 500:print j

problem013.py

plist=[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 plist:sum+=i
print sum

problem014.py

chain=0
for x in range(1,1000000):
    c = 0
    j = x
    while True:
        if j == 1:break
        if j % 2 == 0:j/=2
        else: j = 3*j+1
        c += 1
    if c > chain:
        chain=c
        print x

problem015.py

pro1 = 1
pro2 = 1
for x in [i for i in range(1,41)]:pro1*=x
for x in [i for i in range(1,21)]:pro2*=x

print pro1/pro2/pro2

problem016.py

pro=1
for x in [2 for i in range(1,1001)]:pro*=x
a=str(pro)
sum=0
i=0
while True:
    sum+=int(a[i])
    if i==len(a)-1:break
    i += 1

print sum

problem017.py

a='onetwothreefourfivesixseveneightnine'
b='teneleventwelvethirteenfourteenfifteensixteenseventeeneighteennineteen'
c='twentythirtyfortyfiftysixtyseventyeightyninety'
d='hundred'
e='and'
f='onethousand'
print 900*len(d)+100*len(a)+(999-99-9)*len(e)+(len(a)+len(b)+len(c)*10+8*len(a))*10+len(f)

problem018.py

plist=['75','95 64','17 47 82','18 35 87 10','20 04 82 47 65','19 01 23 75 03 34','88 02 77 73 07 63 67','99 65 04 28 06 16 70 92','41 41 26 56 83 40 80 70 33','41 48 72 33 47 32 37 16 94 29','53 71 44 65 25 43 91 52 97 51 14','70 11 33 28 77 73 17 78 39 68 17 57','91 71 52 38 17 14 91 43 58 50 27 29 48','63 66 04 68 89 53 67 30 73 16 69 87 40 31','04 62 98 27 23 09 70 98 73 93 38 53 60 04 23']
for i in range(15):plist[i]=[int(j) for j in plist[i].split(' ')]
msum=0
for i in range(2**14):
    c = format(i,'b')
    for x in range(14-len(c)):c='0'+c
    sum=75
    j=0
    for k in range(14):
        if c[k]==1:j+=1
        sum+=plist[k+1][j]
    if sum>msum:msum=sum

print msum

problem019.py

x,y=1,0
for i in range(1,1213):
    if x%7==0 and i>12:y+=1
    if i==2:x+=28%7
    elif i%48==2: x += 29%7
    elif i%12==2: x += 28%7
    elif i%12==4 or i%12==6 or i%12==9 or i%12==11:x += 30%7
    else: x += 31%7
print y

problem020.py

pro=1
for x in [i for i in range(1,101)]:pro*=x
a=str(pro)
sum=0
i=0
while True:
    sum+=int(a[i])
    if i==len(a)-1:break
    i += 1

print sum