Initial commit

README.md

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+Project Euler Solutions
+=======================
+
+These are my solutions to the Project Euler problems, written in Python.
+
+The incomplete solutions for the problems which I have started but not yet been able to solve are kept in the 'unsolved' folder.

problem_1.py

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+print sum([i for i in range(1, 1000) if i % 3 == 0 or i % 5 == 0])

problem_11.py

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+with open('problem_11_resource.txt', 'rb') as raw_data:
+
+	data = []
+	for row in raw_data:
+		data.append(row.split())
+
+greatest_product = 0
+
+def product_find():
+	global greatest_product
+	if product > greatest_product:
+		greatest_product = product
+
+# Horizontal
+for row in data:
+	for i in range(17):
+
+		product = 1
+		for n in range(4):
+			product *= int(row[n + i])
+
+		product_find()
+
+# Vertical
+for x in range(20):
+	for y in range(16):
+
+		product = 1
+		for n in range(4):
+			product *= int(data[x][y + n])
+
+		product_find()
+
+#Diagonal Right
+for x in range(17):
+	for y in range(17):
+
+		product = 1
+		for n in range(4):
+			product *= int(data[x + n][y + n])
+
+		product_find()
+
+#Diagonal Left
+for x in range(3, 20):
+	for y in range(17):
+
+		product = 1
+		for n in range(4):
+			product *= int(data[x - n][y + n])
+
+		product_find()
+
+print greatest_product

problem_11_resource.txt

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+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

problem_13.py

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+number = "37107287533902102798797998220837590246510135740250463769376774900097126481248969700780504170182605387432498619952474105947423330951305812372661730962991942213363574161572522430563301811072406154908250230675882075393461711719803104210475137780632466768926167069662363382013637841838368417873436172675728112879812849979408065481931592621691275889832738442742289174325203219235894228767964876702721893184745144573600130643909116721685684458871160315327670386486105843025439939619828917593665686757934951621764571418565606295021572231965867550793241933316490635246274190492910143244581382266334794475817892575867718337217661963751590579239728245598838407582035653253593990084026335689488301894586282278288018119938482628201427819413994056758715117009439035398664372827112653829987240784473053190104293586865155060062958648615320752733719591914205172558297169388870771546649911559348760353292171497005693854370070576826684624621495650076471787294438377604532826541087568284431911906346940378552177792951453612327252500029607107508256381565671088525835072145876576172410976447339110607218265236877223636045174237069058518606604482076212098132878607339694128114266041808683061932846081119106155694051268969251934325451728388641918047049293215058642563049483624672216484350762017279180399446930047329563406911573244438690812579451408905770622942919710792820955037687525678773091862540744969844508330393682126183363848253301546861961243487676812975343759465158038628759287849020152168555482871720121925776695478182833757993103614740356856449095527097864797581167263201004368978425535399209318374414978068609844840309812907779179908821879532736447567559084803087086987551392711854517078544161852424320693150332599594068957565367821070749269665376763262354472106979395067965269474259770973916669376304263398708541052684708299085211399427365734116182760315001271653786073615010808570091499395125570281987460043753582903531743471732693212357815498262974255273730794953759765105305946966067683156574377167401875275889028025717332296191766687138199318110487701902712526768027607800301367868099252546340106163286652636270218540497705585629946580636237993140746255962240744869082311749777923654662572469233228109171419143028819710328859780666976089293863828502533340334413065578016127815921815005561868836468420090470230530811728164304876237919698424872550366387845831148769693215490281042402013833512446218144177347063783299490636259666498587618221225225512486764533677201869716985443124195724099139590089523100588229554825530026352078153229679624948164195386821877476085327132285723110424803456124867697064507995236377742425354112916842768655389262050249103265729672370191327572567528565324825826546309220705859652229798860272258331913126375147341994889534765745501184957014548792889848568277260777137214037988797153829820378303147352772158034814451349137322665138134829543829199918180278916522431027392251122869539409579530664052326325380441000596549391598795936352974615218550237130764225512118369380358038858490341698116222072977186158236678424689157993532961922624679571944012690438771072750481023908955235974572318970677254791506150550495392297953090112996751986188088225875314529584099251203829009407770775672113067397083047244838165338735023408456470580773088295917476714036319800818712901187549131054712658197623331044818386269515456334926366572897563400500428462801835170705278318394258821455212272512503275512160354698120058176216521282765275169129689778932238195734329339946437501907836945765883352399886755061649651847751807381688378610915273579297013376217784275219262340194239963916804498399317331273132924185707147349566916674687634660915035914677504995186714302352196288948901024233251169136196266227326746080059154747183079839286853520694694454072476841822524674417161514036427982273348055556214818971426179103425986472045168939894221798260880768528778364618279934631376775430780936333301898264209010848802521674670883215120185883543223812876952786713296124747824645386369930090493103636197638780396218407357239979422340623539380833965132740801111666627891981488087797941876876144230030984490851411606618262936828367647447792391803351109890697907148578694408955299065364044742557608365997664579509666024396409905389607120198219976047599490197230297649139826800329731560371200413779037855660850892521673093931987275027546890690370753941304265231501194809377245048795150954100921645863754710598436791786391670211874924319957006419179697775990283006991536871371193661495281130587638027841075444973307840789923115535562561142322423255033685442488917353448899115014406480203690680639606723221932041495354150312888033953605329934036800697771065056663195481234880673210146739058568557934581403627822703280826165707739483275922328459417065250945123252306082291880205877731971983945018088807242966198081119777158542502016545090413245809786882778948721859617721078384350691861554356628840622574736922845095162084960398013400172393067166682355524525280460972253503534226472524250874054075591789781264330331690"
+total = 0
+
+for i in range(5000)[::50]:
+	total += int(number[i:i+50:])
+
+print str(total)[:10:]

problem_14.py

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+max_count = 0
+
+def collatz(n):
+	if n == 0:
+		return 1
+
+	if n % 2 == 0:
+		return n/2
+	else:
+		return (3*n) + 1
+
+for i in range(1, 1000000):
+	n = i
+	count = 0
+	while n > 1:
+		n = collatz(n)
+		count += 1
+
+	if count > max_count:
+		max_count = count
+		solution = i
+
+print solution

problem_16.py

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+num = str(2 ** 1000)
+total = 0
+
+for digit in num:
+	total += int(digit)
+
+print total

problem_17.py

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+total = 0
+ones = ['one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine']
+teens = ['ten', 'eleven', 'twelve', 'thirteen', 'fourteen', 'fifteen', 'sixteen', 'seventeen', 'eighteen', 'nineteen']
+teys = ['twenty', 'thirty', 'forty', 'fifty', 'sixty', 'seventy', 'eighty', 'ninety']
+
+# 1 - 9
+for one in ones:
+	print one
+	total += len(one)
+
+#10 - 19
+for teen in teens:
+	print teen
+	total += len(teen)
+
+#20 - 99
+for tey in teys:
+	print tey
+	total += len(tey)
+
+	for one in ones:
+		print tey, one
+		total += len(tey)
+		total += len(one)
+
+for one in ones:
+	print one, 'hundred'
+	total += len(one)
+	total += len('hundred')
+
+	for sub_one in ones:
+		print one, 'hundred', 'and', sub_one
+		total += len(one)
+		total += len('hundred')
+		total += len('and')
+		total += len(sub_one)
+
+	for teen in teens:
+		print one, 'hundred', 'and', teen
+		total += len(one)
+		total += len('hundred')
+		total += len('and')
+		total += len(teen)
+
+	for tey in teys:
+		print one, 'hundred', 'and', tey
+		total += len(one)
+		total += len('hundred')
+		total += len('and')
+		total += len(tey)
+
+		for sub_one in ones:
+			print one, 'hundred', 'and', tey, sub_one
+			total += len(one)
+			total += len('hundred')
+			total += len('and')
+			total += len(tey)
+			total += len(sub_one)
+
+print 'one', 'thousand'
+
+total += len('one')
+total += len('thousand')
+
+print
+print total

problem_18.py

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+with open('problem_18_resource.txt', 'rb') as raw_data:
+	data = []
+	for row in raw_data:
+		data.append(row.split())
+
+greatest_total = 0
+start = int(data.pop(0)[0])
+
+for c in range(8193, 16384):
+
+	this_total = start
+	position = 0
+
+	for i, row in enumerate(data):
+		this_c = str(bin(c))[i+2]
+		position += int(this_c)
+		this_total += int(row[position])
+
+	if this_total > greatest_total:
+		greatest_total = this_total
+
+print greatest_total

problem_18_resource.txt

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+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

problem_2.py

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+fib = [1, 2]
+i = 2
+n = 0
+
+while n < 4000000:
+	n = fib[i - 1] + fib[i - 2]
+	fib.append(n)
+	i += 1
+
+print sum(filter(lambda x: x % 2 == 0, fib))

problem_20.py

@@ -0,0 +1,10 @@
+total = 0
+factorial = 1
+
+for i in range(2, 101):
+	factorial *= i
+
+for c in str(factorial):
+	total += int(c)
+
+print total

problem_21.py

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+def divisor_sum(n):
+	d_sum = 0
+	for d in range(1, n):
+		if n % d == 0:
+			d_sum += d
+	return d_sum
+
+def is_amicable(n1):
+	n2 = divisor_sum(n1)
+	if divisor_sum(n2) == n1 and n1 != n2:
+		return True
+	else:
+		return False
+
+total = 0
+
+for i in range(10000):
+	if is_amicable(i):
+		total += i
+
+print total

problem_25.py

@@ -0,0 +1,14 @@
+fib_1 = 1;
+fib_2 = 1;
+n = 0;
+i = 2;
+
+while len(str(n)) < 1000:
+	n = fib_1 + fib_2
+	print n
+	fib_1 = fib_2
+	fib_2 = n
+	i += 1
+
+print
+print i

problem_26.py

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+from decimal import *
+
+getcontext().prec = 10000
+
+def recursion_length(n):
+	f = str(1/Decimal(n))[2::]
+	for cycle_length in range(1, 10000):
+		part_one = f[0:0+cycle_length:]
+		part_two = f[cycle_length:cycle_length*2:]
+		part_three = f[cycle_length*2:cycle_length*3:]
+		if part_one == part_two and part_two == part_three:
+			return cycle_length
+	return 0
+
+longest_cycle = 0
+
+for i in range(1, 1000):
+	if recursion_length(i) > longest_cycle:
+		i_longest = i
+		longest_cycle = recursion_length(i)
+
+print
+print i_longest

problem_4.py

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+min_limit = 100
+max_limit = 999
+largest = 0
+
+def is_palindrome(n):
+	n = str(n)
+	l = len(n)
+	if l % 2 == 0:
+		if n[:l/2:] == n[:(l/2)-1:-1]:
+			return True
+	else:
+		if n[:((l+1)/2)-1:] == n[:((l+1)/2)-1:-1]:
+			return True
+	return False
+
+for a in range(min_limit, max_limit+1)[::-1]:
+	for b in range(min_limit, max_limit+1)[::-1]:
+		if is_palindrome(a*b) and a*b > largest:
+			largest = a*b
+
+print largest

problem_5.py

@@ -0,0 +1,12 @@
+i = 100000
+found = False
+
+while not found:
+	found = True
+	for n in range(1, 21):
+		if i % n != 0:
+			found = False
+			break
+	i += 20
+
+print i - 20

problem_6.py

@@ -0,0 +1,8 @@
+sum_natural = 0
+sum_squares = 0
+
+for i in range(1, 101):
+	sum_natural += i
+	sum_squares += i**2
+
+print sum_natural**2 - sum_squares

problem_8.py

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+search_number = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"
+
+greatest_product = 0
+
+for i in range(0, 994):
+	product = 1
+	for n in search_number[i:i+5:]:
+		product *= int(n)
+	if product > greatest_product:
+		greatest_product = product
+
+print greatest_product