Soru 10

Summation of primes

Problem 10

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

Asal sayıların toplamı 

Soru 10

10 dan küçük asal sayıların toplamı, 2 + 3 + 5 + 7 = 17 ' dir.

İki milyondan küçük asal sayıların toplamını bulun.

Haskell Kodu 

	primes = filterPrime [2..]
	where filterPrime (p:xs) = p : filterPrime (filter (\x-> mod x p /= 0) xs)
	problem_10 = foldr (+) 0 (takeWhile (<2000000) primes)

view raw problem_10.hs hosted with ❤ by GitHub

Soru 9

Special Pythagorean triplet

Problem 9

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

a² + b² = c²

For example, 3² + 4² = 9 + 16 = 25 = 5².
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

Özel Pisagor üçlüsü

Soru 9

Bir pisagor üçlüsü, a < b < c durumunu sağlayan üç adet doğal sayıdan oluşan ve bunlar,

a² + b² = c²

Denkliği de geçerlidir.

Örneğin, 3² + 4² = 9 + 16 = 25 = 5².
a + b + c = 1000 denkliğini geçerleyen yalnız bir pisagor üçlüsü mevcuttur.
abc çarpımını bulunuz

Python Kodu

	def issquarepyth(a,b,c):
	return (a*a + b*b) == c*c
	def issumok(a,b,c):
	return (a+b+c) == 1000
	def findTriplet():
	a=0
	b=0
	c=0
	while True:
	for b in range(0, c):
	for a in range(0, b):
	if(issquarepyth(a,b,c) and issumok(a,b,c)):
	return a*b*c
	c += 1

view raw Soru9.py hosted with ❤ by GitHub

Soru 8

Largest product in a series

Problem 8

The four adjacent digits in the 1000-digit number that have the greatest product are 

9 × 9 × 8 × 9 = 5832.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

Serideki en büyük çarpım

Problem 8

Aşağıdaki 1000 basamaklı sayıdaki ardışık 4 basamağın çarpımının en büyük değeri 

9 × 9 × 8 × 9 = 5832 'dir.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Ardışık 13 basamak çarpımının en büyük değeri nedir?

Haskell Kodu

	import Data.Char
	num = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"
	prod13 num
	| length num >= 13 = (product$map digitToInt (take 13 num)) : (prod13 (tail num))
	| otherwise = []
	problem_8 = maximum$prod13 num

view raw problem_8.hs hosted with ❤ by GitHub

Python Kodu

	def mthndigits(number,m,n):
	a = str(number)
	return int(a[m:m+n])
	def digitmultiply(number):
	stringfied = str(number)
	product = 1
	for x in stringfied:
	product *= int(x)
	return product
	thenumber = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450
	sequencelength = 13
	prod = mthndigits(thenumber,0,sequencelength)
	max = digitmultiply(prod)
	print(max)
	print(prod)
	i = 1
	prod = 1
	while True:
	prod = digitmultiply(mthndigits(thenumber,i,sequencelength))
	if( prod > max):
	max = prod
	i += 1
	print (max)
	print(max)

view raw Soru8.py hosted with ❤ by GitHub

Soru 7

10001st prime

Problem 7

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10 001st prime number?

10001 nci asal

Soru 7

2, 3, 5, 7, 11, ve 13 olarak llk altı asal sayıyı listelediğimizde, 6 ıncı asal sayının 13 olduğunu görebiliriz.
10 001inci asal sayı kaçtır?

Python Kodu

	def nthPrimeSqrt(n):
	number = 3
	primemultiples = []
	primes = []
	primes.append(2)
	prime = True
	while (len(primes)<=n):
	prime = True
	if number in primemultiples:
	prime = False
	number +=2
	continue
	root = int(math.ceil(math.sqrt(number)))
	for i in range (3, root):
	if number%i == 0:
	prime = False
	break
	if(prime):
	multiple = number
	while multiple <= n:
	multiple *= 2
	primemultiples.append(multiple)
	primes.append(number)
	number += 2
	return primes[n-1]

view raw Soru7v3.py hosted with ❤ by GitHub

Alternatif çözüm 1 için
Alternatif çözüm 2 için

For alternative solution 1 
For alternative solution 2

Soru 6

Sum square difference

Problem 6

The sum of the squares of the first ten natural numbers is,

1² + 2² + ... + 10² = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + ... + 10)² = 55² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Toplam kare farkı

Problem 6

İlk 10 doğal sayının kareleri toplamı, 1² + 2² + ... + 10² = 385' dir.

İlk 10 doğal sayının toplamlarının karesi, (1 + 2 + ... + 10)² = 55² = 3025' dir.

İlk on doğal sayının toplamlarının karesi ile karelerinin toplamının farkı, 
3025 − 385 = 2640 ' dir.

İlk 100 doğal sayının toplamlarının karesi ile karelerinin toplamının farkını bulun.

Haskell Kodu

problem_6 = ((sum [1..100])^2) - (sum $ map (^2) [1..100])

view raw problem_6.hs hosted with ❤ by GitHub

Python Kodu

	def sumofsquares (n):
	sum = 0
	for x in range(1,n+1):
	sum += x*x
	return sum
	def squareofsum(n):
	sum = 0
	for x in range(1,n+1):
	sum += x
	return sum*sum
	print(squareofsum(100) - sumofsquares(100))

view raw Soru6.py hosted with ❤ by GitHub

Soru 5

Smallest multiple

Problem 5

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

En Küçük Kat

Soru 5

2520 1 den 10 a kadar olan bütün sayılara kalansız bölünebilen en küçük sayıdır.

1 den 20 ye kadar olan bütün sayılara kalansız bölünebilen en küçük sayı kaçtır?

Python Kodu

	def divisible (n):
	if(n % 7 != 0):
	return False
	if(n % 9 != 0):
	return False
	if(n % 11 != 0):
	return False
	if(n % 13 != 0):
	return False
	if(n % 16 != 0):
	return False
	if(n % 17 != 0):
	return False
	if(n % 19 != 0):
	return False
	return True
	divisible(2432902008176640000)
	search = 7
	while True:
	if(divisible(search)):
	print(search)
	break
	search +=1

view raw Soru5.py hosted with ❤ by GitHub

For an alternative solution for this problem
Sorunun alternatif bir çözümü için

Soru 4

Largest palindrome product

Problem 4

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.

Find the largest palindrome made from the product of two 3-digit numbers.

En büyük palindrom çarpım

Problem 4

Sağdan Sola ve Soldan Sağa okunuşları aynı olan sayılara Palindrom sayılar denir. 2 basamaklı iki sayının çarpımından oluşturulabilen en büyük palindrom sayı 91 × 99 = 9009 dur.2 tane 3 basamaklı sayının çarpımından oluşturulabilen en büyük palindrom sayıyı bulunuz.

Haskell Kodu

	isPalindrome xs = xs == (reverse xs)
	problem_4 = maximum [x*y|x<-[900..999],y<-[900..999],isPalindrome (show (x*y))]

view raw problem_4.hs hosted with ❤ by GitHub

Python Kodu

	def palindrome(str):
	return str == str[::-1]
	for i in range(100, 999):
	for j in range(100,999):
	if(palindrome(str(i*j))):
	print(i*j)

view raw Soru4.py hosted with ❤ by GitHub

Soru 3

Largest prime factor

Problem 3

The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?

En büyük asal bölen

Soru 3

13195 sayısının asal bölenleri 5, 7, 13 and 29 dir.
600851475143 sayısının en büyük asal böleni kaçtır ?

Python Kodu

	def primer(n):
	notprime = False
	for x in range(2 , n):
	for y in range (2, x):
	if x%y == 0:
	notprime = True
	break
	if notprime == False and n % x == 0:
	print(str(x) + " is prime and is a factor")
	notprime = False
	primer(600851475143)

view raw Soru3.py hosted with ❤ by GitHub

Soru 2

Even Fibonacci numbers 

Problem 2

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

Çift Fibonacci sayıları

Problem 2

Fibonacci dizisindeki her yeni terim kendisinden önceki iki terimin toplamından oluşturulur. 1 ve 2 ile başlayan ilk 10 terim aşağıdaki gibidir.

                                            1, 2, 3, 5, 8, 13, 21, 34, 55, 89,

4.000.000 u aşmayan tüm çift fibonacci sayılarının toplamını bulun.

Haskell Kodu

	fib n
	| n == 1 = 1
	| n == 2 = 2
	| n == 3 = 3
	| otherwise = 2*fib(n-2)+fib(n-3)
	problem_2 = sum [ fib x|x<-[1..32], even (fib x)]

view raw problem_2.hs hosted with ❤ by GitHub

Python Kodu

	def fib (n) :
	if (n == 1 or n==2):
	return 1
	return (fib(n-1) + fib(n-2))
	limit = 4000000
	x = 1
	sum = 0
	a = 0
	while a < limit:
	a = fib(x)
	x += 1
	if a % 2 == 0 :
	sum += a
	print( " sum of the even fibonacci numbers that are smaller than 4000000 is " + str(sum))

view raw Soru2.py hosted with ❤ by GitHub