Project Euler
What is project Euler : All the info here
Project Euler is basically a series of Mathematics/Programming problems.
My progression : 10 / 284 [as of April 4, 2010]
Codes Snippets will come later on.
All the codes written here are done in Python 3.1
Notice : My code is not optimized in any way. I just did it so it would work. I might change it later if I want.
""" Problem 1 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ x = 0 for i in range(1, 1000): if i%3 == 0: x += i elif i%5 == 0: x += i print(x)
""" 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, ... Find the sum of all the even-valued terms in the sequence which do not exceed four million. """ x = 2 i = 2 buffer1 = 1 buffer2 = 0 while i<4000000: buffer2 = i i += buffer1 buffer1 = buffer2 if i%2 == 0: x += i print(x)
</div> <div>""" Problem 3 The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? """ x = 600851475143 primes = ([]) # Array of prime number def isprime(n): for i in range(2, int(n/2)+1): if n % i == 0: #print(i, ' est un diviseur de ', n) return False break return True for i in range(1,int(x**0.5)+1): if x % i == 0: if isprime(i): print(i)</div> <div>
</div> <div>""" 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. """ Numbers = [] Multi = 0 def palindrome(n): for p in range(0, len(n)): if n[p] != n[len(n)-p-1]: return False break return True def FindBigPali(Lower,Upper): big = 0; for x in range(Upper,Lower, -1): for y in range(Upper,Lower, -1): Numbers = [] Multi = x*y while Multi > 0: Numbers.append(int(Multi%10)) Multi = int(Multi/10) if palindrome(Numbers): if(x*y > big): big = x*y return big #Find the biggest palindrome UpperBound = 999 LowerBound = 100 print(FindBigPali(LowerBound,UpperBound)) </div> <div>
""" 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 number that is evenly divisible by all of the numbers from 1 to 20? """ def FindSmallNumber(n): Even = False x = 20 while (True): for i in range(1,n+1): if x % i != 0: #print(x) break #print(i) if i == n and x % i == 0: print(x, ' can be divided by 1 to ', n) return x x += n if x % 10000000 == 0: print(x) # Print to see the progress by steps of 10 000 000 # n is the biggest divider FindSmallNumber(20)
</div>
<div>"""
Problem 6
The sum of the squares of the first ten natural numbers is,
1^(2) + 2^(2) + ... + 10^(2) = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^(2) = 55^(2) = 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.
"""
SumOfSquares = 0;
SquareOfSum = 0;
n = 100
for i in range(1,n+1):
SumOfSquares += i**2
SquareOfSum += i
SquareOfSum = SquareOfSum**2
print('The result is:', SquareOfSum - SumOfSquares)
</div>
<div>
</div>
<div>"""
Problem 7
By listing the first six prime numbers:
2, 3, 5, 7, 11, and 13,
we can see that the 6^(th) prime is 13.
What is the 10001^(st) prime number?
"""
def isprime(n):
for i in range(2, int(n/2)+1):
if n % i == 0:
#print(i, ' est un diviseur de ', n)
return False
break
return True
#Ineficient Algorythm
#Loop while checking if the number is prime
PrimeNumber = 1;
Limit = 10001
x = 1
while(PrimeNumber < Limit):
x += 2
if isprime(x):
PrimeNumber += 1;
if (x - 1) % 10000 == 0:
print('Step :', x)
print('The', Limit, 'th prime number is', x)
This one need to be revised…it works but is not really pretty
</div> <div>""" Problem 8 Find the greatest product of five consecutive digits in the 1000-digit number. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 62229893423380308135336276614282806444486645238749 30358907296290491560440772390713810515859307960866 70172427121883998797908792274921901699720888093776 65727333001053367881220235421809751254540594752243 52584907711670556013604839586446706324415722155397 53697817977846174064955149290862569321978468622482 83972241375657056057490261407972968652414535100474 82166370484403199890008895243450658541227588666881 16427171479924442928230863465674813919123162824586 17866458359124566529476545682848912883142607690042 24219022671055626321111109370544217506941658960408 07198403850962455444362981230987879927244284909188 84580156166097919133875499200524063689912560717606 05886116467109405077541002256983155200055935729725 71636269561882670428252483600823257530420752963450 """ #Create an array with each number X = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450 Str_X = str(X) Result = 0; for i in range(0,len(Str_X)-4): Buffer = 1; for j in range(0,5): Buffer = Buffer * int(Str_X[i+j]) if Buffer > Result: Result = Buffer print(Result)</div> <div>
</div> <div>""" Problem 9 A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,a^(2) + b^(2) = c^(2) For example, 3^(2) + 4^(2) = 9 + 16 = 25 = 5^(2). There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc. """ from math import sqrt a = 0 b = 0 c = 0 def findpytha(n): # Where n is the sum of a, b, c for a in range(2,int(n/2)+1): for b in range(2, int(n/2)+1): c = sqrt(a**2+b**2) if a + b + c == n: return a * b * c #Main print(findpytha(1000))</div> <div>
</div>
<div>"""
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.
"""
def isprime(n):
#isprime function
for x in range(2, int(n**0.5)+1):
if n % x == 0:
return False
return True
# Main
Limit = 2000000
PrimeArray = [2,3]
x = 3
while x < Limit+1:
x += 2
if isprime(x):
PrimeArray.append(x)
if (x - 1) % 100000 == 0:
print('Step :', x)
print(sum(PrimeArray))
