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10.py
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10.py
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from helpers import primegenerator
from functools import reduce
def problem1():
"""
How many numbers < 1000 are multiples of 3 or 5
"""
return sum(i for i in range(1000) if i % 5 == 0 or i % 3 == 0)
def problem2():
s, f_old, f_new = 0, 0, 1
while f_new < 4000000:
if f_new % 2 == 0:
s += f_new
temp = f_new
f_new += f_old
f_old = temp
return s
def problem3(number=600851475143):
"""
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?
"""
p = 2
factors = []
while p < number:
if number % p == 0:
number /= p
factors.append(p)
print("{} and {}".format(p, number))
else:
p += 1
factors.append(number)
return max(factors)
def problem4():
"""
A palindromic number reads the same both ways. The largest palindrome made
from the product of two 2-digit numbers is 9009 = 91 x 99.
Find the largest palindrome made from the product of two 3-digit numbers.
"""
for n in range(1000):
for i in range(n / 2 + n % 2): # first half round up
a = 999 + i - n
b = 999 - i
if str(a * b) == "".join(reversed(str(a * b))):
return a, b
assert False
def problem6():
"""
Find the difference between the sum of the squares of the first one hundred
natural numbers and the square of the sum.
"""
s, ss = 0, 0
for i in range(1, 101):
s += i
ss += i ** 2
return s ** 2 - ss
def problem7(n=10001):
"""
What is the 10 001st prime number?
"""
gen = primegenerator()
for i in range(10000):
next(gen)
yield next(gen)
def problem8():
number = """73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
"""
number = number.replace(" ", "").replace("\n", "")
sup = 0
for i in range(len(number) - 13):
subsequence = number[i : i + 13]
prod = reduce(lambda x, y: int(x) * int(y), subsequence)
if prod > sup:
sup = prod
return sup
def problem9():
"""
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
"""
a, b, c = 0, 0, 0
for i in range(2, 1000): # avoid 0
breaker = False
for j in range(1, i / 2 + i % 2):
a = i - j
b = j
c = 1000 - i
if a ** 2 + b ** 2 == c ** 2:
breaker = True
break
if breaker:
break
return a * b * c
def problem10(n=2000000):
"""
Find the sum of all the primes below 2 million
"""
tot, prime, pg = 0, 0, primegenerator()
while prime < n:
tot += prime
prime = next(pg)
return tot