def digit_factorials():
result = 0
factorials = [eulerlib.factorial(i) for i in range(10)]
for n in range(4 * eulerlib.factorial(8) + 1):
digits_of_n = [int(i) for i in str(n)]
n_fact = sum([factorials[digit] for digit in digits_of_n])
if n == n_fact:
print(n)
result += n_fact
return result - 3
def compute(): TURNS = 15 # Dynamic programming ways = [[1]] for i in range(1, TURNS + 1): row = [] for j in range(i + 1): temp = 0 if j < i: temp = ways[i - 1][j] * i if j > 0: temp += ways[i - 1][j - 1] row.append(temp) ways.append(row) numer = 0 for i in range(TURNS //2 + 1, TURNS + 1): numer += ways[TURNS][i] denom = eulerlib.factorial(TURNS + 1) return str(denom // numer)
def compute():
TURNS = 15
# Dynamic programming
ways = [[1]]
for i in range(1, TURNS + 1):
row = []
for j in range(i + 1):
temp = 0
if j < i:
temp = ways[i - 1][j] * i
if j > 0:
temp += ways[i - 1][j - 1]
row.append(temp)
ways.append(row)
numer = 0
for i in range(TURNS // 2 + 1, TURNS + 1):
numer += ways[TURNS][i]
denom = eulerlib.factorial(TURNS + 1)
return str(denom // numer)
# https://www.nayuki.io/page/project-euler-solutions # https://github.com/nayuki/Project-Euler-solutions # import eulerlib, sys if sys.version_info.major == 2: range = xrange def compute(): # As stated in the problem, 1 = 1! and 2 = 2! are excluded. # If a number has at least n >= 8 digits, then even if every digit is 9, # n * 9! is still less than the number (which is at least 10^n). ans = sum(i for i in range(3, 10000000) if i == factorial_digit_sum(i)) return str(ans) def factorial_digit_sum(n): result = 0 while n >= 10000: result += FACTORIAL_DIGITS_SUM_WITH_LEADING_ZEROS[n % 10000] n //= 10000 return result + FACTORIAL_DIGITS_SUM_WITHOUT_LEADING_ZEROS[n] FACTORIAL_DIGITS_SUM_WITHOUT_LEADING_ZEROS = [sum(eulerlib.factorial(int(c)) for c in str(i)) for i in range(10000)] FACTORIAL_DIGITS_SUM_WITH_LEADING_ZEROS = [sum(eulerlib.factorial(int(c)) for c in str(i).zfill(4)) for i in range(10000)] if __name__ == "__main__": print(compute())
#!/usr/bin/python
from eulerlib import factorial
from eulerlib import num2List
answerL = []
facts = {}
for ii in range( 0, 10 ):
facts[ii] = factorial( ii )
for ii in range( 3, 999999 ):
s = 0
iiL = num2List(ii)
for kk in iiL:
s += facts[kk]
if s == ii:
answerL.append( s )
print sum( answerL )
if sys.version_info.major == 2:
range = xrange
def compute():
# As stated in the problem, 1 = 1! and 2 = 2! are excluded.
# If a number has at least n >= 8 digits, then even if every digit is 9,
# n * 9! is still less than the number (which is at least 10^n).
ans = sum(i for i in range(3, 10000000) if i == factorial_digit_sum(i))
return str(ans)
def factorial_digit_sum(n):
result = 0
while n >= 10000:
result += FACTORIAL_DIGITS_SUM_WITH_LEADING_ZEROS[n % 10000]
n //= 10000
return result + FACTORIAL_DIGITS_SUM_WITHOUT_LEADING_ZEROS[n]
FACTORIAL_DIGITS_SUM_WITHOUT_LEADING_ZEROS = [
sum(eulerlib.factorial(int(c)) for c in str(i)) for i in range(10000)
]
FACTORIAL_DIGITS_SUM_WITH_LEADING_ZEROS = [
sum(eulerlib.factorial(int(c)) for c in str(i).zfill(4))
for i in range(10000)
]
if __name__ == "__main__":
print(compute())
def compute():
n = eulerlib.factorial(100)
ans = sum(map(int, str(n)))
return str(ans)
# http://www.nayuki.io/page/project-euler-solutions
# https://github.com/nayuki/Project-Euler-solutions
#
import eulerlib, sys
if sys.version_info.major == 2:
range = xrange
def compute():
# As stated in the problem, 1 = 1! and 2 = 2! are excluded.
# If a number has at least n >= 8 digits, then even if every digit is 9,
# n * 9! is still less than the number (which is at least 10^n).
ans = sum(i for i in range(3, 10000000) if i == factorial_digit_sum(i))
return str(ans)
def factorial_digit_sum(n):
result = 0
while n >= 10000:
result += FACTORIAL_DIGITS_SUM_WITH_LEADING_ZEROS[n % 10000]
n //= 10000
return result + FACTORIAL_DIGITS_SUM_WITHOUT_LEADING_ZEROS[n]
FACTORIAL_DIGITS_SUM_WITHOUT_LEADING_ZEROS = [sum(eulerlib.factorial(int(c)) for c in str(i)) for i in range(10000)]
FACTORIAL_DIGITS_SUM_WITH_LEADING_ZEROS = [sum(eulerlib.factorial(int(c)) for c in str(i).zfill(4)) for i in range(10000)]
if __name__ == "__main__":
print(compute())
def compute(): n = eulerlib.factorial(100) ans = sum(int(c) for c in str(n)) return str(ans)
#!/usr/bin/python
import eulerlib
def split(anInt):
l = list(str(anInt))
return [int(x) for x in l]
if __name__ == '__main__':
print sum(split(eulerlib.factorial(100)))
def compute(): n = eulerlib.factorial(100) ans = sum(map(int, str(n))) return str(ans)
def binomial(n, k): return eulerlib.factorial(n) // (eulerlib.factorial(k) * eulerlib.factorial(n - k))
def problem020(n):
return sum(map(int, list(str(factorial(n)))))
#!/usr/bin/python
import eulerlib
import math
if __name__ == '__main__':
n = 1000000
nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
nNums = len(nums)
answer = list()
while len(nums) > 1:
f = eulerlib.factorial(nNums - 1)
nNums -= 1
tmp = int(math.ceil(float(n) / float(f)))
answer.append(nums[tmp - 1])
nums.remove(nums[tmp - 1])
n -= f * (tmp - 1)
answer.append(nums[0])
print ''.join(map(str, answer))
eulerlib.factorial(6)
def compute():
n = eulerlib.factorial(100)
ans = sum(int(c) for c in str(n))
return str(ans)
