######################################################################## # Solves problem 53 from projectEuler.net. # Determines the amount of, not necessarily distinct, values of, # combinations of n taken by r for 1 n 100, are greater than one-million? # Copyright (C) 2010 Santiago Alessandri # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] or [email protected] # Visit my wiki at http://san-ss.wikidot.com ######################################################################## from CommonFunctions import factorial if __name__ == "__main__": result = sum( 1 for n in range(1, 101) for r in range(1, n + 1) if factorial(n) // factorial(r) // factorial(n - r) > 1000000 ) print("The result is:", result)
def combinations(n, r):
return factorial(n) // (factorial(n - r))
from CommonFunctions import factorial
# from math import factorial
numberString = str(factorial(10))
sum = 0
for element in numberString:
sum += int(element)
print(numberString, sum)
#!/usr/bin/env python3 ######################################################################## # Solves problem 53 from projectEuler.net. # Determines the amount of, not necessarily distinct, values of, # combinations of n taken by r for 1 n 100, are greater than one-million? # Copyright (C) 2010 Santiago Alessandri # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] or [email protected] # Visit my wiki at http://san-ss.wikidot.com ######################################################################## from CommonFunctions import factorial if __name__ == '__main__': result = sum(1 for n in range(1, 101) for r in range(1, n + 1) if factorial(n) // factorial(r) // factorial(n - r) > 1000000) print("The result is:", result)
def combinations(n, r):
return factorial(n) // (factorial(n - r))
