def solution():
count = 0
for n in xrange(1, 101):
for r in xrange(0, n):
c = combination(n, r)
if c > 1000000:
count += n-2*r+1
break
return count
#! /usr/bin/env python
from util import combination
if __name__ == "__main__":
print combination(40, 20)
def rectangles(a, b):
return combination(a + 1, 2) * combination(b + 1, 2)
from util import combination
def rectangles(a, b):
return combination(a + 1, 2) * combination(b + 1, 2)
best_xy, best_rects = 0, 0
for x in xrange(1, 2000):
for y in xrange(1, 2000):
rects = combination(x + 1, 2) * combination(y + 1, 2)
if abs(rects - 2000000) < abs(best_rects - 2000000):
best_rects = rects
best_xy = x*y
if rects > 2000000:
break
print best_xy
# Lattice paths # Problem 15 # # Starting in the top left corner of a 2x2 grid, and only being able to move to # the right and down, there are exactly 6 routes to the bottom right corner. # # xxxxx xxx-+ xxx-+ x-+-+ x-+-+ x-+-+ # | | x | x | | x | x | | x | | x | | # +-+-x +-xxx +-x-+ xxxxx xxx-+ x-+-+ # | | x | | x | x | | | x | x | x | | # +-+-x +-+-x +-xxx +-+-x +-xxx xxxxx # # How many such routes are there through a 20x20 grid? # # Answer: 137846528820 from util import combination M = 20 N = 20 print combination(M + N, M)
from util import combination
ans = 0
for n in xrange(23, 100+1):
for r in xrange(n+1):
if combination(n, r) > 1000000:
ans += 1
print ans
