def multiplierGen(n = 0):
while True:
if n == 0:
yield 1
else:
yield fact(2 * n) / (fact(n) * fact(n + 1))
n += 1
def getRoutes(n):
# Work out the row
row = n * 2
# Get mid point of row
midpoint = n
return fact(row) / (fact(midpoint)**2)
def challenge053():
count = 0
for n in xrange(1, 101):
for r in xrange(n, 0, -1):
combinations = fact(n) / (fact(r) * fact(n - r))
if combinations > 1000000:
count += 1
return count
def permutations(digits):
prevI = -1
nI = 0
quantities = fact(len(digits))
factors = 1
for i in digits:
if i == prevI:
nI += 1
else:
factors *= fact(nI)
prevI = i
nI = 1
factors *= fact(nI)
return quantities // factors
def getLimit():
factSum = 0
factNine = fact(9)
digits = 1
while True:
digits *= 10
factSum += factNine
print digits, factSum
if factSum < digits: break
return factSum
def play(turns):
den = fact(turns + 1)
lossesAllowed = turns // 2
if not (turns & 1):
lossesAllowed -= 1
chances = 0
probs = range(2, turns + 2)
for losses in xrange(lossesAllowed + 1):
wc = winChance(probs, losses)
chances += wc
prize = den // chances
return prize