#===============================================================================
# What is the value of the first triangle number to have over five hundred divisors?
#===============================================================================
from Common import divisors, trianglenum
i = 1
while True:
if len(divisors(trianglenum(i))) > 500:
break
i += 1
print(trianglenum(i))
#===============================================================================
# Find the next triangle number that is also pentagonal and hexagonal after 40755.
#===============================================================================
from Common import trianglenum, pentagonnum, hexagonnum
trinums = set()
pentnums = set()
hexnums = set()
for i in range(1, 100000):
trinums.add(trianglenum(i))
pentnums.add(pentagonnum(i))
hexnums.add(hexagonnum(i))
for i in trinums:
if i > 40755 and i in pentnums and i in hexnums:
print(i)
break
#===============================================================================
# Using words.txt, a 16K text file containing nearly two-thousand common English words, how many are triangle words?
#===============================================================================
from Common import trianglenum
def wordValue(word):
return sum([ord(c) - ord('A') + 1 for c in word])
trinums = []
for i in range(1, 365): #The longest word in the file has 14 letters, so the highest possible score is 14 * 26 = 364
trinums.append(trianglenum(i))
words = sorted(eval('[' + open('words.txt').read() + ']'))
print(sum([1 for word in words if wordValue(word) in trinums]))