from tools.euler import polygonal
# collect all polygonals in range
fourdigits = []
beginnings, endings = set(), set()
for i in [3, 4, 5, 6, 7, 8]:
row = []
n = 1
p = polygonal(i, n)
while p < 10000:
n += 1
p = polygonal(i, n)
if p < 1000:
continue
row.append(p)
beginnings.add(p // 100)
endings.add(p % 100)
fourdigits.append(row)
# make sure every polygonal can be part of a chain
commons = beginnings & endings
for i in range(6):
newfourdigits = []
for fd in fourdigits[i]:
if fd % 100 in commons and fd // 100 in commons:
newfourdigits.append(fd)
fourdigits[i] = newfourdigits
# recursively look for chain
def find_chain(rows, terms):
from operator import mul
from functools import reduce
from tools.euler import polygonal
total = 0
for n in range(2, 16):
step = (1.0 * n) / polygonal(3, n)
total += int(reduce(mul, [(step * i) ** i for i in range(1, n + 1)], 1.0))
print(total)
from tools.euler import polygonal, sigma
t = 1
while sigma(0, polygonal(3, t)) < 500:
t += 1
polygon = polygonal(3, t)
print(polygon)
def get_term(i):
if i & 1 == 1:
p = (i + 1) // 2
else:
p = -(i // 2)
return polygonal(5, p)
def is_triangle_word(w):
t = sum([ascii_uppercase.index(c) + 1 for c in w])
n = int((2 * t) ** 0.5)
return polygonal(3, n) == t
from tools.euler import polygonal
tN, pN, hN = 285, 165, 143
t, p, h = polygonal(3, tN), polygonal(5, pN), polygonal(6, hN)
while True:
hN += 1
h = polygonal(6, hN)
while p < h:
pN += 1
p = polygonal(5, pN)
while t < p:
tN += 1
t = polygonal(3, tN)
if h == p == t:
break
print(t)
from tools.euler import polygonal
TARGET = 2 * 10**6
closest, closest_rows, closest_cols = 0, 0, 0
for rows in range(1, 100):
for cols in range(rows + 1, 100):
rectangles = polygonal(3, rows) * polygonal(3, cols)
if abs(TARGET - closest) > abs(TARGET - rectangles):
closest, closest_rows, closest_cols = rectangles, rows, cols
args = (closest, closest_rows, closest_cols)
message = "closest=%d rows=%d cols=%d" % args
print(message)
message = "rows*cols=%d" % (closest_rows * closest_cols)
print(message)
import sys
from tools.euler import polygonal
SIZE = 2500
pentas = [polygonal(5, i) for i in range(1, SIZE + 1)]
for a in range(len(pentas)):
for b in range(a + 1, len(pentas)):
if pentas[b] + pentas[a] in pentas and pentas[b] - pentas[a] in pentas:
difference = pentas[b] - pentas[a]
print(difference)
sys.exit(0)