#

# Solution to Project Euler problem 45

# Copyright (c) Project Nayuki. All rights reserved.

#

# https://www.nayuki.io/page/project-euler-solutions

# https://github.com/nayuki/Project-Euler-solutions

#

def compute():

i = 286

j = 166

k = 144

while True:

triangle = i * (i + 1) // 2

pentagon = j * (j * 3 - 1) // 2

hexagon = k * (k * 2 - 1)

minimum = min(triangle, pentagon, hexagon)

if minimum == max(triangle, pentagon, hexagon):

return str(triangle)

if minimum == triangle: i += 1

if minimum == pentagon: j += 1

if minimum == hexagon : k += 1

if __name__ == "__main__":

print(compute())