# Solution of;
# Project Euler Problem 143: Investigating the Torricelli point of a triangle
# https://projecteuler.net/problem=143
# 
# Let ABC be a triangle with all interior angles being less than 120 degrees. 
# Let X be any point inside the triangle and let XA = p, XC = q, and XB = r. 
# Fermat challenged Torricelli to find the position of X such that p + q + r 
# was minimised. Torricelli was able to prove that if equilateral triangles 
# AOB, BNC and AMC are constructed on each side of triangle ABC, the 
# circumscribed circles of AOB, BNC, and AMC will intersect at a single point, 
# T, inside the triangle. Moreover he proved that T, called the 
# Torricelli/Fermat point, minimises p + q + r. Even more remarkable, it can 
# be shown that when the sum is minimised, AN = BM = CO = p + q + r and that 
# AN, BM and CO also intersect at T. If the sum is minimised and a, b, c, p, q 
# and r are all positive integers we shall call triangle ABC a Torricelli 
# triangle. For example, a = 399, b = 455, c = 511 is an example of a 
# Torricelli triangle, with p + q + r = 784. Find the sum of all distinct 
# values of p + q + r ≤ 120000 for Torricelli triangles.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 143
    timed.caller(dummy, n, i, prob_id)
