Riddler_6_24_16.py

import numpy as np


class Point:
    def __init__(self,x,y):
        self.x = x
        self.y = y

    def __repr__(self):
        return "Point({}, {})".format(self.x, self.y)

def ccw(A,B,C):
    return (C.y-A.y)*(B.x-A.x) > (B.y-A.y)*(C.x-A.x)

def intersect(A,C):
    return (ccw(A[0],C[0],C[1]) != ccw(A[1],C[0],C[1])
            and ccw(A[0],A[1],C[0]) != ccw(A[0],A[1],C[1]))

N = 1e5
totals = np.zeros(int(N), dtype=int) + 4
for j in range(int(N)):
    segments = []
    for i in range(3):
        theta1 = np.random.uniform(0.0, 2 * np.pi)
        p1 = Point(np.cos(theta1), np.sin(theta1))
        theta2 = np.random.uniform(0.0, 2 * np.pi)
        p2 = Point(np.cos(theta2), np.sin(theta2))
        segments.append((p1, p2))
    totals[j] += (intersect(segments[0], segments[1])
                  + intersect(segments[0], segments[2])
                  + intersect(segments[1], segments[2]))
print(totals.mean())