Monte Carlo code to solve the Four Square Ranches (Riddler Classic), https://fivethirtyeight.com/features/can-you-find-the-honest-prince/

four_square_ranches.py

import numpy as np
import time
import matplotlib.pyplot as plt


def isConvex(dx, dy):
    for j in range(4):
        if dx[j]*dy[(j+1) % 4] < dy[j]*dx[(j+1) % 4]:
            return False
    return True


def runSimulation(runs):
    total = 0
    init_time = time.time()

    for j in range(runs):
        # generate coordinates for four point
        coordX = np.random.random_sample(4)
        coordX[1:3] *= -1.0  # flip X coordinates
        coordY = np.random.random_sample(4)
        coordY[2:4] *= -1.0  # flip Y coordinates

        # plot points to check code correctness
        # plt.scatter(coordX, coordY)
        # plt.plot([-1, 1], [0, 0])
        # plt.plot([0, 0], [-1, 1])
        # plt.show()

        total += isConvex(np.roll(coordX, -1) - coordX, np.roll(coordY, -1) - coordY)

    print("N=", runs, "  convex prob =", total/runs,
          '    run time (hr) = {0:.3f}'.format((time.time() - init_time)/3600.0))

    return total


#   =====   MAIN PROGRAM   =====

runSimulation(200*1000*1000)