My Solution to the December 18th FiveThirtyEight Riddler using Python

geyser.py

from sympy import symbols
from sympy import integrals as Int
from itertools import permutations


class geyser:
    '''
    This is a python-based solution to the geyser problem presented on
    FiveThirtyEight.com. It uses Sympy to evaluate an integral. With that
    result, we create a general function for solving with the supplied rates.
    '''
    def __init__(self, A, B, C):
        # Define symbols
        self.terms = symbols('x y z')

        # Define Rates
        self.bounds = [A, B, C]

        # Define joint pdf
        self.joint_pdf = 1 / (A * B * C)

    def set_bounds(self, bounds):
        '''
        The key to the integration is the bounds.
        '''
        for i in range(2, 0, -1):
            if bounds[i] < bounds[i - 1]:
                bounds[i - 1] = bounds[i]

        for i in range(2):
            if bounds[i] > bounds[i + 1]:
                bounds[i] = bounds[i + 1]

        return bounds

    def uni_integral(self, terms, bounds):
        bounds = self.set_bounds(bounds)

        return Int.integrate(self.joint_pdf,
                             (terms[2], terms[1], bounds[2]),
                             (terms[1], terms[0], bounds[1]),
                             (terms[0], 0, bounds[0]))

    def all_integrals(self):
        integrals = []

        for p in permutations([0, 1, 2]):
            terms = [self.terms[i] for i in p]
            bounds = [self.bounds[i] for i in p]

            integrals.append(self.uni_integral(terms, bounds))

        self.integrals = integrals

    def print_sol(self):
        collapsed = [self.integrals[i] + self.integrals[i + 1]
                     for i in range(0, 5, 2)]

        self.results = {i[1]: collapsed[i[0]]
                        for i in enumerate(['A', 'B', 'C'])}

        print("P(A < B, C) = ", round(self.results['A'], 4))
        print("P(B < A, C) = ", round(self.results['B'], 4))
        print("P(C < A, B) = ", round(self.results['C'], 4))


def main():
    ''' Run fivethirtyeight example '''

    # Show the simple solution
    my_geyser = geyser(2, 4, 6)
    my_geyser.all_integrals()
    my_geyser.print_sol()

if __name__ == "__main__":
    main()