system_of_equations_venn_sum.py

# See diagram: https://i.imgur.com/UWDrqcH.png

# We need 8 equations to solve the diagram, but I can only come up with 5.
# For three more equations, we will assume a value for X, A, and D.
# If sympy times out, we will cancel the attempt.

# Values for X: 7 choose 4, 35 possible values.
# Values for A: 7.
# (Naive) Maximum loops: 7*35 = 245.
# (actual) maximum loops: 4 * 35 = 140. A has to be in the circle for the solution for X we're using.

# Timeout setup ( https://stackoverflow.com/questions/40915527/kill-function-after-a-given-amount-of-time )
TIMEOUT = 5 # seconds
import signal
class TimeoutException(Exception):
    pass

def timeout_handler(s, f):
    raise TimeoutException

signal.signal(signal.SIGALRM, timeout_handler)

def limited_execution(func):
    def wraps(*args, **kwargs):
        try:
            signal.alarm(TIMEOUT)
            result = func(*args, **kwargs)
            signal.alarm(0)
            return result
        except TimeoutException:
            return None
    return wraps


# System of Equations setup

from sympy import Eq, solve, var
var('a, b, c, d, e, f, g, x')

#@limited_execution
def solve_soe(X, A, D):
    equations = [
        Eq(a + d + f + g, 2 * x),
        Eq(b + d + e + g, 3 * x),
        Eq(c + f + e + g, 4 * x),
        Eq(a + b + c + d + e  + f + g, 28),
        Eq(a * b * c * d * e * f * g, 5040),
        Eq(x, X),
        Eq(a, A),
        Eq(d, D)
        ]

    return solve(equations)

# 7 choose 4 combination setup ( https://www.geeksforgeeks.org/permutation-and-combination-in-python )
from itertools import combinations

def main():
    for comb in combinations([1,2,3,4,5,6,7], 4):
        X = sum(comb) / 2.0
        for A in range(1,7+1):
            if A not in comb: continue # A is in the 2X sum group; if A is not in this combination, it's not a solution
            for D in range(1,7+1):
                if D == A: continue
                elif D not in comb: continue
            print(f"X = sum({comb})/2 = {X}, A = {A}, D = {D}")
            print(solve_soe(X, A, D))