product120sequence.py

"""
Goal is to fill the empty spots in the initial tuple with positive integers
in a way that always four consecutive number have a product of 120.
"""

import numpy
initial = (None, None, 2, None, None, 4, None, None, None, None, None, 3, None, None)  # tuple is immutable
possible_factors = [2, 3, 4, 5, 6, 10, 15]  # all possible factors of 120 if there are 4 factors


# test if every 4 consecutive numbers have a product of 120
def test(iteration):
    current_pos = 0
    while current_pos <= len(iteration) - 4:
        current_list = iteration[slice(current_pos, current_pos + 4)]
        if None in current_list:
            return
        if numpy.prod(current_list) != 120:
            return False 
        current_pos += 1
    return True
    

def rec_step(iteration, next_pos):
    # test if end is reached
    if len(iteration) <= next_pos:
        if test(iteration): # print valid solution
            print(iteration)
        return
    # test intermediate result to abort early
    if next_pos >=4:
        if not test(iteration[slice(0, next_pos)]):
            return
    # try every possible value for empty slots
    if iteration[next_pos] is None:
        list_iteration = list(iteration)
        for factor in possible_factors:
            list_iteration[next_pos] = factor
            rec_step(tuple(list_iteration), next_pos + 1)
    else: # skip already filled values
        rec_step(iteration, next_pos + 1)

rec_step(initial, 0)