Howard's goblins https://www.facebook.com/howard.dale.3/posts/10152106759878462?stream_ref=5

howards-goblins.py

#!python3
"""Solves Howard's goblins puzzle using backtracking. https://www.facebook.com/howard.dale.3/posts/10152106759878462?stream_ref=5 """
from collections import deque

class Game:
    def __init__(self):
        self.goblins = [0]*7
        self.history = deque()

    def time(self):
        return len(self.history)

    def move(self, x):
        for i in range(len(self.goblins)):
            if (self.time()+1) % (i+1) == 0:
                self.goblins[i] += x
        self.history.append(x)

    def undo(self):
        last_move = self.history.pop()
        for i in range(len(self.goblins)):
            if (self.time()+1) % (i+1) == 0:
                self.goblins[i] -= last_move

    def pretty_history(self):
        return ''.join('+' if x==1 else '-' for x in self.history)

    def pretty_goblins(self):
        return ','.join(str(x).rjust(2) for x in self.goblins)

# unit test
def unit_test():
    G = Game()
    assert G.goblins == [0,0,0,0,0,0,0]
    G.move(1)
    assert G.goblins == [1,0,0,0,0,0,0]
    G.move(1)
    assert G.goblins == [2,1,0,0,0,0,0]
    G.move(-1)
    assert G.goblins == [1,1,-1,0,0,0,0]
    G.undo()
    assert G.goblins == [2,1,0,0,0,0,0]
    G.undo()
    assert G.goblins == [1,0,0,0,0,0,0]
    G.undo()
    assert G.goblins == [0,0,0,0,0,0,0]

unit_test()

if __name__ == "__main__":
    G = Game()

    while True:
        if any(abs(position) > 1 for position in G.goblins):
            # dead. backtrack.
            print("{0} {1} {2}".format(G.pretty_goblins(), G.pretty_history(), "BUST"))
            while G.history[-1] == -1:
                G.undo()
            G.undo()
            G.move(-1)
        else:
            print("{0} {1}".format(G.pretty_goblins(), G.pretty_history()))
            G.move(1)