---
author: ''
category: ''
date: 2015-10-28 15:24:41 UTC
description: ''
link: ''
priority: ''
slug: brute-force-works
tags: python
title: Brute Force Works
type: text
updated: 2015-10-28 15:24:41 UTC
url_type: ''
---
Last night, Juanjo Conti tweeted this:

.. raw:: html

   <blockquote class="twitter-tweet" lang="es"><p lang="es" dir="ltr">Usando exactamente una vez los dígitos 1, 3, 4 y 6 y cualquiera de las cuatro operaciones básicas, obtener 24.</p>&mdash; Juanjo Conti (@jjconti) <a href="https://twitter.com/jjconti/status/659155109549592576">octubre 27, 2015</a></blockquote>
   <script async src="//platform.twitter.com/widgets.js" charset="utf-8"></script>

Or, in english: "Using exactly once the digits 1,3,4 and 6, and any of the four basic operations, obtain 24."

I first spent a couple of minutes thinking about it and then it hit me: there is no point in **thinking** this sort of problem, because:

1) Brute forcing it will take less time
2) What you do while "thinking" it is sort of lame, isn't it?

So, here is a more-or-less general solution for any of these problems.

.. code:: python

    from __future__ import print_function, division
    import itertools

    numbers = ['1','3','4','6']
    target = 24

    # Having '' as an operation allows for solution (14-6)*3, which
    # may or may not be valid depending on rule interpretation.
    operations =  ['*','/','+','-','']

    t1='(({0}{4}{1}){5}{2}){6}{3}'
    t2='{0}{4}({1}{5}({2}{6}{3}))'

    for nums in itertools.permutations(numbers):
        for ops1 in itertools.combinations_with_replacement(operations, 3):
            for ops2 in itertools.permutations(ops1):
                for t in (t1, t2):
                    s = t.format(*(nums+ops2))
                    #print(repr(s))
                    try:
                        if eval(s) == target:
                            print(s)
                    except (ZeroDivisionError, SyntaxError, TypeError):
                        continue

Of course you can make it solve any problem of this class by adjusting numbers and target.
There is also a possible extra solution if ``eval(s) == -target`` where you just need to add
a unary - to the expression, but who cares.

Did I miss something? Is this really a general solution?