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Date: Mon, 9 Dec 2013 21:03:21 -0500
Subject: Fwd: Programming puzzle with boolean circuits
From: Joel Goldstick <joel.goldstick@gmail.com>
To: "python-list@python.org" <python-list@python.org>
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Chris, and all.. Since you posted yours, I post this for your pleasure.  I
couldn't figure out what you were doing.

#!/usr/bin/env python

"""
This is a puzzle brought up on the python mailing list.
The goal is to take 3 bits and invert them using boolean logic, but
restricted to only 2 NOT gates
Here is a solution I found via google:
http://www.thelowlyprogrammer.com/2008/05/not-puzzle-solution.html
"""

def invert_three(a,b,c):

    """ give three boolean values, return their inverted values
    Only 2 NOT operators are allowed
    Deduce these truths
    """
    all_ones = a and b and c
    two_or_three = (a and b) or (a and c) or (b and c)
    zero_or_one = not two_or_three
    one_one = zero_or_one and (a or b or c)
    zero_or_two = not (all_ones or one_one)
    zero_ones = zero_or_one and zero_or_two
    two_ones = zero_or_two and two_or_three

    # the output is true if all the inputs are zero, or if one of the
inputs is zero and it is either b or c
    # or two inputs are zero and they are b and c
    # ditto for other two inputs
    x = zero_ones or (one_one and (b or c)) or (two_ones and (b and c))
    y = zero_ones or (one_one and (a or c)) or (two_ones and (a and c))
    z = zero_ones or (one_one and (b or a)) or (two_ones and (b and a))
    return int(x), int(y), int(z)

if __name__ == "__main__":
    for a in range(2):
        for b in range(2):
            for c in range(2):
                print "Input: ", a, b, c,
                x, y, z = invert_three(a,b,c)
                print "Output: ", x, y, z


-- 
Joel Goldstick
http://joelgoldstick.com

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<div dir=3D"ltr">Chris, and all.. Since you posted yours, I post this for y=
our pleasure.=C2=A0 I couldn&#39;t figure out what you were doing.<br><div>=
<br>#!/usr/bin/env python<br><div class=3D"gmail_quote"><div dir=3D"ltr"><d=
iv class=3D"gmail_extra">
<br>&quot;&quot;&quot;<br>This is a puzzle brought up on the python mailing=
 list.<br>The goal is to take 3 bits and invert them using boolean logic, b=
ut restricted to only 2 NOT gates<br>
Here is a solution I found via google:=C2=A0 <a href=3D"http://www.thelowly=
programmer.com/2008/05/not-puzzle-solution.html" target=3D"_blank">http://w=
ww.thelowlyprogrammer.com/2008/05/not-puzzle-solution.html</a><br>&quot;&qu=
ot;&quot;<br>
<br>def invert_three(a,b,c):<br>
<br>=C2=A0=C2=A0=C2=A0 &quot;&quot;&quot; give three boolean values, return=
 their inverted values<br>=C2=A0=C2=A0=C2=A0 Only 2 NOT operators are allow=
ed<br>=C2=A0=C2=A0=C2=A0 Deduce these truths<br>=C2=A0=C2=A0=C2=A0 &quot;&q=
uot;&quot;<br>=C2=A0=C2=A0=C2=A0 all_ones =3D a and b and c<br>=C2=A0=C2=A0=
=C2=A0 two_or_three =3D (a and b) or (a and c) or (b and c)<br>

=C2=A0=C2=A0=C2=A0 zero_or_one =3D not two_or_three<br>=C2=A0=C2=A0=C2=A0 o=
ne_one =3D zero_or_one and (a or b or c)<br>=C2=A0=C2=A0=C2=A0 zero_or_two =
=3D not (all_ones or one_one)<br>=C2=A0=C2=A0=C2=A0 zero_ones =3D zero_or_o=
ne and zero_or_two<br>=C2=A0=C2=A0=C2=A0 two_ones =3D zero_or_two and two_o=
r_three<br>

=C2=A0=C2=A0=C2=A0 <br>=C2=A0=C2=A0=C2=A0 # the output is true if all the i=
nputs are zero, or if one of the inputs is zero and it is either b or c<br>=
=C2=A0=C2=A0=C2=A0 # or two inputs are zero and they are b and c<br>=C2=A0=
=C2=A0=C2=A0 # ditto for other two inputs<br>=C2=A0=C2=A0=C2=A0 x =3D zero_=
ones or (one_one and (b or c)) or (two_ones and (b and c))<br>

=C2=A0=C2=A0=C2=A0 y =3D zero_ones or (one_one and (a or c)) or (two_ones a=
nd (a and c))<br>=C2=A0=C2=A0=C2=A0 z =3D zero_ones or (one_one and (b or a=
)) or (two_ones and (b and a))<br>=C2=A0=C2=A0=C2=A0 return int(x), int(y),=
 int(z)<br>=C2=A0=C2=A0=C2=A0 <br>if __name__ =3D=3D &quot;__main__&quot;:<=
br>

=C2=A0=C2=A0=C2=A0 for a in range(2):<br>=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0 for b in range(2):<br>=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=
=C2=A0=C2=A0=C2=A0=C2=A0 for c in range(2):<br>=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 print &quot=
;Input: &quot;, a, b, c, <br>=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 x, y, z =3D invert_three(a,b,=
c)<br>=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0=C2=A0=C2=A0 print &quot;Output: &quot;, x, y, z<br clear=3D"all">

</div></div></div><br clear=3D"all"><br>-- <br><div dir=3D"ltr"><div>Joel G=
oldstick<br></div><a href=3D"http://joelgoldstick.com" target=3D"_blank">ht=
tp://joelgoldstick.com</a><br></div>
</div></div>

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