# Fwd: Programming puzzle with boolean circuits

Joel Goldstick joel.goldstick at gmail.com
Tue Dec 10 03:03:21 CET 2013

```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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