A solution to Jon Erickson's math puzzle

solution_eval.py

# http://books.google.com/books?id=0FW3DMNhl1EC&lpg=PA1&ots=tt-xF-JWXq&dq=jon%20erickson%20art%20of%20exploitation%20math%20problem&pg=PA1#v=onepage&q=math%20problem&f=false
#
# Use each of the numbers 1, 3, 4, and 6 exactly once with any of the four basic math operations 
# (addition, subtraction, multiplication, and division) to total 24.  Each number must be used 
# once and only once, and you may define the order of operations; for example, 3 * (4 + 6) + 1 = 31
# is valid, however incorrect, since it doesn't total 24.

from fractions import Fraction
import itertools

def treeify(operators, operands):
    if len(operands) == 1:
        yield operands[0]

    for i, op in enumerate(operators):
        for left in treeify(operators[:i], operands[:i+1]):
            for right in treeify(operators[i+1:], operands[i+1:]):
                yield (left, op, right)

def expr(tree):
    return str(tree).replace(',', '').replace('\'', '')

def main():
    i_operators = itertools.product(['+', '-', '*', '/'], repeat=3)
    i_operands = itertools.permutations(['f1', 'f3', 'f4', 'f6'])

    for i in [1, 3, 4, 6]:
        globals()['f%s' % i] = Fraction(i)
    
    for operators, operands in itertools.product(i_operators, i_operands):
        for tree in treeify(operators, operands):
            e = expr(tree)
            try:
                if eval(e) == 24:
                    print e.replace('f', '')
            except ZeroDivisionError:
                pass

if __name__ == '__main__':
    main()