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Solving Car Talk Puzzlers with Python

If you're not familiar with Car Talk, it's a horrible talk radio show hosted by Tom and Ray Magliozzi (aka Click and Clack the Tappet brothers). Every week there is a new puzzler and every so often it's math oriented. After hearing this week's mathy puzzler, I thought it would be fun to dig into the archives (2009 and 2008) and try solving a few of them in Python. Here's what I came up with:
# 2008-10-20 The Perfect Square Dance!
import itertools, math

for numbers in itertools.permutations(range(1, 19)):
for a, b in zip(numbers[::2], numbers[1::2]):
sqrt = math.sqrt(a + b)
if not str(sqrt).endswith('.0'):
if a == 1:
sallys_partner = b
elif b == 1:
sallys_partner = a
print 'Sally danced with %d' % sallys_partner

# 2008-10-27 One is the Magic Number
print ''.join(str(n) for n in xrange(0, 1000000)).count('1')

# 2008-12-08 It's Math Time!
for ab in xrange(10, 100):
cab = ab ** 2
if str(cab)[1:] == str(ab):
print cab

# 2009-05-26 Equate This!
from __future__ import division # Avoids truncation.
import random

numbers = [2, 3, 4, 5]
operations = ['*', '**', '+', '-', '/']

while True:
equation = ''
for i, number in enumerate(numbers):
equation += str(number)
if i < len(numbers) - 1:
equation += operations[i]
result = eval(equation)
if result == 26:
print equation

# 2009-06-08 Number One
print len([n for n in xrange(0, 1000000) if '1' not in str(n)])
I'd like to see someone good with Ruby, Perl, or Lua do the same so we can compare solutions.

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