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'):
      break
    if a == 1:
      sallys_partner = b
    elif b == 1:
      sallys_partner = a
  else:
    print 'Sally danced with %d' % sallys_partner
    break

# 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
    break

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

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

while True:
  random.shuffle(numbers)
  random.shuffle(operations)
  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
    break

# 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.