# list of all possible values

Discussion in 'Python' started by David Gibb, Jul 13, 2009.

1. ### David GibbGuest

Hi guys.

I was thinking about a problem I had: suppose I have a list of
possible values. I want to to have a list of all possible lists of
length n whose values are in that original list.

For example: if my values are ['a', 'b', 'c'], then all possible lists
of length 2 would be: aa, ab, ac, ba, bb, bc, ca, cb, cc.

I created a recursive program to do it, but I was wondering if there
was a better way of doing it (possibly with list comprehensions).

Here's my recursive version:

vals = ['a', 'b', 'c']

def foo(length):
if length <=0:
return []
if length == 1:
return [[x] for x in vals]
else:
return [x + [y] for x in foo(length - 1) for y in vals]

print foo(3)

Thanks,
David

David Gibb, Jul 13, 2009

2. ### BearophileGuest

David Gibb:
> For example: if my values are ['a', 'b', 'c'], then all possible lists
> of length 2 would be: aa, ab, ac, ba, bb, bc, ca, cb, cc.

>>> from itertools import product
>>> list(product("abc", repeat=2))

[('a', 'a'), ('a', 'b'), ('a', 'c'), ('b', 'a'), ('b', 'b'), ('b',
'c'), ('c', 'a'), ('c', 'b'), ('c', 'c')]

Bye,
bearophile

Bearophile, Jul 13, 2009

3. ### Andreas TawnGuest

> David Gibb:
> > For example: if my values are ['a', 'b', 'c'], then all possible

lists
> > of length 2 would be: aa, ab, ac, ba, bb, bc, ca, cb, cc.

>
> >>> from itertools import product
> >>> list(product("abc", repeat=2))

> [('a', 'a'), ('a', 'b'), ('a', 'c'), ('b', 'a'), ('b', 'b'), ('b',
> 'c'), ('c', 'a'), ('c', 'b'), ('c', 'c')]
>
> Bye,
> bearophile

Certainly possible with list comprehensions.

>>> a = "abc"
>>> [(x, y) for x in a for y in a]

[('a', 'a'), ('a', 'b'), ('a', 'c'), ('b', 'a'), ('b', 'b'), ('b', 'c'),
('c', 'a'), ('c', 'b'), ('c', 'c')]

But I like bearophile's version better.

Cheers,

Drea

Andreas Tawn, Jul 13, 2009
4. ### David GibbGuest

> Certainly possible with list comprehensions.
>
>>>> a = "abc"
>>>> [(x, y) for x in a for y in a]

> [('a', 'a'), ('a', 'b'), ('a', 'c'), ('b', 'a'), ('b', 'b'), ('b', 'c'),
> ('c', 'a'), ('c', 'b'), ('c', 'c')]
>
> But I like bearophile's version better.
>

Andreas,

Thanks, but I think you were missing my point. I should have explained better.

The advantage that bearophile's version is generic with respect to the
number of elements in each combination. To go from 2 element pairs
(e.g. ('a', 'c')) to 5 element pairs (e.g. ('a', 'c', 'b', 'b', 'e'))
requires only a change in a parameter passed to itertools.

I don't see how you would do that with list comprehensions. You're
example works nicely with 2 element pairs, but it seems to me like
you'd need to recode it if you wanted to change it to 5 element pairs.

Am I wrong about that? Can you think of a way to write a function
that, using list comprehensions, takes a list of values and the size
of each combination, and returns the len(list)**(combination size)
possible combinations using those values?

Thanks again,
David

David Gibb, Jul 16, 2009
5. ### Andreas TawnGuest

> > Certainly possible with list comprehensions.
> >
> >>>> a = "abc"
> >>>> [(x, y) for x in a for y in a]

> > [('a', 'a'), ('a', 'b'), ('a', 'c'), ('b', 'a'), ('b', 'b'), ('b',

'c'),
> > ('c', 'a'), ('c', 'b'), ('c', 'c')]
> >
> > But I like bearophile's version better.
> >

>
> Andreas,
>
> Thanks, but I think you were missing my point. I should have explained

better.
>
> The advantage that bearophile's version is generic with respect to the
> number of elements in each combination. To go from 2 element pairs
> (e.g. ('a', 'c')) to 5 element pairs (e.g. ('a', 'c', 'b', 'b', 'e'))
> requires only a change in a parameter passed to itertools.
>
> I don't see how you would do that with list comprehensions. You're
> example works nicely with 2 element pairs, but it seems to me like
> you'd need to recode it if you wanted to change it to 5 element pairs.
>
> Am I wrong about that? Can you think of a way to write a function
> that, using list comprehensions, takes a list of values and the size
> of each combination, and returns the len(list)**(combination size)
> possible combinations using those values?
>
> Thanks again,
> David

David,

I think my post got caught in the nebulous email eddys and seems to have
taken 16 hours to arrive on the list. It was meant to be a reply to your

Having said that, I think I missed the point of that post too ;o)

Maybe someone smarter than me can come up with a way to dynamically nest
the fors in a list comprehension, but I certainly can't do it.

Sorry for the confusion.

Cheers,

Drea

Andreas Tawn, Jul 16, 2009
6. ### MensanatorGuest

On Jul 16, 11:49 am, "Andreas Tawn" <> wrote:
> > > Certainly possible with list comprehensions.

>
> > >>>> a = "abc"
> > >>>> [(x, y) for x in a for y in a]
> > > [('a', 'a'), ('a', 'b'), ('a', 'c'), ('b', 'a'), ('b', 'b'), ('b',

> 'c'),
> > > ('c', 'a'), ('c', 'b'), ('c', 'c')]

>
> > > But I like bearophile's version better.

>
> > Andreas,

>
> > Thanks, but I think you were missing my point. I should have explained

> better.
>
> > The advantage that bearophile's version is generic with respect to the
> > number of elements in each combination. To go from 2 element pairs
> > (e.g. ('a', 'c')) to 5 element pairs (e.g. ('a', 'c', 'b', 'b', 'e'))
> > requires only a change in a parameter passed to itertools.

>
> > I don't see how you would do that with list comprehensions. You're
> > example works nicely with 2 element pairs, but it seems to me like
> > you'd need to recode it if you wanted to change it to 5 element pairs.

>
> > Am I wrong about that? Can you think of a way to write a function
> > that, using list comprehensions, takes a list of values and the size
> > of each combination, and returns the len(list)**(combination size)
> > possible combinations using those values?

>
> > Thanks again,
> > David

>
> David,
>
> I think my post got caught in the nebulous email eddys and seems to have
> taken 16 hours to arrive on the list. It was meant to be a reply to your
> first post, not your second.
>
> Having said that, I think I missed the point of that post too ;o)
>
> Maybe someone smarter than me can come up with a way to dynamically nest
> the fors in a list comprehension, but I certainly can't do it.

Well, I don't use list comprehension, but you can certainly
make dynamic for loops. Not that this is a replacement for
itertools (I wrote it before itertools had the ability to do
all this).

def ooloop6(a, n, perm=True, repl=True):
if (not repl) and (n>len(a)): return
r0 = range(n)
r1 = r0[1:]
if perm and repl: # ok
v = ','.join(['c%s' % i for i in r0])
f = ' '.join(['for c%s in a' % i for i in r0])
e = ''.join(["p = [''.join((",v,")) ",f,"]"])
exec e
return p
if (not perm) and repl: # ok
v = ','.join(['c%s' % i for i in r0])
f = ' '.join(['for c%s in a' % i for i in r0])
i = ' and '.join(['(c%s>=c%s)' % (j,j-1) for j in r1])
e = ''.join(["p = [''.join((",v,")) ",f," if ",i,"]"])
exec e
return p
if perm and (not repl): # ok
v = ','.join(['c%s' % i for i in r0])
f = ' '.join(['for c%s in a' % i for i in r0])
i = ' and '.join([' and '.join(['(c%s!=c%s)' % (j,k) for k in
range(j)]) for j in r1])
e = ''.join(["p = [''.join((",v,")) ",f," if ",i,"]"])
exec e
return p
if (not perm) and (not repl): # ok
v = ','.join(['c%s' % i for i in r0])
f = ' '.join(['for c%s in a' % i for i in r0])
i = ' and '.join(['(c%s>c%s)' % (j,j-1) for j in r1])
e = ''.join(["p = [''.join((",v,")) ",f," if ",i,"]"])
exec e
return p

print '0123456789 taken 2 at a time'

p = ooloop6('0123456789',2,True,True)
print
print 'Permutations with Replacement: %6d' % (len(p))
print p

p = ooloop6('0123456789',2,True,False)
print
print 'Permutations without Replacement: %6d' % (len(p))
print p

p = ooloop6('0123456789',2,False,True)
print
print 'Combinations with Replacement: %6d' % (len(p))
print p

p = ooloop6('0123456789',2,False,False)
print
print 'Combinations without Replacement: %6d' % (len(p))
print p

print

print '0123456789 taken 3 at a time'

p = ooloop6('0123456789',3,True,True)
print
print 'Permutations with Replacement: %6d' % (len(p))
print p

p = ooloop6('0123456789',3,True,False)
print
print 'Permutations without Replacement: %6d' % (len(p))
print p

p = ooloop6('0123456789',3,False,True)
print
print 'Combinations with Replacement: %6d' % (len(p))
print p

p = ooloop6('0123456789',3,False,False)
print
print 'Combinations without Replacement: %6d' % (len(p))
print p

0123456789 taken 2 at a time

Permutations with Replacement: 100
['00', '01', '02', '03', '04', '05', '06', '07', '08', '09', '10',
'11', '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
'22', '23', '24', '25', '26', '27', '28', '29', '30', '31', '32',
'33', '34', '35', '36', '37', '38', '39', '40', '41', '42', '43',
'44', '45', '46', '47', '48', '49', '50', '51', '52', '53', '54',
'55', '56', '57', '58', '59', '60', '61', '62', '63', '64', '65',
'66', '67', '68', '69', '70', '71', '72', '73', '74', '75', '76',
'77', '78', '79', '80', '81', '82', '83', '84', '85', '86', '87',
'88', '89', '90', '91', '92', '93', '94', '95', '96', '97', '98',
'99']

Permutations without Replacement: 90
['01', '02', '03', '04', '05', '06', '07', '08', '09', '10', '12',
'13', '14', '15', '16', '17', '18', '19', '20', '21', '23', '24',
'25', '26', '27', '28', '29', '30', '31', '32', '34', '35', '36',
'37', '38', '39', '40', '41', '42', '43', '45', '46', '47', '48',
'49', '50', '51', '52', '53', '54', '56', '57', '58', '59', '60',
'61', '62', '63', '64', '65', '67', '68', '69', '70', '71', '72',
'73', '74', '75', '76', '78', '79', '80', '81', '82', '83', '84',
'85', '86', '87', '89', '90', '91', '92', '93', '94', '95', '96',
'97', '98']

Combinations with Replacement: 55
['00', '01', '02', '03', '04', '05', '06', '07', '08', '09', '11',
'12', '13', '14', '15', '16', '17', '18', '19', '22', '23', '24',
'25', '26', '27', '28', '29', '33', '34', '35', '36', '37', '38',
'39', '44', '45', '46', '47', '48', '49', '55', '56', '57', '58',
'59', '66', '67', '68', '69', '77', '78', '79', '88', '89', '99']

Combinations without Replacement: 45
['01', '02', '03', '04', '05', '06', '07', '08', '09', '12', '13',
'14', '15', '16', '17', '18', '19', '23', '24', '25', '26', '27',
'28', '29', '34', '35', '36', '37', '38', '39', '45', '46', '47',
'48', '49', '56', '57', '58', '59', '67', '68', '69', '78', '79',
'89']

0123456789 taken 3 at a time

Permutations with Replacement: 1000
['000', '001', '002', '003', '004', '005', '006', '007', '008', '009',
'010', '011', '012', '013', '014', '015', '016', '017', '018', '019',
'020', '021', '022', '023', '024', '025', '026', '027', '028', '029',
'030', '031', '032', '033', '034', '035', '036', '037', '038', '039',
'040', '041', '042', '043', '044', '045', '046', '047', '048', '049',
'050', '051', '052', '053', '054', '055', '056', '057', '058', '059',
'060', '061', '062', '063', '064', '065', '066', '067', '068', '069',
'070', '071', '072', '073', '074', '075', '076', '077', '078', '079',
'080', '081', '082', '083', '084', '085', '086', '087', '088', '089',
'090', '091', '092', '093', '094', '095', '096', '097', '098', '099',
'100', '101', '102', '103', '104', '105', '106', '107', '108', '109',
'110', '111', '112', '113', '114', '115', '116', '117', '118', '119',
'120', '121', '122', '123', '124', '125', '126', '127', '128', '129',
'130', '131', '132', '133', '134', '135', '136', '137', '138', '139',
'140', '141', '142', '143', '144', '145', '146', '147', '148', '149',
'150', '151', '152', '153', '154', '155', '156', '157', '158', '159',
'160', '161', '162', '163', '164', '165', '166', '167', '168', '169',
'170', '171', '172', '173', '174', '175', '176', '177', '178', '179',
'180', '181', '182', '183', '184', '185', '186', '187', '188', '189',
'190', '191', '192', '193', '194', '195', '196', '197', '198', '199',
'200', '201', '202', '203', '204', '205', '206', '207', '208', '209',
'210', '211', '212', '213', '214', '215', '216', '217', '218', '219',
'220', '221', '222', '223', '224', '225', '226', '227', '228', '229',
'230', '231', '232', '233', '234', '235', '236', '237', '238', '239',
'240', '241', '242', '243', '244', '245', '246', '247', '248', '249',
'250', '251', '252', '253', '254', '255', '256', '257', '258', '259',
'260', '261', '262', '263', '264', '265', '266', '267', '268', '269',
'270', '271', '272', '273', '274', '275', '276', '277', '278', '279',
'280', '281', '282', '283', '284', '285', '286', '287', '288', '289',
'290', '291', '292', '293', '294', '295', '296', '297', '298', '299',
'300', '301', '302', '303', '304', '305', '306', '307', '308', '309',
'310', '311', '312', '313', '314', '315', '316', '317', '318', '319',
'320', '321', '322', '323', '324', '325', '326', '327', '328', '329',
'330', '331', '332', '333', '334', '335', '336', '337', '338', '339',
'340', '341', '342', '343', '344', '345', '346', '347', '348', '349',
'350', '351', '352', '353', '354', '355', '356', '357', '358', '359',
'360', '361', '362', '363', '364', '365', '366', '367', '368', '369',
'370', '371', '372', '373', '374', '375', '376', '377', '378', '379',
'380', '381', '382', '383', '384', '385', '386', '387', '388', '389',
'390', '391', '392', '393', '394', '395', '396', '397', '398', '399',
'400', '401', '402', '403', '404', '405', '406', '407', '408', '409',
'410', '411', '412', '413', '414', '415', '416', '417', '418', '419',
'420', '421', '422', '423', '424', '425', '426', '427', '428', '429',
'430', '431', '432', '433', '434', '435', '436', '437', '438', '439',
'440', '441', '442', '443', '444', '445', '446', '447', '448', '449',
'450', '451', '452', '453', '454', '455', '456', '457', '458', '459',
'460', '461', '462', '463', '464', '465', '466', '467', '468', '469',
'470', '471', '472', '473', '474', '475', '476', '477', '478', '479',
'480', '481', '482', '483', '484', '485', '486', '487', '488', '489',
'490', '491', '492', '493', '494', '495', '496', '497', '498', '499',
'500', '501', '502', '503', '504', '505', '506', '507', '508', '509',
'510', '511', '512', '513', '514', '515', '516', '517', '518', '519',
'520', '521', '522', '523', '524', '525', '526', '527', '528', '529',
'530', '531', '532', '533', '534', '535', '536', '537', '538', '539',
'540', '541', '542', '543', '544', '545', '546', '547', '548', '549',
'550', '551', '552', '553', '554', '555', '556', '557', '558', '559',
'560', '561', '562', '563', '564', '565', '566', '567', '568', '569',
'570', '571', '572', '573', '574', '575', '576', '577', '578', '579',
'580', '581', '582', '583', '584', '585', '586', '587', '588', '589',
'590', '591', '592', '593', '594', '595', '596', '597', '598', '599',
'600', '601', '602', '603', '604', '605', '606', '607', '608', '609',
'610', '611', '612', '613', '614', '615', '616', '617', '618', '619',
'620', '621', '622', '623', '624', '625', '626', '627', '628', '629',
'630', '631', '632', '633', '634', '635', '636', '637', '638', '639',
'640', '641', '642', '643', '644', '645', '646', '647', '648', '649',
'650', '651', '652', '653', '654', '655', '656', '657', '658', '659',
'660', '661', '662', '663', '664', '665', '666', '667', '668', '669',
'670', '671', '672', '673', '674', '675', '676', '677', '678', '679',
'680', '681', '682', '683', '684', '685', '686', '687', '688', '689',
'690', '691', '692', '693', '694', '695', '696', '697', '698', '699',
'700', '701', '702', '703', '704', '705', '706', '707', '708', '709',
'710', '711', '712', '713', '714', '715', '716', '717', '718', '719',
'720', '721', '722', '723', '724', '725', '726', '727', '728', '729',
'730', '731', '732', '733', '734', '735', '736', '737', '738', '739',
'740', '741', '742', '743', '744', '745', '746', '747', '748', '749',
'750', '751', '752', '753', '754', '755', '756', '757', '758', '759',
'760', '761', '762', '763', '764', '765', '766', '767', '768', '769',
'770', '771', '772', '773', '774', '775', '776', '777', '778', '779',
'780', '781', '782', '783', '784', '785', '786', '787', '788', '789',
'790', '791', '792', '793', '794', '795', '796', '797', '798', '799',
'800', '801', '802', '803', '804', '805', '806', '807', '808', '809',
'810', '811', '812', '813', '814', '815', '816', '817', '818', '819',
'820', '821', '822', '823', '824', '825', '826', '827', '828', '829',
'830', '831', '832', '833', '834', '835', '836', '837', '838', '839',
'840', '841', '842', '843', '844', '845', '846', '847', '848', '849',
'850', '851', '852', '853', '854', '855', '856', '857', '858', '859',
'860', '861', '862', '863', '864', '865', '866', '867', '868', '869',
'870', '871', '872', '873', '874', '875', '876', '877', '878', '879',
'880', '881', '882', '883', '884', '885', '886', '887', '888', '889',
'890', '891', '892', '893', '894', '895', '896', '897', '898', '899',
'900', '901', '902', '903', '904', '905', '906', '907', '908', '909',
'910', '911', '912', '913', '914', '915', '916', '917', '918', '919',
'920', '921', '922', '923', '924', '925', '926', '927', '928', '929',
'930', '931', '932', '933', '934', '935', '936', '937', '938', '939',
'940', '941', '942', '943', '944', '945', '946', '947', '948', '949',
'950', '951', '952', '953', '954', '955', '956', '957', '958', '959',
'960', '961', '962', '963', '964', '965', '966', '967', '968', '969',
'970', '971', '972', '973', '974', '975', '976', '977', '978', '979',
'980', '981', '982', '983', '984', '985', '986', '987', '988', '989',
'990', '991', '992', '993', '994', '995', '996', '997', '998', '999']

Permutations without Replacement: 720
['012', '013', '014', '015', '016', '017', '018', '019', '021', '023',
'024', '025', '026', '027', '028', '029', '031', '032', '034', '035',
'036', '037', '038', '039', '041', '042', '043', '045', '046', '047',
'048', '049', '051', '052', '053', '054', '056', '057', '058', '059',
'061', '062', '063', '064', '065', '067', '068', '069', '071', '072',
'073', '074', '075', '076', '078', '079', '081', '082', '083', '084',
'085', '086', '087', '089', '091', '092', '093', '094', '095', '096',
'097', '098', '102', '103', '104', '105', '106', '107', '108', '109',
'120', '123', '124', '125', '126', '127', '128', '129', '130', '132',
'134', '135', '136', '137', '138', '139', '140', '142', '143', '145',
'146', '147', '148', '149', '150', '152', '153', '154', '156', '157',
'158', '159', '160', '162', '163', '164', '165', '167', '168', '169',
'170', '172', '173', '174', '175', '176', '178', '179', '180', '182',
'183', '184', '185', '186', '187', '189', '190', '192', '193', '194',
'195', '196', '197', '198', '201', '203', '204', '205', '206', '207',
'208', '209', '210', '213', '214', '215', '216', '217', '218', '219',
'230', '231', '234', '235', '236', '237', '238', '239', '240', '241',
'243', '245', '246', '247', '248', '249', '250', '251', '253', '254',
'256', '257', '258', '259', '260', '261', '263', '264', '265', '267',
'268', '269', '270', '271', '273', '274', '275', '276', '278', '279',
'280', '281', '283', '284', '285', '286', '287', '289', '290', '291',
'293', '294', '295', '296', '297', '298', '301', '302', '304', '305',
'306', '307', '308', '309', '310', '312', '314', '315', '316', '317',
'318', '319', '320', '321', '324', '325', '326', '327', '328', '329',
'340', '341', '342', '345', '346', '347', '348', '349', '350', '351',
'352', '354', '356', '357', '358', '359', '360', '361', '362', '364',
'365', '367', '368', '369', '370', '371', '372', '374', '375', '376',
'378', '379', '380', '381', '382', '384', '385', '386', '387', '389',
'390', '391', '392', '394', '395', '396', '397', '398', '401', '402',
'403', '405', '406', '407', '408', '409', '410', '412', '413', '415',
'416', '417', '418', '419', '420', '421', '423', '425', '426', '427',
'428', '429', '430', '431', '432', '435', '436', '437', '438', '439',
'450', '451', '452', '453', '456', '457', '458', '459', '460', '461',
'462', '463', '465', '467', '468', '469', '470', '471', '472', '473',
'475', '476', '478', '479', '480', '481', '482', '483', '485', '486',
'487', '489', '490', '491', '492', '493', '495', '496', '497', '498',
'501', '502', '503', '504', '506', '507', '508', '509', '510', '512',
'513', '514', '516', '517', '518', '519', '520', '521', '523', '524',
'526', '527', '528', '529', '530', '531', '532', '534', '536', '537',
'538', '539', '540', '541', '542', '543', '546', '547', '548', '549',
'560', '561', '562', '563', '564', '567', '568', '569', '570', '571',
'572', '573', '574', '576', '578', '579', '580', '581', '582', '583',
'584', '586', '587', '589', '590', '591', '592', '593', '594', '596',
'597', '598', '601', '602', '603', '604', '605', '607', '608', '609',
'610', '612', '613', '614', '615', '617', '618', '619', '620', '621',
'623', '624', '625', '627', '628', '629', '630', '631', '632', '634',
'635', '637', '638', '639', '640', '641', '642', '643', '645', '647',
'648', '649', '650', '651', '652', '653', '654', '657', '658', '659',
'670', '671', '672', '673', '674', '675', '678', '679', '680', '681',
'682', '683', '684', '685', '687', '689', '690', '691', '692', '693',
'694', '695', '697', '698', '701', '702', '703', '704', '705', '706',
'708', '709', '710', '712', '713', '714', '715', '716', '718', '719',
'720', '721', '723', '724', '725', '726', '728', '729', '730', '731',
'732', '734', '735', '736', '738', '739', '740', '741', '742', '743',
'745', '746', '748', '749', '750', '751', '752', '753', '754', '756',
'758', '759', '760', '761', '762', '763', '764', '765', '768', '769',
'780', '781', '782', '783', '784', '785', '786', '789', '790', '791',
'792', '793', '794', '795', '796', '798', '801', '802', '803', '804',
'805', '806', '807', '809', '810', '812', '813', '814', '815', '816',
'817', '819', '820', '821', '823', '824', '825', '826', '827', '829',
'830', '831', '832', '834', '835', '836', '837', '839', '840', '841',
'842', '843', '845', '846', '847', '849', '850', '851', '852', '853',
'854', '856', '857', '859', '860', '861', '862', '863', '864', '865',
'867', '869', '870', '871', '872', '873', '874', '875', '876', '879',
'890', '891', '892', '893', '894', '895', '896', '897', '901', '902',
'903', '904', '905', '906', '907', '908', '910', '912', '913', '914',
'915', '916', '917', '918', '920', '921', '923', '924', '925', '926',
'927', '928', '930', '931', '932', '934', '935', '936', '937', '938',
'940', '941', '942', '943', '945', '946', '947', '948', '950', '951',
'952', '953', '954', '956', '957', '958', '960', '961', '962', '963',
'964', '965', '967', '968', '970', '971', '972', '973', '974', '975',
'976', '978', '980', '981', '982', '983', '984', '985', '986', '987']

Combinations with Replacement: 220
['000', '001', '002', '003', '004', '005', '006', '007', '008', '009',
'011', '012', '013', '014', '015', '016', '017', '018', '019', '022',
'023', '024', '025', '026', '027', '028', '029', '033', '034', '035',
'036', '037', '038', '039', '044', '045', '046', '047', '048', '049',
'055', '056', '057', '058', '059', '066', '067', '068', '069', '077',
'078', '079', '088', '089', '099', '111', '112', '113', '114', '115',
'116', '117', '118', '119', '122', '123', '124', '125', '126', '127',
'128', '129', '133', '134', '135', '136', '137', '138', '139', '144',
'145', '146', '147', '148', '149', '155', '156', '157', '158', '159',
'166', '167', '168', '169', '177', '178', '179', '188', '189', '199',
'222', '223', '224', '225', '226', '227', '228', '229', '233', '234',
'235', '236', '237', '238', '239', '244', '245', '246', '247', '248',
'249', '255', '256', '257', '258', '259', '266', '267', '268', '269',
'277', '278', '279', '288', '289', '299', '333', '334', '335', '336',
'337', '338', '339', '344', '345', '346', '347', '348', '349', '355',
'356', '357', '358', '359', '366', '367', '368', '369', '377', '378',
'379', '388', '389', '399', '444', '445', '446', '447', '448', '449',
'455', '456', '457', '458', '459', '466', '467', '468', '469', '477',
'478', '479', '488', '489', '499', '555', '556', '557', '558', '559',
'566', '567', '568', '569', '577', '578', '579', '588', '589', '599',
'666', '667', '668', '669', '677', '678', '679', '688', '689', '699',
'777', '778', '779', '788', '789', '799', '888', '889', '899', '999']

Combinations without Replacement: 120
['012', '013', '014', '015', '016', '017', '018', '019', '023', '024',
'025', '026', '027', '028', '029', '034', '035', '036', '037', '038',
'039', '045', '046', '047', '048', '049', '056', '057', '058', '059',
'067', '068', '069', '078', '079', '089', '123', '124', '125', '126',
'127', '128', '129', '134', '135', '136', '137', '138', '139', '145',
'146', '147', '148', '149', '156', '157', '158', '159', '167', '168',
'169', '178', '179', '189', '234', '235', '236', '237', '238', '239',
'245', '246', '247', '248', '249', '256', '257', '258', '259', '267',
'268', '269', '278', '279', '289', '345', '346', '347', '348', '349',
'356', '357', '358', '359', '367', '368', '369', '378', '379', '389',
'456', '457', '458', '459', '467', '468', '469', '478', '479', '489',
'567', '568', '569', '578', '579', '589', '678', '679', '689', '789']
>>>

>
> Sorry for the confusion.
>
> Cheers,
>
> Drea

Mensanator, Jul 16, 2009