Sort a List, in a List of Lists of Lists

• To: mathgroup at smc.vnet.net
• Subject: [mg113797] Sort a List, in a List of Lists of Lists
• From: leigh.pascoe at inserm.fr
• Date: Sat, 13 Nov 2010 00:59:27 -0500 (EST)

Dear Mathgroup,

I have a lsit of Lists of Lists:

{{{1,2},{2,1},{1,1}},{{1,1},{1,1},{1,2}},{{2,1},{2,2},{1,2}},{{2,2},{1,2},{2,2}},{{1,1},{2,1},{1,2}},{{1,2},{2,2},{2,2}}}

I would like to sort the elements in the lowest level of brackets to give

{{{1, 2}, {1, 2}, {1, 1}}, {{1, 1}, {1, 1}, {1, 2}}, {{1, 2}, {2,
2}, {1, 2}}, {{2, 2}, {1, 2}, {2, 2}}, {{1, 1}, {1, 2}, {1,
2}}, {{1, 2}, {2, 2}, {2, 2}}}

i.e retaining the same structure with the paired elements in the
original order. I can't seem to get the syntax right to do this apart
from the obvious

{{Sort[{1, 2}], Sort[{2, 1}], Sort[{1, 1}]}, {Sort[{1, 1}],
Sort[{1, 1}], Sort[{1, 2}]}, {Sort[{2, 1}], Sort[{2, 2}],
Sort[{1, 2}]}, {Sort[{2, 2}], Sort[{1, 2}],
Sort[{2, 2}]}, {Sort[{1, 1}], Sort[{2, 1}],
Sort[{1, 2}]}, {Sort[{1, 2}], Sort[{2, 2}], Sort[{2, 2}]}}

I must have a blind spot for the correct command. Can someone please
help me with what should be a straightforward sort. As I want to carry
this out on several hundred thousand pairs I need a more efficient