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#!/usr/bin/perl

...
my @list = ( '1,cat', '2,dog', '22,mouse', '11,eel', '001,elk', '13,mi
+nk');

print join "\n", sort { $a=~s/,.+//r <=> $b =~ s/,.+//r  } @list;

1,cat
001,elk
...
11,eel
13,mink
22,mouse