You could, if you go with AgentM's suggestion (and you should listen to merlyn's advice), set up a method in A.pm that would look like so (assuming your object is a reference to an anonymous hash):

sub the_problem {
    my $self = shift;
    $self->{_the_problem} = shift if (@_); # sets _the_problem to the 
+value we've been passed *if* we've been passed a value
    $self->{_the_problem}; # returns the current value of _the_problem
}
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It's important to put this method in A.pm so B and C can inherit this method.

In the script which uses the modules, you would then set this property by calling the method with arguments.

use strict;
use A::B::C; #use your modules.  Pay attention to btrott's advice abov
+e on Exporter etc.
...

my $foo = new A::B::C;
$foo->the_problem("argle bargle"); # $foo->{_the_problem} now eq 'argl
+e bargle'

print $foo->the_problem();     # prints "argle bargle"
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Philosophy can be made out of anything. Or less -- Jerry A. Fodor