Richard,
OK, here is the deal.
'Delete' is an ordinary permission that can apply to folders or files, and is inherited by default. If you have that permission on a folder, you can delete any file in it, unless someone blocked inheritance and removed your permission to delete it. To delete a folder you must have Delete permission on the folder and on every last item inside. If you try to delete a folder and just one item inside is blocked, Windows will give you an error message, and nothing will be deleted. It scans through the whole folder first before deleting anything.
'Delete Subfolders and Files' is a special permission that does not behave in an ordinary way. It is only assigned to, and inherited by, folders. When you have this permission on a folder, it has the effect of granting 'Delete' to any subfolder or file inside, and to files inside any subfolders that inherit 'Delete Subfolders and Files' from their parent, and so on. With this permission, you could delete a file without any explicit or inherited 'Delete' permission, or even if the owner explicitly assigned 'Deny Delete' to you! You can't even tell by looking at the file's permissions. This permission is implemented and enforced by the immediate containing folder.
There are some quirks and exceptions, but those are rare situations, and they only occur when trying to delete files or subfolders on a local drive.
'Delete Subfolders and Files' has been around since Windows NT; you just couldn't see it. It was granted with Full Control. The idea was to give some more power to a non-administrator folder owner to delete items other users might have moved into a folder he owns, where the folder owner is not assigned 'Delete' permission to those items. This will generally happen when a user moves something from one folder with different permissions to another on the same volume. If the ordinary users (who are not folder owners) cannot edit permissions on anything, and you don't ever block inheritance, then the 'Delete Subfolders and Files' permission for the folder owner can always provide the intended power. If the ordinary users can and choose to block inheritance and remove the owner's 'Delete Subfolders and Files' permission on a subfolder he drags into the owner's folder, as well as the 'Delete' permissions on the files inside, then the folder owner would have to get an Administrator to take ownership, and change permissions, to delete it.
Basically, the Windows online help does not make clear that 'Delete Subfolders and Files', unless allowed to be inherited, does not extend beyond the subfolders inside the folder on which it is applied.
Administrators will have this permission on any folder where they have Full Control, but they generally don't rely on it, because, by default, they can just take ownership and grant themselves Full Control to anything on the system.
So, in your case, you can see why User A cannot delete Folder B. If you did everything the same but did not create File B, then User A should be able to delete Folder B.
As for "User A can see File B," this is a bit confusing, because if all rights were removed for User A from Folder B (including List Folder), he should get "Access Denied" trying to open the window in Explorer, or possibly a blank window over the network. Can you check your settings, and test it again, and let us know?
Jeffrey Fox
J.D. Fox Micro
http://www.jdfoxmicro.com/