Assistance Developing Query

Good Day;

I would appreciate assistance developing a query that I haven't been
able to develop without using a second table. I wish to count the
number of records that are still open on the first of each month.
Each record has an open date and a close date or the close date is
null i.e., the record is not yet closed. I've previously beaten this
by building a table, simply a list of the dates for the first of each
month for the next ten years or so, and then selecting values based
upon a date selected from that table. However I'd be happier if I
could do it without the second table. I'd be prepared to accept the
Min(Date) for each month as being the first of the month.

I've included some DDL statements to build and populate the table if
that helps. Since the selection is rather small and all the open
dates are very close together I think the result will be simply a
decreasing count from the month the first record is opened till today.

A pseudo code select statement might look like

Select Min(DateOpened) As DateOfInterest, Count(*) as [Qty Still Open]
FROM DetailT
Where DateReceived > DateOfInterest or DateReceived is Null and
DateOpened < DateOfInterest
Group by Min(DateOpened)
Order by Min(DateOpened)

I hope I've explained it sufficiently well.

CREATE TABLE [dbo].[DetailT] (
[Autonum] [int] IDENTITY (1, 1) NOT NULL ,
[QDNumber] [varchar] (50) COLLATE SQL_Latin1_General_CP1_CI_AS NULL ,
[DateOpened] [smalldatetime] NOT NULL ,
[DateReceived] [smalldatetime] NULL ,

)
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('C15788', '06/04/2005 9:35', 07/04/2005)
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('B16091', '06/04/2005 9:36', '07/04/2005')
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('B15001', '06/04/2005 9:51', '08/04/2005')
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('M18696', '06/04/2005 9:56', '06/04/2005')
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('C14969', '06/04/2005 10:05', '10/04/2005')
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('O10091', '06/04/2005 10:08', '12/04/2005')
Insert into DetailT (QDNumber, DateOpened)
VALUES('D01197', '06/04/2005 10:13')
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('H15001', '06/04/2005 10:15', '08/04/2005')
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('J15090', '06/04/2005 10:24', '08/04/2005')
Insert into DetailT (QDNumber, DateOpened)
VALUES('J01202', '06/04/2005 10:31')
Insert into DetailT (QDNumber, DateOpened)
VALUES('G01193', '06/04/2005 10:32')
Insert into DetailT (QDNumber, DateOpened)
VALUES('K01164', '06/04/2005 10:35')
Insert into DetailT (QDNumber, DateOpened)
VALUES('K01162', '06/04/2005 10:48')
Insert into DetailT (QDNumber, DateOpened)
VALUES('F01124', '06/04/2005 10:59')
Insert into DetailT (QDNumber, DateOpened)
VALUES('H01147', '06/04/2005 11:01')
Insert into DetailT (QDNumber, DateOpened)
VALUES('S15068', '06/04/2005 11:10')
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('E12322', '06/04/2005 11:32', '07/04/2005')
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('A12205', '06/04/2005 11:37', '06/04/2005')
Insert into DetailT (QDNumber, DateOpened, DateReceived)
VALUES('D12259', '06/04/2005 11:40', '07/04/2005')
Insert into DetailT (QDNumber, DateOpened)
VALUES('C03394', '06/04/2005 11:51')

If you made it this far thank you for your patience. Any help would be
appreciated.

Thank you.

Bill