Combine Multiple PDF files with common names to a Single PDF

Hello, I have a large number of scanned documents that were scanned as single pdf documents but need to be merged into a single pdf file with multiple pages.  I have Adobe Acrobat Pro on my desktop but in my 15 minutes of review and searching the internet I cannot find a way automate a process to merge the many pdf images.  In my search I found a number of possible tools that may assist with merging the pdf’s.  They are: PDFTK and PDFSAM.  Here is a sample of the files we would like to merge so you understand the task:

5050.pdf

5050a.pdf

5050b.pdf

4225.pdf

4225a.pdf

4225b.pdf

925.pdf

925a.pdf

I guess it would be a big help if we could combine pdf images with common filenames to the first 4 characters.  IE: %%%%*.pdf  They pdf’s should be combined in the common ascending sort order in the finished merged document.   Therefore the list above should be reduced to the following as merged documents:

5050.pdf

4225.pdf

925.pdf

Any suggestions or ideas to accomplish this task using Adobe Acrobat XI?  The GUI is definitely not the way to go because we have thousands or files that need to be combined...

Thanks, Curt