Sorry, but when I saw this post I just had to write the script in PwoerShell. Quick-and-dirty (replace the fake directory names with the names you want):
Here is a script file that will ask for the three directory names and assumes the current directory as the destination.
You can replace the Read-Host parts in the param section with hard-coded values if you like, example:
So what does the script do? It gathers the contents of each directory as a collection and combines the collections, which it then sorts in descending order of last modified time. It then grabs the first file in the result (which is the newest file) and copies it.