Extension cord can't plug into christmas light string?
Thanks for the pictures! It looks like the problem is that your extension cord is polarized, but your Christmas lights aren't. The best solution is to replace the electrical receptacle at the end of the first set of lights with a polarized one. They sell replacement receptacles for Christmas lights. 



You could use a ground plug adapter to do this, but you would need to trim the polarized neutral plug to fit in a non-polarized hole which is a bad idea. It will be fine for this season, but once you take your lights down for the season you'll forget that you have a modified adapter that could be reused for something else and hurt somebody.