The tricky part is in the regex. The first time through, $_ is just one x, so the first part of the match works. But the match is reversed, so the number doesn't print.

On subsequent passes, that part fails. The second half of it grabs a certain number of x's. Then, it looks for the same number of x's, repeated a certain number of times. For example, with two, the first grouping matches, but the second doesn't. Reverse the non-matching flag, and it prints the number. On the third try, same thing.

On the fourth pass, the first part matches two x's, and so does the second. Reverse that flag, and it won't print. Basically, all this does it use the grouping feature of the regex engine to perform a factorial operation.