a bit of history https://www.nytimes.com/2018/04/17/magazine/how-liberty-university-built-a-billion-dollar-empire-online.html
Several of the major dailies do this (NYT, WaPo, etc.). They monitor the number of stories you read by your cookies. However, remember that cookies are exclusive to the browser you're using. In other words, if you've maxed out your articles on Explorer, you can still access the article on, say, Firefox or Google Chrome. Or Microsoft Edge. Get it? You've got 10 freebie articles per month, per browser. So enjoy your 30, 40, or 50 articles . . . Another alternative: If you max out but don't want to change browsers to view an article, just clear out your cookies. But reaize that by doing it this way, you risk also clearing out your history, memorized passwords, tracking of articles read in forums such as DI, etc.
You can also delete cookies only associated with specific sites rather than all at once. I do this all the time to avoid these types of limits without affecting anything else.
Sorry - in error, I posted mass cookie deletion methods for several popular browsers. Don't have the answer.
Here's another perspective on Liberty http://www.patheos.com/blogs/friendlyatheist/2018/04/17/liberty-universitys-online-education-program-is-a-bust-for-desperate-students/
and then this https://www.vox.com/2018/4/18/17252510/online-degree-jerry-falwell-jr-liberty-university-propublica-nytimes
It depends on your browser. In Chrome, you can go to chrome://settings/siteData and search for individual cookies to delete there (e.g. "nytimes"). Firefox has a similar search feature under Options > Privacy > "remove individual cookies." I have no idea about IE or Edge, as I don't use those browsers.