There are a couple of ways you could do this. You could use session variables which you set each time they enter the content. Then when she returns to the page listing the contests, it would check her session variables and see if any contests have been visited and not to display those.
The second way is similar to the first but instead of sessions you could use cookies. These are little bit less reliable than sessions, but again you would record any contests she entered into a cookie file on the user's computer and check that file when it comes to listing the contests again. Then you have that page not list any contests found in the cookie.
The third way is (if this is a database project) to simply record the user's identity (whether it be their IP, their account if they have one etc) and the ID of the contest they visited. Then have PHP simply list any contests that the user doesn't already have listed for their account in the database.
Link to Sessions information in PHPLink to Cookies information in PHPHope this helps.