Everything is possible but you’ve got to provide the community here with an example of what you’ve attempted and what you’re working with.
This sounds like what you’d want is some sort of randomization of which post get’s categorized triggered by a CRON. Randomization can be taxing though.
You should see if you can come up with some sort of logic that you can implement to develop a pattern for which post is next displayed. For example, if all of the ‘posts’ are published already and since you’re changing the one that gets displayed every 3 days, you could develop a CRON that adds a ‘featured’ category to the oldest published date. The CRON would first find the post that is currently ‘featured’ remove that category, then move up one in terms of publication and add featured to that.
That’s just an example. You could also hook into the Posts post type and add the ‘Page Attributes’ panel so that you can assign an ‘Order’ value. Then you can record the lowest Order value to a custom wp_options meta field in the DB. Every three days you’d run your CRON to check what the current value in the DB is, grab the next one up and change the ‘category’ on that post, then update the record in the options DB to indicate what you changed it to.
My point is, there are multiple ways you can achieve the desired effect, the problem is that since no one here knows what you’re working with, what you’ve tried, etc., it’s impossible to give you an exact answer.