I am looking for a solution that allows me to print the following:

Cat 1        Cat 2        Cat 3
 Post 1       Post 1       Post 1
 Post 2       Post 2       Post 2
 Post 3                    Post 3
                           Post 4

EDIT

I am looking for something that will only require one database query! So if you have a foreach in your code followed by a new WP_Query then that is not what I am looking for (I am planning to put this onto my website’s homepage).