is black is red and is an outside grandchild of is red and is an inside grandchild of it might seem that this list doesn' cover all the possibilities we'll return to this question after we've explored these three possibility is black if is blackwe get free ride the node we've just inserted is always red if its parent is blackthere' no red-to-red conflict (rule )and no addition to the number of black nodes (rule thus no color rules are violated we don' need to do anything else the insertion is complete possibility is redx is outside if is red and is an outside grandchildwe need single rotation and some color changes let' set this up with the workshop applet so we can see what we're talking about start with the usual at the rootand insert and you'll need to do color flip before you insert the now insert which is xthe new node figure shows how this looks the message on the workshop applet says errorparent and child both redso we know we need to take some action