Here is one that has always stumped me.
Lets say two space ships leave Earth at the same time but going in opposite directions. Each ship accelerates to nearly the speed of light (as close as relativity will allow) and goes for one year. From the perspective on Earth, each ship is going close to the speed of light, but in opposite directions.
Because nothing can go faster than the speed of light relative to anything else, from the perspective of each ship they are going close to the speed of light away from the other ship and much less than that away from Earth. So from Earth, each ship is moving away at the speed of light, but from each ship Earth is moving away much slower than the speed.of light.
After one year, both ships stop. From Earth, each ship is one light year away. From each ship, Earth is less than one light year away and the other ship is one light year away, because the other ship could not have moved further from them than one light year in one year.
Now let’s really complicate it by throwing in relativistic time dilation. Since each ship was going at close to the speed of light, time moved slower for them. During the one year that passed on Earth, only a few months passed on each ship (depending on how close to the speed of light they were going). So from their perspective, the other ship could be no further than a few light months away and Earth much less.
That isn't exactly true. From the earth's frame of reference, both ships will appear to be going (close to) the speed of light, and (relative to each other) will be going (close to) twice the speed of light.
But from the frame of reference of either ship, I believe the earth will be receding fast, and the other ship just a little bit faster. Because of time dilation, both earth and the other ship will be moving at less than the speed of light.