electromagnetism - Would a solenoid move if a magnet went through it?

If you were to have a solenoid (0 current) floating still in space, and shot a magnet through it, would the solenoid move, or would it only create a DC current (what if it has a closed/open circuit)? Does the magnet slow down (if so by how much)? What if you increased the speed/power of the magnet drastically, would anything change?

(Feel free to link anything that could help explain solenoids/E&M fields better.)