How to construct non computer-based, Paper Parsons Problem
If you have a metal surface to work on, such as some whiteboards, you can get "magnetic paper". These are sheets of various sizes that are magnetic and can be written on with markers or printed on. With erasable markers they can be reused. They can also be cut to size with a scissors. They will, of course, stick to any metal surface and can be removed and replaced. 

Search for "magnetic paper" to find several varieties and brands.