Please read this thread
Patenting will only help you if your invention can be used as a technical improvement not earlier known to the world.
(and best an improvement that can also be used in a general area and not twisty puzzles: patenting is expensive)
As you can read, both Verdes and I go for a design protection. Which can be very strong (even stronger than a patent dependent on the basis/use of a patent). If it looks like my puzzle for the generally informed public, the other puzzle maker is quite easily infringing my rights (which can be enforced).