A puzzle ring was a type of ring for fingers that was made up of interconnected bands. At a glance, the ring appeared to be an endless knot. They could be peeled apart easily, and reassembly was a form of puzzle.
Before John Crichton flew up in the Space Shuttle to test the Farscape-1 pod, his father gave him a puzzle ring. The ring had been given to Jack by Yuri Gagarin for good luck. When Crichton was captured by Peacekeepers on a commerce planet, one of the guards found the ring and thought that it was a "field resourcefulness exercise." While he was occupied with it, Crichton took his pulse pistol and freed Ka D'Argo and Aeryn Sun. ("Premiere")
Crichton retrieved the ring and kept it with him. When the Ancients briefly led him to believe he had returned to Earth, he gave the ring back to his "father"; when the Ancients' ruse was uncovered, the ring was returned to him. ("A Human Reaction")
The ring was lost during the attack on the Gammak Base. Crichton gave Ka D'Argo the ring for good luck, but after the base was destroyed, Crichton and D'Argo found themselves floating helplessly in space. As D'Argo lost consciousness, he let go of the ring and it floated away. ("Family Ties")