Tricky Ternary Triskeles (TTT) Puzzle

The triskeles symbol of three human legs dates back to ancient Greece. It is a symbol of motion, strength, and progress, all characteristics that you will need to solve this puzzle.

The goal of the puzzle is to completely remove the string from the frame and return it back again to the start, thus completing the eternal cycle. It may seem like it takes an eternity to solve since it requires the string to pass through 78 rings before it can be removed!

Printing

There are two files: TTT_ring.stl and TTT_frame.stl. Print 6 copies of the ring and 1 copy of the frame. For my frame, I printed the middle third layers in a different color to highlight the triskeles symbol

Assembly

Once you have printed the frame and 6 rings, you can snap the rings into the holes in the frame. The rings should have a little bit of give, so you can pull them apart and insert into the square holes. The rings may wiggle a little - some glue could help keep them rigid, but that is not necessary. I didn't use any glue for mine.

                                                                              Partially Assembled Puzzle

You'll need a string of length around 18 inches or longer. The string I used in the pictures can be found here. These can be cut to size and have a break-away clasp which comes in handy if you get all tangled up or want to reset the puzzle without going through all the steps.

The start position of the string is shown below

Theory

This is an example of a n-ary puzzle, meaning the solution length grows exponentially as you add more rings. Each pair of rings represent a single base-3 digit. This puzzle has three base-3 digits, and it can be extended to more rings. The number of moves (or passes through a ring) is 3 * (3^(rings/2) - 1). In this case, there are 6 rings, and therefore 78 moves are required.

Here's a straightened-out version that illustrates the pattern and how it can be extended. It's the same puzzle, just straight rather than wrapped around.