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Overlapping (Celtic Knot) Puzzle

I am in no way a programmer so please be patient with me on this.

I am trying to create a visual puzzle based of a Celtic Knot, The basic concept is to rotate a series of rings to match up symbols on each loop Generally Consisting of 3 Rings/Loops with multiple overlaps, To complete each puzzle you need to match anywhere from 6-18 symbols at the same time.

I figure the best place to start will be the simple Celtic knot design:
3 Loops interlocking with 6 intersections, Each loop will have 16 sections.

Visualizing the puzzle isn’t the hard part for me, its creating the rules behind the puzzle to allow for a Single solution through randomization…

I have no idea where to start, i have some some theory Pseudo code for this, but i always tend to over or under complicate everything.

Does anyone know where to start with this all?