Author presents solutions to Triple Cross and the related Port to Port puzzle. Hidden behind links are javascript implementations of the puzzles. Re: Triple Cross: "This solution was constructed by using computer searches to find sequences that move specific tiles without moving others. This means it is mostly just lists of sequences without any visible underlying strategy. If anyone has a more transparent method, I would like to know about it." post 
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I have a collection of puzzles. Triple Cross is one I have been unable to solve. My kids recently unearthed my puzzle which prompted my excursion on the web.
I adopted the notation from the author... especially using `/` to denote changing the vertical plungers. I sketched the permutations from six sequences of movement which return all the plungers to their initial positions.
Permutations of Triple Cross.
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https://www.jaapsch.net/puzzles/javascript/triplecj.htm HEIGHT 300 Javascript Triple Cross
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It might be interesting to explore common abstractions between a Rubik's cube and Triple Cross. See Cubist Planes.