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Here is a solution of two rings and a closed loop with 15 arcs, all matching their paths. See how the rings have symmetrical path patterns and contain one "double" tile each. Double tiles have an arc that connects the same level — 1-1, 2-2, 3-3, 4-4 and 5-5. All the other tiles step up or down between different levels. See also how on the larger loop the arcs turn in and out, so that converse edges meet — 1 to 5, 2 to 4 — while 3 meets 3 either way. That's a valuable hint for solving, saving the 3's to the last.
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