I did take a quick look at these square strips, and gained the impression that the set of paths potentially continuing from a given segment might be restricted to a roughly exponential horn-shaped region extending away from each endpoint: it would follow that no closed loops are possible. However I am presently unable to quantify this insight; nor have I yet found a neat computational model for enumerating such paths, that avoids incurring somewhat messy technical details. WFL On 3/18/18, Dan Asimov <dasimov@earthlink.net> wrote:

I am incapable of stating my puzzle correctly, even though I know exactly what I mean. Why is it so difficult for everyone else?

4th try?: ----- Each square Q is adjacent to exactly 2 others, Q- and Q+, such that each pair ((Q-, Q) and (Q, Q+) is perpendicular and shares one of 2 adjacent edges of Q, and Q- and Q+ lie on opposite sides of the plane of Q. -----

—Dan

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