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I think that the interesting part of the original problem is that it
requires the solver to realize that plane geometry is not involved.
The path has two corners and three equal legs, returning to the
On a plane surface, this must be an equilateral triangle.
But the problem, stated on a plane surface, would make two of the
legs parallel - impossible on a plane surface.
So we need a surface where either a "southern" path is not parallel
to a northern path, or two of the corners are oincident - impossible
on a planar surface.