It's a math problem. Read TFA.
As a pure math problem it’s got a few constraints such as the track not physically intersecting with itself which go beyond the stated question.
So yes it’s a toy problem, but one constrained by real world objects.
The real world is irrelevant in the trolly problem or the 4 color theorem etc.
You may personally be interested in it as a purely mathematical problem, but he’s looking for a real world answer so poor abstractions are useless. On the other hand “I would first check for track flatness. When locked in with extra effort, the loop will warp a little, basically going into 3d instead of flat 2d.” is a useful shortcut.
Based on his history in StackExchange, it is unlikely Lezzup is looking for a real world answer. The top tags of his posts are: mathematics, sudoku, geometry, logical-deduction, sequence, and enigmatic-puzzle.
The fastest solution is going to be a combination of heuristics and multiple forms of mathematical modeling. Something like 1 does it look reasonable, 2 do the internal angles add up correctly, then 3 a more precise assessment based on actual curves and piece lengths. Doing 3 when it already failed 2 is redundant.
the stack overflow answers are math.
Try thinking for a few seconds before posting such a meritless dismissal.
That gives you the impression that goldcd fully comprehended the scope of the inquiry?