As it seems that English is not his first language, and that quote you offered appears to contradict "I know I could just take one piece out, and put it back in to feel it myself, but I am looking for a more logical way, so I am able to reason it", and based on the provenance of his other postings, these appeals to contort the question into some kind of uninteresting material science one are not credible.

There’s no contradiction to “logical methods” including things like noticing the pieces curve into 3D space because they don’t fit together. Saying you don’t want to rely on taking it apart doesn’t invalidate simple inspection.

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.