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 Dec30 comment Puzzle: How Many Possibilities Are There Between Connected Points? @BukLau you choose pairs one by one and then divide by number or orders we could choose these pairs in Dec30 comment Puzzle: How Many Possibilities Are There Between Connected Points? Total number of possible connections in the $2n$ point problem is: $$\frac{1}{n!}\prod_{i=1}^n \binom {2i}{2}$$ Dec9 awarded Caucus Nov25 comment Distinguish between clockwise and counterclockwise polygon If the polygon is convex it is enough to check the cross product of any two given consecutive edges, treated as vectors with the same origin. For polygon $ABCDE$ it would be $CB \times CD$ Nov14 accepted What is a sparse subset? Nov14 reviewed No Action Needed Prove by induction for$P(x)$ Nov14 revised Is this combinatorial problem for noncommutative variables known? added definition Nov14 suggested approved edit on Is this combinatorial problem for noncommutative variables known? Nov14 comment Is this combinatorial problem for noncommutative variables known? Binomial(n, floor(n/2)) -> oeis.org/A001405 has description well fitting your problem: it is also the number of distinct strings of length n, each of which is a prefix of a string of balanced parentheses Nov14 comment What is a sparse subset? @QiaochuYuan what does that mean in terms of subsets of vectors then? Nov14 answered Proof By Induction Fibonacci Numbers Nov14 revised Proof By Induction Fibonacci Numbers improved formatting Nov14 suggested approved edit on Proof By Induction Fibonacci Numbers Nov14 asked What is a sparse subset? Nov9 awarded Yearling Sep30 awarded Explainer Sep24 awarded Autobiographer Nov9 awarded Yearling Apr2 answered How do I prove: $\cos (\theta + 90^\circ) \equiv - \sin \theta$ Feb8 awarded Revival