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How many closed polygons will $n$ coplanar lines, all intersecting each other (no three concurrent), form on the plane?

Can we find a recursion formula for this?? Is there a way out?


marked as duplicate by Parcly Taxel, Community Mar 2 '18 at 3:57

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  • $\begingroup$ I have edited it.. $\endgroup$ – Ryan Scott Mar 2 '18 at 4:00
  • $\begingroup$ It is no more a duplicate problem.. $\endgroup$ – Ryan Scott Mar 2 '18 at 4:01
  • $\begingroup$ Is it $\frac{n^2-3n+2}{2}$ ?? $\endgroup$ – Of course it's not me Mar 2 '18 at 4:02
  • $\begingroup$ How did you get it? $\endgroup$ – Ryan Scott Mar 2 '18 at 4:09

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