# n points on a circle

WanderingKing
Posers and Puzzles 08 Mar '15 15:35
1. 08 Mar '15 15:35
If you put n distinct points on a circle, and draw chords through them, how many pieces is the circle dissected into? We assume no three chords intersect at one point.
2. wolfgang59
Mr. Wolf
08 Mar '15 22:36
Originally posted by WanderingKing
If you put n distinct points on a circle, and draw chords through them, how many pieces is the circle dissected into? We assume no three chords intersect at one point.
Each new chord can either not cross any other in which case only one new piece is added.
OR
The new chord can cross all existing chords in which case "n" new pieces are added.

Therefore n chords will create P pieces where n < P-1 < n(n+1)/2
3. DeepThought
09 Mar '15 16:43
Originally posted by wolfgang59
Each new chord can either not cross any other in which case only one new piece is added.
OR
The new chord can cross all existing chords in which case "n" new pieces are added.

Therefore n chords will create P pieces where n < P-1 < n(n+1)/2
While that is true for each chord, I think Wanderingking wants all chords drawable from a given point. So say there are n points, if you add another point you have to add n chords.
4. wolfgang59
Mr. Wolf
09 Mar '15 18:35
Originally posted by DeepThought
While that is true for each chord, I think Wanderingking wants all chords drawable from a given point. So say there are n points, if you add another point you have to add n chords.