Posers and Puzzles

Posers and Puzzles

  1. Joined
    29 Oct '09
    Moves
    1421
    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. Standard memberwolfgang59
    Mr. Wolf
    at home
    Joined
    09 Jun '07
    Moves
    46120
    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. Standard memberDeepThought
    Losing the Thread
    Cosmopolis
    Joined
    27 Oct '04
    Moves
    80321
    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. Standard memberwolfgang59
    Mr. Wolf
    at home
    Joined
    09 Jun '07
    Moves
    46120
    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.
    Yep. I misread what he is asking for.
    But I'm unclear as to what he wants ... it can't be all chords from a given point because he states "no three chords intersect at one point".
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