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Posers and Puzzles

Posers and Puzzles

  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. Standard member wolfgang59
    Infidel
    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 member DeepThought
    Losing the Thread
    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 member wolfgang59
    Infidel
    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".