A regular nonagon has 27 diagonals, and these diagonals intersect in the interior of the nonagon at 126 distinct points.

Nonagon with diagonals

Show that it is possible to select 13 diagonals of a regular nonagon such that the selected diagonals have 13 points of intersection within the nonagon.

The image is provide as a reference and visual aid. The diagonals are colored according to length, but this is only for aesthetic purposes.

  • 2
    $\begingroup$ If there hadn't been a "no-computers" tag, I could have told you that there are exactly 8 solution down to rotations and reflections. But the tag is there. $\endgroup$
    – Florian F
    Jan 3, 2022 at 19:27
  • $\begingroup$ @FlorianF I might have already known that. $\endgroup$ Jan 3, 2022 at 21:22

1 Answer 1


enter image description here

The easiest way to count is

Diagonals: 3 horizontal, 3 pairs crossing in the middle, 4 that cross one of the horizontal lines

Intersections: 3 in the middle, 5 left, 5 right


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