Skip to content

Puzzle: diagonals in a polygon

March 28, 2007 am31 7:37 am

One of my favorite little puzzles is “How many diagonals are there in a polygon?”

For solvers here I have three questions:

  1. What is the answer? (answers here)
  2. How many different routes of solution can we find? (different solutions here)
  3. How can we modify this problem to make it easier? (easier versions, here)
One Comment leave one →
  1. March 28, 2007 am31 7:58 am 7:58 am

    Define
    vertices: The points where two line segments come together (corners)
    diagonal:a line segment connecting two non-adjacent vertices of a polygon: A closed plane figure made up of several line segments that are joined together.

    Let n = number of vertices. Then the number of diagonals is:
    n-3 + n – 3 + n – 4 + n – 5 + n – 6 + … until subtraction is n-1.
    = (n-2)*n – 3 – sum(3:n-1)

    So, for instance, you have 7 vertices in the picture above. That means n = 7. The number of diagonals is then 5*7 – 3 – 3-4-5-6 = 35-21 = 14.
    A square would have 4 vertices. 2*4 – 3 – 3 = 2.
    A pentagon would have 5 vertices: 3*5 – 3 – 3 – 4 = 5.

    Unfortunately for me, it’s very late and I could be making lots of mistakes here.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: