The Star: Astronomy 101

 

This one is really hard.  Pay attention, because there are rules in order to do this fairly.  Below is a star pattern.  I suggest you make a copy of this on several pieces of paper.

You can draw two lines through any part of the star in order to create a total of 10 triangles.  In order for it to be a triangle it must

1. Be a triangle
2. Not have any line going through its inside.  The triangle must be empty inside.

You can bisect a triangle to make two.  The lines can interset to create a triangle on the outside of the star.  Let's look at some examples:

To the right we start out with five triangles.  The line cuts through one triangle, creating a smaller one and discounting the larger one.  The total number of triangles is still five.

Below we see that we have formed triangle #2 using the two lines.  We also create triangle #3 on the outside.  Notice that triangle #4 and #1 are NOT part of bigger triangles since a line goes through the original #4 and #1.

Below  we create triangle #2 on the outside and create two triangles (#7 and #6) by bissecting the larger triangle.  We do NOT count the larger triangle composed of 6 and 7.  Also, if any lines go through the inside of a triangle it is no longer counted as a triangle.

Now, can you figure out how to make 10 of them?

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