Since it is the same puzzle all the time. It is alternate placement of the gem and then move it to a circle connected by the line:
1. Click on a corner - see that the gem goes to that circle.
2. Then you have to move that gem to the next circle by clicking on a circle that is connected by a line.
3.Find a circle that is 2 lines away But connected by lines from where the gem in step 2 is placed. Click another gem there.
4. Click the circle that is in between the 2 gems so that the gem is now close to the gem on step 2.

Or:
Number the jewels clockwise from the top: 1, 2, 3, 4, 5, 6, 7, 8.
Place gem on 4, click on 1.
Place gem on 3, click on 6.
Place gem on 8, click on 3.
Place gem on 5, click on 8.
Place gem on 2, click on 5.
Place gem on 7, click on 2.
Place gem on 4, click on 7.