32,224: Here are 32 lines and 224 triangles, which is a
record, so far. Here is a table of even numbered stars: Return to my Puzzle pages
Go to my home page
© Copyright 2001, Jim Loy
Part VI
Part V showed how stars with an odd number of vertices can be used to establish records, with this puzzle. Here is a similar idea with stars with an even number of vertices. Draw a star with an even number of vertices, draw lines connecting the opposite vertices, and draw lines halfway between these lines (through the center).
32,224: Here are 32 lines and 224 triangles, which is a
record, so far. Here is a table of even numbered stars:
| vertices | lines | triangles |
| 10 | 20 | 80 |
| 12 | 24 | 120 |
| 14 | 28 | 168 |
| 16 | 32 | 224 |
| 18 | 36 | 288 |
| 20 | 40 | 320 |
| 22 | 44 | 440 |
The number of lines is twice the number of vertices. And the number of triangles is the number of vertices squared minus twice the number of vertices (V^2-2V).
36,288: Above is another 36,288. In part IV (where there is another 36,288) I said that this may not be optimal. These stars (like those with an odd number of vertices) seem to be effective because every new line intersects many other lines, producing many new triangles (from other triangles or from quadrilaterals).
Go back to David Coles' Triangle Puzzle (Part V).