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Cutting planes with polygons (Posted on 2006-09-06) Difficulty: 3 of 5
Into how many regions can you partition the plane with m n-sided regular polygons?

For example, with two squares you can achieve up to 10 regions by choosing the right size and position of your squares.

See The Solution Submitted by JLo    
Rating: 4.0000 (2 votes)

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re: Who dares: Not I | Comment 12 of 16 |
(In reply to Who dares: What if we have general polygons? by JLo)

The problem in trying to find a formula for any simple polygons is I don't even know if I have the optimal arrangement for two quadrilaterals.  (I have two darts forming 10 regions.)

With two self-intersecting quadrilaterals I have formed 12 regions.

  Posted by Jer on 2006-09-11 11:20:23
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