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Witch's Hat

Age 11 to 16
Challenge Level

Thanks to Cubes, Aisling and Brandon for their ideas on how to make a wizard's hat or a witch's hat.  Cubes suggested cutting out two triangles and sticking them together.  Aisling and Brandon both suggested rolling a piece of paper into a cone.

Either of these methods would work to make a pointy hat.  

But there is a better way to make a conical hat.

Alice worked through this problem and found a very surprising answer. She sent in some work which you can find here.

She only found the tallest wizard's hat, can you do something similar to find the witch's hat, fez or top hat?