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Hex

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

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LOGO Challenge 6 - Triangles and Stars

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

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Hexagon Cut Out

Weekly Problem 52 - 2012
An irregular hexagon can be made by cutting the corners off an equilateral triangle. How can an identical hexagon be made by cutting the corners off a different equilateral triangle?

Regular Hexagon Loops

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2


A hexagon loop is a closed chain of hexagons that meet along a whole edge and in which each hexagon must touch exactly two others.


 

They do not need to be symmetrical or short:





Can you find any rules connecting the numbers of tiles, the inside perimeter and the outside perimeter?

You might want to start by exploring square loops or growing sequences like these:



If you haven't got a supply of regular hexagons you could work on these regular hexagon sheets


With thanks to Don Steward, whose ideas formed the basis of this problem.