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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.