Math Forum - Problem of the Week

Patio Stones

part of one ring is illustrated here

Recently I was in California visiting my sister Kathy and she asked me to help her select some stones from a catalog to pave an area in her yard. We selected a hexagonal paving stone because we could create a lovely tessellation!

We thought of setting one stone in the center and then fitting six stones around the center stone to make one "ring."

Kathy looked at that design and decided she would need to add a second ring of stones around the first ring to pave the area she had in mind.

How many stones did she need to buy in all?

Use this Java applet, Pattern Blocks, from Utah State's National Library of Virtual Manipulatives to help you think about the question:

Extra: How many additional stones would she need to make a 3rd ring? a 4th ring? an nth ring?

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