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Age 11 to 14 Short
Challenge Level


A shape consisting of a number of regular hexagons is made by continuing the pattern shown in the diagram, with each extra hexagon sharing one side with the preceding one.
Each hexagon has a side length of 1cm.



How many hexagons are required for the perimeter of the whole shape to have length 1002cm?


If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.