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Pinned Squares

Age 14 to 16
Challenge Level Yellow starYellow starYellow star
  • Problem
  • Student Solutions

Pin those squares down! A geoboard is a piece of wood with pins hammered into it. The diagram shows a 5 by 5 board with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins as shown. What is the total number of squares that can be made on a 5 by 5 board? 

pinned board

How many squares can be made on an N by N board?
 
A virtual pinboard is available here.

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Pick's Theorem

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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