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Matchsticks

Age 7 to 11
Challenge Level Yellow star
  • Problem
  • Student Solutions

This solution comes from Henry. Well done!

To make a square, we need three more matchsticks.

To make a second square, we need three more matchsticks.

I noticed that for each square we make we need three matchsticks, in addition to the one we had at the beginning. Therefore to make 10 squares we need a total of 31 matchsticks. For 20 squares we need 61 matchsticks and for 50 squares we need 151.

The general pattern isif $n$ is the number of squares, we use $3n + 1$ matchsticks in total.


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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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