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Symmetry Challenge

Age 7 to 11
Challenge Level Yellow starYellow starYellow star
Primary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

The 3 by 3 grid has 4 lines of symmetry. How might this help?

Try shading only one square. What symmetries are possible?
Try shading 2, 3, 4, ... squares. What symmetries are now possible?

How helpful would this table be?

  Lines of symmetry
  0 1 2 3 4
Shaded squares 1        
2          
3          
4          

What other rows or columns could you add to this table?

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Eight Dominoes

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

Prime Magic

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

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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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