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Possible Pairs

Age 7 to 11
Challenge Level Yellow star
  • Problem
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Elizabeth wrote to us to say:

I first was a bit stuck. Then I made a table of the grid. I made it so I would be able to mix all the facts up and try new combinations. I used symbols such as ticks and crosses. I was also surprised at how much time it took.

I discovered that every card on its own can be made into a triangle. 

Thank you, Elizabeth, for sharing your method. It is a shame you didn't send us a picture of your grid. We would love to see it if you still have it!

If you have thought about whether there are some cards that are particularly 'good'/'bad' and why, please send us your conclusions, along with your reasoning. Equally, if you have been working on the number of possible pairs using any two of the cards, please get in touch.

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Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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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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