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How many triangles can you make on the 3 by 3 pegboard?

Cutting Corners

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


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

Possible Pairs

Age 7 to 11
Challenge Level

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.