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Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Cuisenaire Squares

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?


We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Broken Toaster

Age 7 to 11 Short Challenge Level:

Why do this problem?

This problem would make a good short challenge, for example first thing in the morning as you are taking the register. It requires some logical thinking and quickly leads to a generalisation.

Key questions

Is there a way to make sure both 'slots' of the toaster are always being used?

Possible extension

Many children will be able to find a general rule for the minimum length of time taken for any number of slices of toast. Can they explain why the rule always works?

Possible support

Using something to represent the slices of bread might help, for example, playing cards which are different on each side so that it is easier to keep track of what has been done.